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Accelerating constitutive modeling by automatic tangent generation
Author(s) -
Rothe Steffen,
Hartmann Stefan
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210146
Subject(s) - hyperelastic material , linearization , tangent , viscoplasticity , finite element method , constitutive equation , computation , finite strain theory , operator (biology) , mathematics , tangent modulus , tangent stiffness matrix , nonlinear system , computer science , mathematical analysis , structural engineering , engineering , algorithm , physics , geometry , biochemistry , chemistry , modulus , quantum mechanics , repressor , transcription factor , gene , stiffness matrix
Within the framework of finite elements the linearization within a Newton‐like method requires the computation of the so‐called consistent tangent operator. There are several possibilities to get these derivatives. Three methods, namely analytical, numerical and automatic differentiation, for tangent generation will be analyzed concerning the simulation time and applicability for three different constitutive models. These models are a finite strain hyperelasticity model, finite strain viscoplasticity model for metal powders and a small strain thermoviscoplasticity model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)