Implementation of material constitutive equations in finite element codes

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Implementation of material constitutive equations in finite element codes J. Besson Centre des Matériaux, École des Mines de Paris, UMR CNRS 7633, BP 87 Evry cedex 91003 Implementation of constitutive equations 1

∂∆? ?

internal state variables

tangent matrix

besson centre des matériaux

must provide

constitutive equation

ecole de mines de paris

time increment

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Publié par

pefav

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Constitutive equation

Implementation of material constitutive equations in niteelement codes

J. Besson Centre des Matériaux, École des Mines de Paris, UMR CNRS 7633, BP 87 Evry cedex 91003

Implementation of constitutive equations

Introduction

Why is it important to know how to implement material constitutive equations in FE codes ?

Few constitutive equations are avaliable in commercial codes

Implement new constitutive equations in FE codes (ABAQUS, ANSYS, MARC, . . . , ASTER, CAST3M, . . . , Zébulon, WARP3D)

Understand convergence problems

Introduction

Outline

Denitionof a constitutive equation (FE code point of view)

Numerical integation methods (explicites/implicites)

Consistent tangent matrix

Particular case : von Mises material

Convergence

Introduction

Denitionof a constitutive equation

For a displacement based FE formulation, nodal displacements are assumed to be known and therefore the deformations The constitutive equation must then supply: (i) stressesand (ii) the consistent tangent matrixL=∂ /∂εfor a given strain incrementε.

Complex constitutive equations are characterized by internal state variables[A]: the constitutive equation must provide an update of these variables consistent with the strain and time increment.

Denition