Co jste chtěli vědět o ABAQUSu … OBECNÝ PŘEHLED: ABAQUS je program pro řešení technických úloh metodou konečných prvků Mechanika poddajných těles Termomechanika.

Co jste chtěli vědět o ABAQUSu … OBECNÝ PŘEHLED: ABAQUS je program pro řešení technických úloh metodou konečných prvků Mechanika poddajných těles Termomechanika Akustika Analýza elektrotermických a elektromechanických jevů

Co jste chtěli vědět o ABAQUSu … Mechanika poddajných těles Obvyklá klasifikace na úlohy Statické Dynamické Jsou implementována obě základní schémata integrace dynamických úloh – IMPLICITNÍ i EXPLICITNÍ

Co jste chtěli vědět o ABAQUSu … Mechanika poddajných těles Typická jsou nelineární řešení: lineární procedury jsou koncipovány jako takzvané poruchy (perturbation step) ‏ F... airscrew thrust G... engine weight P... perturbation force due to the wind gusts static preload dynamic load

Co jste chtěli vědět o ABAQUSu … Mechanika poddajných těles Statika Analýza posuvů a napětí *STATIC Stabilita *BUCKLING; Creep, viskoelasticita-plasticita *VISCO

Co jste chtěli vědět o ABAQUSu … Mechanika poddajných těles Dynamika (implicitní) ‏ Klasické členění přímá integrace – přechodové a ustálené děje *DYNAMIC; *STEADY STATE DYNAMIC, DIRECT Modální analýza – přechodové a ustálené děje *MODAL DYNAMIC; *STEADY STATE DYNAMIC Náhodné buzení *RESPONSE SPECTRUM; *RANDOM RESPONSE

Co jste chtěli vědět o ABAQUSu … Nelineární statika Zdroje nelinearity: Posuvy rovnováha v deformovaném stavu Rotace natočení není vektor, ale transformace Deformace je třeba vhodných měr deformace Materiál elastické-inelastické, s okamžitou odezvou … Vazby nelineární rovnice, jednostranné vazby

Co jste chtěli vědět o ABAQUSu … Zdroje nelinearity: Posuvy rovnováha v deformovaném stavu Abaqus – Analysis step – vždy velké posuvy Perturbační step – malé posuvy

Co jste chtěli vědět o ABAQUSu … Zdroje nelinearity: Rotace Abaqus – Analysis step – vždy velké rotace (pozor na přírůstkové definice vynucených rotací

Zdroje nelinearity: Deformace Stretch Green-Lagrangeův tensor Co jste chtěli vědět o ABAQUSu … Hlavní stretch vektory

Zdroje nelinearity: Integrovaná deformace (default) ‏ Logaritmická deformace Nominální deformace Green-Lagrange (default u skořepin a nosníků pro malé deformace Co jste chtěli vědět o ABAQUSu …

Zdroje nelinearity: Materiály: Elastické nedissipační (hyperelastické …) ‏ Inelastické dissipují energii (plasticita …) ‏ Co jste chtěli vědět o ABAQUSu …

Zdroje nelinearity: Hyperelastické materiály: Co jste chtěli vědět o ABAQUSu …

Zdroje nelinearity: Plastické materiály: Klasická plasticita kovů Misesova nebo Hillova plocha plasticity Zpevnění Ideálně plastický materiál Isotropní Kinematické Johnson - Cook Co jste chtěli vědět o ABAQUSu …

Zdroje nelinearity: VAZBY: Vazbové rovnice Jednostranné vazby - kontakt Co jste chtěli vědět o ABAQUSu …

Zdroje nelinearity: VAZBOVÉ ROVNICE Klasické – lineární *EQUATION nelineární *MPC *COUPLING *RIGID BODY Lagrangeovské – tzv. konektor elementy *ELEMENT, TYPE=C3D2 *CONNECTOR SECTION Co jste chtěli vědět o ABAQUSu …

Zdroje nelinearity: Jednostranné vazby – kontakt MASTER – SLAVE (finite/small sliding) ‏ Hard (Lagrangeovy multiplikátory) ‏ Augmented Lagrange Softened Co jste chtěli vědět o ABAQUSu …

Využití a zneužití Příklad-Harmonická převodovka INTERAKCE Obecná tendence modelovat MKP soustavy více těles.

INTERAKCE

Obecná tendence modelovat MKP soustavy více těles. INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS Vazby mezi různými stupni volnosti v různých uzlech Implementovány klasicky eliminačním postupem (jeden – eliminovaný - DoF je funkcí ostatních a nesmí být použit dvakrát) ‏ Pro běžné modely postačí předdefinovaná množina Je-li to nutné, lze implementovat jako uživatelský podprogram

Obecná tendence modelovat MKP soustavy více těles. INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS Předdefinované MPC Linear/Bilinear/Quadratic/BiQuadratic ….

Obecná tendence modelovat MKP soustavy více těles. INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS Předdefinované MPC Beam

Obecná tendence modelovat MKP soustavy více těles. INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS Předdefinované MPC Cyclsym – cyklická symetrie

Obecná tendence modelovat MKP soustavy více těles. INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS Předdefinované MPC Link Pin

Obecná tendence modelovat MKP soustavy více těles. INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS Předdefinované MPC Revolute Slider

Obecná tendence modelovat MKP soustavy více těles. INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS Předdefinované MPC Universal joint Shell-to-solid

INTERAKCE NELINEÁRNÍ VAZBOVÉ ROVNICE – MULTIPOINT CONSTRAINS

INTERAKCE PROPOJENÍ – COUPLING Spojení jednoho – řídícího (master) uzlu s množinou ostatních (slave) uzlů DISTRIBUTING – pohyb master uzlu je „průměrem“ 6 rovnic (pro 6 DoF) ‏ KINEMATIC – pohyb master uzlu řídí pohyb všech ostatních 6 x N rovnic (pro N slave uzlů) ‏

INTERAKCE PROPOJENÍ – COUPLING

INTERAKCE DOKONALE TUHÁ TĚLESA – RIGID BODY Zjednodušují modely tam, kde Jena část je podstatně měkčí nežli druhá Napjatost není předmětem zájmu Je třeba modelovat propojovací detaily s uvažováním kontaktu

INTERAKCE DOKONALE TUHÁ TĚLESA – RIGID BODY Atributy: REFERENČNÍ UZEL (povinný) neeliminovaný DoF ELEMENTY hmota, kontaktní interakce ANALYTICKÉ PLOCHY kontaktní interakce VAZBOVÉ UZLY interakce vazbou

INTERAKCE DOKONALE TUHÁ TĚLESA – RIGID BODY

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ CONNECTOR ELEMENTY Neeliminují stupeň volnosti Spojují nejvíce dva uzly Mají konstitutivní vlastnosti Elasticitu Tlumení Hysterezi (friction) ‏ Mají podmínku definované vnitřní síly nebo posuvu (aktuátory) ‏

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENTY Základní typy: AXIAL NoneContact force for friction: NoneFriction scaling constants: Constitutive reference lengths: Connector stops: Optional.Orientation at : Optional.Orientation at : Kinetic force output: Available components: NoneConstraint force output: NoneKinematic constraints: BasicBasic or assembled: AXIAL

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENTY Základní typy: CARTESIAN NoneContact force for friction: NoneFriction scaling constants: Constitutive reference lengths: Connector stops: IgnoredOrientation at : OptionalOrientation at : Kinetic force output: Available components: NoneConstraint force output: NoneKinematic constraints: BasicBasic or assembled: CARTESIAN

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: JOIN NoneContact force for friction: NoneFriction scaling constants: NoneConstitutive reference lengths: NoneConnector stops: IgnoredOrientation at : OptionalOrientation at : NoneKinetic force output: NoneAvailable components: Constraint force output: Kinematic constraints: BasicBasic or assembled: JOIN

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: LINK NoneContact force for friction: NoneFriction scaling constants: NoneConstitutive reference lengths: NoneConnector stops: IgnoredOrientation at : IgnoredOrientation at : NoneKinetic force output: NoneAvailable components: Constraint force output: Kinematic constraints: BasicBasic or assembled: LINK

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: RADIAL THRUST NoneContact force for friction: NoneFriction scaling constants: Constitutive reference lengths: Connector stops: IgnoredOrientation at : RequiredOrientation at : Kinetic force output: Available components: NoneConstraint force output: NoneKinematic constraints: BasicBasic or assembled: RADIAL-THRUST

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: SLIDE PLANE Contact force for friction: NoneFriction scaling constants: Constitutive reference lengths: Connector stops: IgnoredOrientation at : RequiredOrientation at : Kinetic force output: Available components: Constraint force output: Kinematic constraints: BasicBasic or assembled: SLIDE-PLANE

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: SLOT Contact force for friction: NoneFriction scaling constants: Constitutive reference lengths: Connector stops: IgnoredOrientation at : RequiredOrientation at : Kinetic force output: Available components: Constraint force output: Kinematic constraints: BasicBasic or assembled: SLOT

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: ALIGN NoneContact force for friction: NoneFriction scaling constants: NoneConstitutive reference angles: NoneConnector stops: OptionalOrientation at : OptionalOrientation at : NoneKinetic moment output: NoneAvailable components: Constraint moment output: Kinematic constraints: BasicBasic or assembled: ALIGN

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: CARDAN NoneContact force for friction: NoneFriction scaling constants: Constitutive reference angles: Connector stops: OptionalOrientation at : RequiredOrientation at : Kinetic moment output: Available components: NoneConstraint moment output: NoneKinematic constraints: BasicBasic or assembled: CARDAN

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: CONST.VELOCITY NoneContact force for friction: NoneFriction scaling constants: NoneConstitutive reference angles: NoneConnector stops: OptionalOrientation at : RequiredOrientation at : NoneKinetic moment output: NoneAvailable components: Constraint moment output: Kinematic constraints: BasicBasic or assembled: CONSTANT VELOCITY

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: EULER NoneContact force for friction: NoneFriction scaling constants: Constitutive reference angles: Connector stops: OptionalOrientation at : RequiredOrientation at : Kinetic moment output: Available components: NoneConstraint moment output: NoneKinematic constraints: BasicBasic or assembled: EULER

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: FLEXION- TORSION NoneContact force for fricition: NoneFriction scaling constants: Constitutive reference angles: Connector stops: OptionalOrientation at : RequiredOrientation at : Kinetic moment output: Available components: NoneConstraint moment output: NoneKinematic constraints: BasicBasic or assembled: FLEXION-TORSION

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: REVOLUTE NoneContact moment for friction: NoneFriction scaling constants: Constitutive reference angles: Connector stops: OptionalOrientation at : RequiredOrientation at : Kinetic moment output: Available components: Constraint moment output: Kinematic constraints: BasicBasic or assembled: REVOLUTE

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: ROTATION NoneContact force for friction: NoneFriction scaling constants: Constitutive reference angles: Connector stops: OptionalOrientation at : OptionalOrientation at : Kinetic moment output: Available components: NoneConstraint moment output: NoneKinematic constraints: BasicBasic or assembled: ROTATION

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT Základní typy: UNIVERSAL NoneContact force for friction: NoneFriction scaling constants: Constitutive reference angles: Connector stops: OptionalOrientation at : RequiredOrientation at : Kinetic moment output: Available components: Constraint moment output: Kinematic constraints: BasicBasic or assembled: UNIVERSAL

INTERAKCE VAZBY S LAGRANGEOVSKOU FORMULACÍ - CONNECTOR ELEMENT CARDAN FLEXION TORSION RADIAL THURST

INTERAKCE KONTAKT Obecný kontakt v ABAQUSU *CONTACT PAIR Povrch master, povrch slave Kinematika – penetrace, posunutí (sliding) ‏ Síly kontaktní tlak kontaktní smyk

INTERAKCE OBECNÝ KONTAKT Kontakt poddajných těles - Hertzův

INTERAKCE OBECNÝ KONTAKT Kontakt s tuhými tělesy

INTERAKCE OBECNÝ KONTAKT Selfkontakt

INTERAKCE SPECIÁLNÍ FORMULACE GAP elementy SLIDE LINE TUBE TO TUBE

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: SMALL SLIDING Pár master stěna - slave uzel je vyhledán na počátku analýzy Slave uzel nesmí penetrovat tečnou rovinou k master stěně slave master Lokální kontaktní rovina

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: SMALL SLIDING Definice lokální kontaktní roviny

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: SMALL SLIDING Definice lokální kontaktní roviny Efekt vyhlazování normál *SURFACE, TRIM

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: SMALL SLIDING Definice lokální kontaktní roviny Efekt vyhlazování normál slave surface master surface

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: SMALL SLIDING Kontaktní síly deformation a a b, s s b c c FbFb FbFb F s = -F b FaFa FsFs FcFc NLGEOM kontaktní síly

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: SMALL SLIDING kontaktní síly NLGEOM deformation a a s, b s b c c FbFb F s = -F b F a = 0 F c = 0 F s = -F b

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: SMALL SLIDING příklad Contact lines

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING 201 202 501 502 101 102 103 master surface 201 101 202 501 502 t = 0 t = t 1 t = t 2 Pár master stěna - slave uzel je vyhledáván průběžně Slave uzel nesmí penetrovat master stěnou

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING Vyhlazování - smoothing parabolic segment *CONTACT PAIR,SMOOTH=0,INTERACTION=MYSURF *CONTACT PAIR,SMOOTH=0.2,INTERACTION=MYSURF

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING Vyhlazování - smoothing *CONTACT PAIR,SMOOTH=f,INTERACTION=MYSURF

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING Vyhlazování – příklad r = 10 mm r = 12 mm r = 16 mm symetrie kontakt Uloženo ve směru x

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING Vyhlazování – příklad vnější vnitřní

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING Vyhlazování – příklad Vnější je master 100x větší tlak

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING Vyhlazování – příklad Vnitřní je master Nulový tlak

INTERAKCE OBECNÝ KONTAKT - KINEMATIKA: FINITE SLIDING Vyhlazování – příklad Vnější je master Potlačeno vyhlazování Master surface: outer *CONTACT PAIR,SMOOTH=0, INTERACTION=MYSURF

Cyklus iterací Cyklus krok Cyklus inkrement Cyklus pokus START Nový krok (step)‏ Nový inkrement Nový pokus (attempt)‏ Nová iteraceSestavení tečné matice Řešení Aktualizace Výpočet nevyváž. sil Konvergence?Konverguje? Konec kroku? Konec analýzy? Redukce (cutback)‏ Výpočet KONEC! Výpis výsledků Ano Ne Ano Pokračovat? NEZKONVERGOVALO! Ne Reset počíta- dla iterací

ABAQUS v kontaktních úlohách rozděluje iterace na Kontaktní (SDI) ‏ Rovnovážné Nejprve jsou iterovány kontaktní iterace (až do ustálení statusu kontaktních uzlů) bez kontroly rovnováhy Poté jsou prováděny rovnovážné iterace až do dosažení rovnováhy Změní-li se v průběhu rovnovážných iterací status kontaktních uzlů, je vnořen podcyklus SDI Řízení výpočtu a konvergence (zejména ve statice) ‏ Konvergence kontaktních úloh

KRITÉRIA KONVERGENCE KONTAKTU Kontaktní (slave) uzel má status Uzel je v kontaktu Nebyla překročena třecí reakce (sticking) ‏ Byla překročena třecí reakce (sliding) ‏ Uzel není v kontaktu Změna statusu: Uzel nebyl v kontaktu Penetrace Uzel je v kontaktu Uzel byl v kontaktu (sticking) Překročení reakce Uzel v kontaktu (sliding) ‏ Uzel byl v kontaktu (sliding) Zmenš. Smyk. sil Uzel v kontaktu (sticking) ‏ Uzel byl v kontaktu Tah. Reakce Uzel není v kontaktu Řízení výpočtu a konvergence (zejména ve statice) ‏ Konvergence kontaktních úloh

KRITÉRIA KONVERGENCE KONTAKTU V průběhu SDI se mění status kontaktních párů. Konvergence je dosaženo, jestliže ve dvou po sobě jdoucích iteracích se status nezmění Řízení výpočtu a konvergence (zejména ve statice) ‏ Konvergence kontaktních úloh

Cyklus iterací Cyklus krok Cyklus inkrement Cyklus pokus START Nový krok (step)‏ Nový inkrement Nový pokus (attempt)‏ Nová iteraceSestavení tečné matice Řešení Aktualizace Výpočet nevyváž. sil Kontakt OK? Zmenšení kroku? Konvergence?Konverguje? Konec kroku? Konec analýzy? Změna vazeb Redukce (cutback)‏ Výpočet KONEC! Výpis výsledků Ano Ne Ano Ne Ano Pokračovat? NEZKONVERGOVALO! Ne Reset počíta- dla iterací Cyklus kontaktních iterací SDI

PŘÍKLAD Řízení výpočtu a konvergence (zejména ve statice) ‏ Konvergence kontaktních úloh

PŘÍKLAD První inkrement nezkonvergoval Všechny iterace typu SDI Počet pokusů (attempt) vede ke snížení inkrementu pod povolenou hodnotu Řízení výpočtu a konvergence (zejména ve statice) ‏ Konvergence kontaktních úloh SEVERE DISCONTINUITY ITERATION 11 ENDS CONTACT CHANGE SUMMARY: 1 CLOSURES 6 OPENINGS. SEVERE DISCONTINUITY ITERATION 12 ENDS CONTACT CHANGE SUMMARY: 1 CLOSURES 3 OPENINGS. ***NOTE: SUBDIVISION AFTER 12 ITERATIONS FOR SEVERE DISCONTINUITIES ***ERROR: TOO MANY ATTEMPTS MADE FOR THIS INCREMENT: ANALYSIS TERMINATED

PŘÍKLAD Řešení: zvýšit počet povolených SDI Řízení výpočtu a konvergence (zejména ve statice) ‏ Konvergence kontaktních úloh *CONTROLS, PARAMETERS=TIME INCREMENTATION,,,,,,25

Řízení výpočtu a konvergence (zejména ve statice) ‏ Konvergence kontaktních úloh  *CONTACT CONTROLS, AUTOMATIC TOLERANCES ABAQUS calculates allowable tolerances for overclosure and separation pressure Automatically adapts tolerances to current modeling situation  Derived from force and displacement correction convergence criteria (R max, c max )‏ Can alleviate contact “chattering”  Contact points switch between open and overclosed in successive iterations  Insignificant overclosures and/or negative contact pressures can preclude convergence

Additional Features

Overview Master Surface Normals at Symmetry Planes Adjusting Surfaces Tied Surfaces Node-Based Surfaces Automatic Resolution of Initial Interferences Precise Specification of Clearance or Overclosure Resolving User-Prescribed Overclosures Contact Pair Removal and Reintroduction Automatic Conversion of 3-D Quadratic Elements Contact with Triangular/Tetrahedral Elements Pre-Tensioning of Cross-Sections Pressure Penetration

Master Surface Normals at Symmetry Planes

–The default normal vectors that ABAQUS/Standard creates at nodes along a symmetry plane will often be inaccurate for curved surfaces. The inaccurate master surface normals are caused by the faceted geometry of the model. symmetry plane slave surface master surface slave surface unadjusted normal N 1 adjusted normal N 1 1001 y x

Master Surface Normals at Symmetry Planes –If the default normal for node 1 on the master surface, N 1, is used, node 100 will never “see” the master surface (because of the symmetry condition it cannot move in the y -direction). –Even if the outer cylinder was the master surface, there would still be a problem with the default nodal normal vector along the symmetry plane. symmetry plane master surface slave surface N 100 1001

Master Surface Normals at Symmetry Planes Node 1 will “see” the master surface. However, the contact condition will apply a constraint in the (vertical) y -direction because N 100 has a vertical component. –This constraint will conflict with the one imposed by the symmetry boundary condition, causing numerical problems (overconstraint). When the symmetry plane is defined with the XSYMM, YSYMM, or ZSYMM boundary conditions, ABAQUS/Standard will automatically adjust the normals of master surface nodes with those boundary conditions. The adjusted normal will be parallel to the symmetry plane. This capability is not yet available for three-dimensional, finite-sliding problems.

Adjusting Surfaces

–The slave nodes of any contact pair can be “adjusted” automatically so that they are initially in contact with the master surface. This process is useful when preprocessors do not place nodes in “exact” positions. ABAQUS modifies coordinates of slave nodes before the analysis starts. The adjustment does not generate any strain. –With the small-sliding formulation better results are obtained when surfaces are initially in contact. Anchor points and initial contact plane orientations are calculated more accurately.

Adjusting Surfaces –Two methods can be used to specify which nodes should be adjusted. 1. Give an absolute distance: –All initially open slave nodes that fall within the specified adjust band ( a ) are moved onto the master surface. –All initially overclosed slave nodes are relocated to the surface. –The adjustment distance ( a ) is measured along the normal direction to the master surface.

Adjusting Surfaces Configuration after adjustment and prior to start of analysis: slave nodes outside adjust bands are unaffected Initial configuration as specified by user

Adjusting Surfaces 2. Give a node set that contains a group of slave nodes: –Only slave nodes in the node set will be adjusted. –Slave nodes that penetrate the master surface and are not in the node set will remain overclosed at the start of the analysis and, thus, will create strain.

Adjusting Surfaces *NSET, NSET=CONNODE : *CONTACT PAIR, INTERACTION=DRY, ADJUST=CONNODE

Adjusting Surfaces –Warning: With either method only surface nodes are relocated. Gross (large) adjustments can severely distort initial element shapes. Specifying precise initial clearance or overclosure is discussed later in this lecture.

Tied Surfaces

–In ABAQUS fully constrained contact behavior is defined using tie constraints. –A tie constraint provides a simple way to bond surfaces together permanently. Easy mesh transitioning. –Surface-based constraint using a master-slave formulation. –The constraint prevents slave nodes from separating or sliding relative to the master surface. Tie constraints

Tied Surfaces –Slave nodes that contact the master surface at the start of the simulation will be tied to it. Slave nodes not initially tied will remain unconstrained throughout the analysis; they will never “see” the master surface and will be able to penetrate it. A table is printed in the data (.dat ) file listing each slave node and the master surface nodes to which it will be tied if the preprocessor printout of the model data is requested: *PREPRINT, MODEL=YES

Tied Surfaces –Usage: *TIE, NAME= name, POSITION TOLERANCE= a slave, master The POSITION TOLERANCE parameter has the same interpretation as the ADJUST parameter on the  CONTACT PAIR option. The default value is 5% of the typical element size in the master surface.

Tied Surfaces –By default, all slave nodes in the tolerance region are moved strain-free onto the master surface. Use ADJUST=NO if the slave nodes should not be moved. *TIE, NAME= name, POSITION TOLERANCE= a, ADJUST=NO –Rotations of the tied slave nodes are not constrained if the NO ROTATION parameter is used. –Boundary conditions should not be applied to the nodes on the slave surface of a tie constraint pair; doing so will overconstrain the model at those nodes.

Tied Surfaces Example: Tube crush problem BotTube BotPlate The bottom of the tube is attached to the bottom plate via tie constraints.

Tied Surfaces *TIE,NAME=TubePlateTie, POSITION TOLERANCE=0.01, ADJUST=YES Surface-based constraint. (Can select either predefined surfaces or regions directly in the viewport.)‏ Slave nodes can be moved onto the master surface in the initial configuration without any strain. Only slave nodes within this distance from the master surface are tied to the master surface. Both translational and rotational degrees of freedom can be constrained. Warnings will be issued in the data (.dat ) file for these nodes. Edit Constraint dialog box

Tied Surfaces Alternative to tie constraint –Tied contact is an alternative to defining tie constraints: *CONTACT PAIR, INTERACTION=DRYFRIC, TIED, ADJUST= a slave, master The ADJUST parameter is required with tied contact. –Advantages to using  TIE instead of  CONTACT PAIR, TIED Degrees of freedom of the slave surface nodes will be eliminated. Wavefront reduction. Both rotational and translational degrees of freedom can be tied.

Node-Based Surfaces

–Node-based surfaces are rarely needed since nearly all slave surfaces can be modeled using the element-based or analytical surfaces. –Node-based surfaces are useful when a single point or set of points (not a surface) will contact another body. The body can be deformable or rigid. –A node-based surface is necessary when the slave surface consists of: Substructure retained degrees of freedom User-defined elements Shell element edges

Node-Based Surfaces Example of node-based surface: GUI interface Select this type of slave, and choose the nodes involved in contact (set or directly in viewport)‏ Prompt when choosing a slave surface Strings: node- based surface Ball: element- based surface

Node-Based Surfaces Example of node-based surface: Keywords interface *SURFACE, TYPE=NODE, NAME=STRINGS STRINGS, *CONTACT PAIR, INTERACTION=SMOOTH STRINGS, BALL define surface containing contact nodes previously defined surface Strings : node- based surface Ball : element- based surface

Node-Based Surfaces –The cross-sectional area associated with a slave node can be specified on the data lines. This area is used to compute contact stresses from nodal forces. By default, this area is equal to one. –Different cross-sectional areas may be specified for different slave nodes by using several data lines under the  SURFACE option. –Node-based surfaces and tie constraints: The node-based surface can be either the master or the slave. If a node-based master surface is specified: –The actual distance from a slave node to the surface is the closest distance to any node on the master surface. –The default POSITION TOLERANCE is 5% of a typical distance between the master nodes.

Node-Based Surfaces –Node-based master surfaces cannot be used with  CONTACT PAIR, TIED. –Limitations: The contact stress values are the forces transmitted through the slave node divided by the constant area. Node-based surfaces should be used only for nodes with displacement (and rotation) degrees of freedom. Node-based surfaces do not provide heat conduction capabilities in coupled temperature-displacement analysis.

Interference Fit Problems

–Interference fits can be resolved automatically. The interference is ramped off gradually during the step. End of step: interference is resolved Beginning of step: initial interference v is prescribed by initial coordinates Interference is gradually ramped off over the course of the step; deformation occurs as a result v

v Interference Fit Problems Automatic resolution of initial interferences –Syntax for resolving initial interferences automatically: *CONTACT INTERFERENCE, SHRINK slave, master Identify the slave and master surface of the contact pair with the contact interference Automatically calculates initial interference, v, and resolves interference over the course of the step; available only in the first step.

Interference Fit Problems –ABAQUS computes the interference from the initial coordinates. This process requires the precise specification of the nodal coordinates if the initial interference is small. –A more exact technique for this case will be described shortly.

Interference Fit Problems Specifying allowable interferences –The contact interference V can also be prescribed manually such that all constraints in the specified contact pair will follow: By default, the allowable interference, is ramped from V to 0 over the course of the step:

Interference Fit Problems –A time variation of other than a ramp function can be specified using the AMPLITUDE parameter: *CONTACT INTERFERENCE, AMPLITUDE= ampname slave, master, V –If interferences must be modified from step to step, use the OP parameter (default: OP=MOD): *CONTACT INTERFERENCE, OP=[ MOD | NEW ] slave, master, V V In ABAQUS/CAE, the value of the interference may be modified in any step.

Interference Fit Problems –Specifying contact interference manually is similar to allowing automatic resolution (shrink fit), except that is specified manually and is the same for the whole contact pair. Converged solutions are obtained in which overclosure is nonzero. v(0)‏ v(t i )‏

–The interference fit options can also be used to shift slave surfaces before beginning the contact calculation: *CONTACT INTERFERENCE slave, master, v, n 1, n 2, n 3 where n i are the direction cosines that govern the shift. –Example: The constraint is not modified: h  0 at the end of the step. Interference Fit Problems master surface n v

Interference Fit Problems –Such a shift can affect the final position of the slave nodes if coarse meshes are used. Without shift node a is closer to right surface With shift node a is closer to bottom surface

Precise Specification of Clearance or Overclosure

–There are two methods that can be used to specify a precise clearance or overclosure:  CLEARANCE  CONTACT INTERFERENCE –These methods are useful since normally it is not possible to prescribe a precise clearance or overclosure through the initial nodal coordinates of the structures.

Precise Specification of Clearance or Overclosure Using  CLEARANCE –The  CLEARANCE option can be used to prescribe a precise initial clearance or overclosure if the initial value is small relative to the model dimensions. –The  CLEARANCE option can be used only with small-sliding contact problems. –The initial clearance or overclosure value calculated at every slave node is overwritten by the value specified using the  CLEARANCE option. –The  CLEARANCE option is part of the model definition of the analysis. –When an initial overclosure is specified, the two bodies will deform during the step to resolve the prescribed overclosure and will appear to be separated by the specified amount at the end of the step. –Use the MASTER and SLAVE parameters to identify which contact pair has the precise clearance or overclosure.

Precise Specification of Clearance or Overclosure –To prescribe a constant initial clearance or overclosure: Set the VALUE parameter equal to the initial clearance (a positive value) or overclosure (a negative value), c, for the entire set of slave nodes. *CLEARANCE, MASTER= master, SLAVE= slave, VALUE= c –This option is not currently supported by ABAQUS/CAE; you may use the keywords editor to add it to your model, however. Although each set of nodes lies on a circle, the clearance is not constant.

Precise Specification of Clearance or Overclosure –To prescribe an initial spatially varying clearance or overclosure on the slave surface: Use the TABULAR parameter, and specify the node number or node set and the corresponding clearance or overclosure at the nodes on the data lines following the option. *CLEARANCE, MASTER= master, SLAVE= slave, TABULAR With the TABULAR definition of the initial clearances, the data can be read from an external file by setting the INPUT parameter equal to the file’s name (including the path name if the file is not in the directory where the job was submitted).

Precise Specification of Clearance or Overclosure Using  CONTACT INTERFERENCE –The  CONTACT INTERFERENCE option can be used to prescribe a precise clearance or overclosure in the history definition of the analysis: Can be used with small-sliding or finite-sliding contact Can be used in any step: need not be an initial value

Precise Specification of Clearance or Overclosure –To prescribe an initial clearance (omit Step 1, below, to prescribe a clearance at a later time): 1. Use ADJUST to move the slave surface precisely onto the master surface: *CONTACT PAIR, [SMALL SLIDING,] ADJUST= a slave, master

2. Use the  CONTACT INTERFERENCE option to specify a precise value for the clearance: *CONTACT INTERFERENCE, AMPLITUDE=CLEAR slave, master, c 3. Define an amplitude that is constant throughout the step: *AMPLITUDE, NAME=CLEAR 0., 1., t f, 1. The two bodies will appear to overclose each other in subsequent steps. This step is equivalent to allowing a “free play” of c. Precise Specification of Clearance or Overclosure c0c0

–To prescribe an initial overclosure (omit Step 1, below, to prescribe a non-initial overclosure): 1. Use ADJUST to move the slave surface precisely onto the master surface: *CONTACT PAIR, [SMALL SLIDING,] ADJUST= a slave, master

2. Use  CONTACT INTERFERENCE to specify a precise (negative) value for the clearance: *CONTACT INTERFERENCE, AMPLITUDE=OVER slave, master, - c 3. Define an amplitude that is ramped up over the step: *AMPLITUDE, NAME=OVER 0., 0., t f, 1. The two bodies will deform to resolve the prescribed overclosure and will appear to be separated by the amount, c, at the end of the step. Precise Specification of Clearance or Overclosure c0c0

Resolving User-Prescribed Overclosures

–For small-sliding contact precise contact overclosures prescribed by means of the  CLEARANCE option can be resolved in the usual way by the  CONTACT INTERFERENCE option. For example, the user may have two surfaces that should overclose by exactly 0.1, but the meshing may not be precise enough to achieve this at every slave node. The following option can be used in the model definition: *CLEARANCE, MASTER= master, SLAVE= slave, VALUE=-0.1 –Even though the coordinate adjustments are not reflected in ABAQUS/Viewer, they are accounted for in subsequent contact calculations. In particular, this precise overclosure can be resolved gradually over the step by the following option: *CONTACT INTERFERENCE, SHRINK slave, master

Contact Pair Removal and Reintroduction

–Contact pairs have computational cost, even when they are not in contact. With NLGEOM and large sliding the search algorithm must locate the point on the master surface closest to each slave node at each iteration. Contact plane orientations must be updated in small-sliding problems with NLGEOM. Contact state (open/closed) must be computed for all slave nodes.

Contact Pair Removal and Reintroduction –Contact pair removal: The removal of active (closed) contact pairs is often useful for “springback” calculations. –A springback calculation is performed to determine the elastic recovery of a structure after the removal of dies or other contacting bodies. Deformation of the structure will occur as contact pairs are removed. –ABAQUS/Standard automatically stores the contact forces acting on the nodes involved in the removed contact pair. These forces are ramped to zero over the duration of the removal step.

Contact Pair Removal and Reintroduction –Contact pair reintroduction: Contact surfaces are reintroduced into the model instantaneously. The constraints imposed by any overclosed contacting nodes are applied to the model at the start of the reintroduction step. –If surfaces that are reintroduced into the model are severely overclosed, the interference fit options will have to be used to ramp down the overclosure gradually during the step.

Contact Pair Removal and Reintroduction –Use the Interaction Manager of ABAQUS/CAE or the  MODEL CHANGE option if editing an input file to remove inoperative contact pairs in ABAQUS/Standard temporarily. Contact pairs are easily reintroduced in later steps. Underlying surfaces remain intact—only contact pairs are affected. This option is particularly useful in “forming” problems with multiple dies.

Contact Pair Removal and Reintroduction Keywords interface for contact pair removal/reintroduction –Contact pairs are part of the model data in ABAQUS/Standard. All contact pairs that will ever be needed must be defined as part of the initial model. –Syntax for contact pair removal: *MODEL CHANGE, TYPE=CONTACT PAIR, REMOVE slave_1, master_1 slave_2, master_2... –Syntax for contact pair reintroduction: Can be used only for contact pairs that were previously defined and removed. *MODEL CHANGE, TYPE=CONTACT PAIR, ADD slave _1, master _1 slave _2, master _2...

Automatic Conversion of 3-D Quadratic Elements

–Transmission of pressure across element faces is basic to contact problems. Pressure is applied to element faces by using element shape functions to calculate the equivalent consistent nodal loads. Constant pressure on an element face: –For linear elements produces consistent nodal loads that are equal –For quadratic elements produces consistent nodal loads that vary across the element face Quadratic elements can be problematic in contact problems because of the wide variation in nodal loads.

Automatic Conversion of 3-D Quadratic Elements –Constant pressure load applied to a two-dimensional quadratic element: –Constant pressure load applied to a three-dimensional, quadratic, serendipity element (no midface node): Uneven nodal forces lead to uneven contact stress distributions in nonmatching meshes. Contact algorithm cannot function properly because corner forces oppose the pressure. These elements cannot be used for contact.

Automatic Conversion of 3-D Quadratic Elements –ABAQUS automatically converts those three-dimensional serendipity elements that form the slave surfaces of a contact pair to three- dimensional Lagrange elements by adding midface nodes. Shells: S8R5  S9R5. Bricks: C3D20  C3D27, C3D20R  C3D27R. Wedges: C3D15  C3D15V. –Variable node solids: midface nodes are added only to those faces forming part of a slave surface. C3D27, C3D27R: may have 21–27 nodes. C3D15V: may have 15–18 nodes. –First-order elements show better convergence in contact problems than second-order elements. However, if the second-order elements converge, they can produce more accurate results with fewer elements.

Automatic Conversion of 3-D Quadratic Elements –Temperatures, user-defined fields, and mass flow rates are accounted for properly. The user prescribes values of these variables at the corner and edge nodes. ABAQUS calculates the values of these variables at the automatically generated midface nodes by interpolating from the corner and edge nodes.

Contact with Triangular/Tetrahedral Elements

–Do not use second-order “regular” tetrahedral, wedge, or 6-node shell or membrane elements (C3D10, C3D15, STRI65, M3D6) in contact problems with “classical” hard contact. These elements can be used in contact problems, however, with a penalty- based contact formulation. p qq q “Classical” hard contact algorithm cannot function properly because corner forces are zero.

Contact with Triangular/Tetrahedral Elements –With hard contact, these zero nodal forces result in a poor prediction of the contact pressure and may lead to convergence problems. –10-node tetrahedrons can be used in slave surfaces with TIED contact. –Second-order triangles (CAX6, CPE6, CPS6) may show a noisy contact distribution and may cause convergence difficulties. –When modeling contact with 6-node triangles or 10-node tetrahedra, use the “modified” family of elements: CAX6M, CPE6M, CPS6M, C3D10M. –The key benefits are: Uniform contact pressure property Minimal shear and volumetric locking Robustness during finite deformation Can be used with “classical” hard contact

Contact with Triangular/Tetrahedral Elements Example: Upsetting of a cylindrical billet –Contours of contact pressure with C3D10M elements do not show the vanishing pressures from which C3D10 elements suffer when hard contact is used.

ABAQUS/Standard Contact Formulation

Overview The Constraint Approach The Contact Constraint “Classical” Hard Contact Alternatives to “Classical” Hard Contact Debonding (Crack Propagation)‏

The Constraint Approach

–Contact problems require the imposition of constraints between points that are in contact. Constraints must be applied in the normal direction to avoid penetration. Constraint: No penetration h  0 h < 0h = 0 No penetration; no constraint required Constraint enforced; positive contact pressure  h

The Constraint Approach –Two common techniques for imposing such constraints are: Lagrange multiplier method. Penalty method. –ABAQUS uses the Lagrange multiplier method, which has the following advantages: Accuracy—constraint is satisfied exactly. There are no matrix conditioning problems. Constraint force is available immediately as the value of the Lagrange multiplier. Implementation is straightforward.

The Constraint Approach –The Lagrange multiplier method has the following disadvantages: It adds one variable for each contact constraint. Proper elimination sequence is required since the method makes the system of equations nonpositive definite (it introduces negative eigenvalues).

The Contact Constraint

–Contact condition is a single, usually nonlinear constraint at each potential contact point: where h = the overclosure (penetration) between the points and u N = the kinematic degrees of freedom. Constraint is enforced only if h  0. h  h h < 0 h > 0 Constraint satisfied; enforcement unnecessary Constraint violated; must be enforced

The Contact Constraint –The contact constraint is enforced by introducing a Lagrange multiplier, p. Augmented potential: where  = the potential energy of the unconstrained system and  L = the Lagrange multiplier contribution. “Hard” contact constraint: Contribution to the potential: where A = the area associated with contact constraint, and p = contact pressure associated with contact constraint.

The Contact Constraint –Take the variation of the augmented potential function: –(The summation is implied over the repeated superscript N.)‏ –The second variation, d  *, yields the (tangent) stiffness. This stiffness includes a tangential stiffness term proportional to the surface curvature. The stiffness term proportional to the surface curvature is unsymmetric for three-dimensional, finite-sliding problems with highly curved master surfaces.

The Contact Constraint –Proper calculation of this term is essential to good convergence of the full Newton method when finite sliding is used. Non-smooth contact surfaces result in singular curvature tensor  convergence is not guaranteed. Smoothness of contact surfaces is extremely important in finite-sliding problems.

The Contact Constraint –Lagrange multipliers are internal variables. Users can see them only when: The preprocessor’s count of elements/degrees of freedom increases to include them. Equation solver problems occur. –The benefit of using the Lagrange multiplier method in purely linear problems (linear constraints, materials, etc.) is that once the contact surface is known, the problem is solved. Example: pure interference fit problems with no other nonlinearities are solved in ABAQUS without iteration.

“Classical” Hard Contact

–“Classical” hard contact is the default local behavior in all contact problems. Pressure is transmitted across a contact pair according to this relationship. Hard contact is enforced using the Lagrange multiplier method. Pressure stress-clearance relationship for hard contact Clearance Contact pressure Any pressure possible when in contact No pressure when no contact Clearance

Alternatives to “Classical” Hard Contact

Augmented Lagrange Method (penalty contact in the normal direction)‏ –This method might be best described as a compromise between Lagrange multiplier and penalty method, in that it enables exact representation of contact constraints while using penalty terms to facilitate the iteration procedure. –In the first series of equilibrium iterations, contact compatibility is determined based on the penalty stiffness. Once equilibrium is achieved, the penetration tolerance is checked. If penetration tolerance is exceeded, the contact pressure is augmented and the iterations continue.

Alternatives to “Classical” Hard Contact –To invoke this approach, use *SURFACE BEHAVIOR, AUGMENTED LAGRANGE penalty stiffness (optional)‏ –To modify the penetration tolerance or penalty stiffness, use *CONTACT CONTROLS, RELATIVE PENETRATION TOLERANCE=, ABSOLUTE PENETRATION TOLERANCE=, STIFFNESS SCALE FACTOR=

Alternatives to “Classical” Hard Contact –The relative penetration tolerance is relative to the average surface facet length which is printed in the data (.dat ) file. –Since the penalty stiffness is chosen to give very close results compared to the Lagrange Method, the user will not see dramatic changes in the convergence rate unless the stiffness is scaled down.

Alternatives to “Classical” Hard Contact Other alternatives –The  SURFACE BEHAVIOR option provides alternatives to hard contact: Softened contact Contact without separation  SURFACE BEHAVIOR is used as a suboption of the  SURFACE INTERACTION option to define the characteristics of a contact pair. *SURFACE INTERACTION, NAME= name *SURFACE BEHAVIOR, [PRESSURE- OVERCLOSURE, NO SEPARATION] data –The  CONTACT CONTROLS option allows contact subject to tolerances.

Alternatives to “Classical” Hard Contact Softened contact –The PRESSURE- OVERCLOSURE parameter on the  SURFACE BEHAVIOR option modifies the contact from “hard” to “soft.” Soft contact is useful as an approximation of surface conditions. Examples: –Surface coatings –Gaskets –Laying a pipe onto the muddy seabed, where the seabed is the softened surface J-tube ring supports J-tube Restraint/release mechanism Riser BA C 500 m

Alternatives to “Classical” Hard Contact Exponential format cc cc  0.9999c 1 p p0p0 6ch exponential p–h relationship linear p–h relationship

Alternatives to “Classical” Hard Contact –The contact pressure between surfaces increases exponentially when the penetration (overclosure), h, is less than 6c : –At penetrations greater than 6c, the pressure-overclosure relationship is linear. Syntax: *SURFACE INTERACTION, NAME= name *SURFACE BEHAVIOR, PRESSURE- OVERCLOSURE=exponential c, p o Surfaces come into contact when clearance measured in the normal direction reduces to c. Both c and p o must be positive. p o c

Alternatives to “Classical” Hard Contact –To choose p o and c, consider the stiffness of the exponential pressure- overclosure relationship. Set p o and c to match the stiffness of the surface being modeled. –If only a single stiffness value k is available: Approximate the pressure-clearance relationship using a linear relationship for positive clearance, as follows: –Set p o to the expected contact pressure, p. If this value is not known, use an average value of stress expected in the structure. –Set c such that the desired contact stiffness, k, is obtained:

Alternatives to “Classical” Hard Contact –Always check for overclosure at closed contact points. If the overclosure is too severe, the pressure at zero clearance p o needs to be changed and the analysis must be run again. To decrease the amount of overclosure, increase the expected contact pressure at zero clearance, p o. To increase the amount of overclosure, decrease the expected contact pressure at zero clearance, p o.

Alternatives to “Classical” Hard Contact Tabular format –Input data pairs ( p i, h i ) to define a piecewise linear relationship between pressure and overclosure. clearance c pressure p overclosure h

Alternatives to “Classical” Hard Contact –Syntax: *SURFACE INTERACTION, NAME= name *SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=tabular p i, h i p 1 = 0, so the first data pair is (0, h 1 ). h 1 must be negative, indicating a clearance. Data must be entered such that p i and h i increase monotonically. For overclosure greater than the last value of h, ABAQUS will use the stiffness of the last piecewise linear segment.

Alternatives to “Classical” Hard Contact Linear format *SURFACE INTERACTION, NAME= name *SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=linear slope of the p-h curve

Alternatives to “Classical” Hard Contact Softened contact constraint –The soft contact constraint is enforced with Lagrange multipliers. During iteration contact stress is recovered from the Lagrange multiplier  contact stress may be incompatible with penetration. clearance contact pressure incompatibility error c p0p0 pnpn p n + 1 –The difference in clearance is expressed in terms of an “incompatibility error.” –This is NOT a runtime error; its role in establishing the correct contact state is analogous to that played by a force residual in determining force equilibrium. –The figure above shows an example using the exponential format.

Alternatives to “Classical” Hard Contact The default tolerance for convergence: incompatibility error  0.005c for p > p 0. The tolerance for 0  p  p 0 is linearly interpolated between 0.005c at p = p 0 and 0.1c at p = 0. –The tolerance at p = 0 can be modified with the  CONTROLS option.

Alternatives to “Classical” Hard Contact Example: Deep drawing of a cylindrical cup –Uses two-sided contact on a shell structure to model the clamping of the blank between the die and the blank holder. –Shell elements in ABAQUS/Standard cannot model two-sided hard contact because the thickness change is calculated by assuming that the material is incompressible. –Softened contact is used to impose the proper clamping pressure. –The clamping pressure increases exponentially as the blank is compressed between the die and the blank holder. R p = 50 mm R H = 56.25 mm R = 13 mm R p = 5 mm R B = 100 mm R D = 51.25 mm t = 0.82 mm r F softened contact used

Alternatives to “Classical” Hard Contact Contact without separation –The NO SEPARATION parameter on the  SURFACE BEHAVIOR option causes the surfaces to be bonded for the rest of the analysis once contact is established. Only normal contact is affected—relative sliding is still allowed. Different from TIE constraint—  TIE causes initially touching surfaces to be bonded in all directions throughout the analysis. The degrees of freedom that are bonded include all translational (and possibly rotational) degrees of freedom, temperature, and electrical potential. –Syntax: *SURFACE INTERACTION, NAME= name *SURFACE BEHAVIOR, NO SEPARATION Toggle off to invoke NO SEPARATION

Alternatives to “Classical” Hard Contact –Useful for modeling truly “sticky” conditions (adhesives). –Commonly used to avoid numerical problems if loss of contact is not expected to be significant. Check the sign of contact pressure to ensure that this assumption is reasonable. Pressure should be either a positive or a relatively small negative number. Large negative pressures indicate that the interface is carrying a large tensile load—does not make physical sense unless the interface is truly bonded.

Alternatives to “Classical” Hard Contact –Often used with the  FRICTION, ROUGH option. Rough friction is used to model perfectly rough frictional contact in which no sliding occurs. Corresponds to infinite friction coefficient . Nonzero shear stresses, regardless of sign of contact pressure, when used with the  SURFACE BEHAVIOR, NO SEPARATION option.

Alternatives to “Classical” Hard Contact Contact subject to tolerances –The  CONTACT CONTROLS option can be used to define contact tolerances, as shown at right (modified “hard” contact): contact pressure clearance Any pressure possible, up to a negative pressure of magnitude p o popo c No pressure transmitted when no contact (up to overclosure of c )‏

Alternatives to “Classical” Hard Contact –In this alternative local contact condition: Surfaces do not contact until they have “overclosed” by a distance, c ; and/or Surfaces do not separate until the normal stress between them has reached a tensile value, p o. The maximum number of points permitted to violate contact conditions in any increment is mpt. –Syntax: *CONTACT CONTROLS, PERRMX= p o, UERRMX= c, [MASTER=..., SLAVE=...], MAXCHP= mpt

Alternatives to “Classical” Hard Contact –Physical application: adhesive interfaces. Nonzero p o gives a sliding interface that can transfer both tensile and compressive stress. –Numerical application: improve convergence in cases of contact chatter. Use only as last resort. First try modifying the problem definition slightly to eliminate the uncertainty. This option also has a set of automatic alternative tolerances (use the AUTOMATIC TOLERANCES parameter) that should help eliminate chatter.

Alternatives to “Classical” Hard Contact Example: Deep drawing of a cylindrical cup –The contact state between the stretched sheet and the flat punch is undetermined. –A small curvature is introduced in the nose of the punch to eliminate chatter. –Alternatively, apply a small initial pressure load to the underside of the sheet to eliminate chatter. R p = 50 mm R H = 56.25 mm R = 13 mm R p = 5 mm R B = 100 mm R D = 51.25 mm t = 0.82 mm r flat-nosed punch

Alternatives to “Classical” Hard Contact User-defined behavior –The user subroutine UINTER : Provides a very general interface to define the constitutive behavior across the interface between two surfaces. Replaces all built-in options that define contact behavior; thus, the  SURFACE BEHAVIOR option and its suboptions cannot be used in conjunction with  SURFACE INTERACTION, USER. –The routine requires the user to define both normal and tangential stresses at the slave node at the current point in time. –All decisions regarding the contact status of a slave node must be made inside the user subroutine. –Syntax: *SURFACE INTERACTION, USER

Alternatives to “Classical” Hard Contact Interface: SUBROUTINE UINTER(STRESS,DDSDDR,FLUX,DDFDDT,DDSDDT,DDFDDR, 1 STATEV,SED,SFD,SPD,SVD,SCD,PNEWDT,RDISP,DRDISP, 2 TEMP,DTEMP,PREDEF,DPRED,TIME,DTIME,CINAME,SLNAME,MSNAME, 3 PROPS,COORDS,ALOCALDIR,DROT,AREA,CHRLNGTH,NODE,NDIR,NSTATV, 4 NPRED,NPROPS,MCRD,KSTEP,KINC,KIT,LINPER,LOPENCLOSE,LSTATE, 5 LSDI,LPRINT)‏ C INCLUDE ’ABA_PARAM.INC’ C CHARACTER*80 CINAME,SLNAME,MSNAME DIMENSION STRESS(NDIR),DDSDDR(NDIR,NDIR),FLUX(2),DDFDDT(2,2), 1 DDSDDT(NDIR,2),DDFDDR(2,NDIR),STATEV(NSTATV), 2 RDISP(NDIR),DRDISP(NDIR),TEMP(2),DTEMP(2),PREDEF(2,NPRED), 3 DPRED(2,NPRED),TIME(2),PROPS(NPROPS),COORDS(MCRD), 4 ALOCALDIR(3,3),DROT(2,2)‏ user coding to define STRESS, DDSDDR, FLUX, DDFDDT, DDSDDT, DDFDDR, and, optionally, STATEV, SED, SFD, SPD, SVD, SCD, PNEWDT, LOPENCLOSE, LSTATE, LSDI RETURN END

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Co jste chtěli vědět o ABAQUSu … OBECNÝ PŘEHLED: ABAQUS je program pro řešení technických úloh metodou konečných prvků Mechanika poddajných těles Termomechanika.

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