Implementation of material constitutive equations in finite element codes

Description

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

Sujets

• Constitutive equation

Informations

• Publié par: pefav
• Nombre de lectures: 33
• Langue: English

Extrait

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

1

  

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

2

    

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

3

  

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 increment
ε.    

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

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Role of the constitutive equation in the FEM

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