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Identification and estimation of constitutive parameters for material laws in elastoplasticity
Author(s) -
Kreißig R.,
Benedix U.,
Görke U.J.,
Lindner M.
Publication year - 2007
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.200790027
Subject(s) - discretization , finite element method , constitutive equation , mathematics , nonlinear system , inverse problem , boundary value problem , context (archaeology) , parameter identification problem , numerical analysis , mathematical optimization , mathematical analysis , physics , structural engineering , engineering , paleontology , model parameter , quantum mechanics , biology
The paper summarizes the comprehensive experience of the authors in the numerical identification and estimation of parameters for anisotropic elastoplastic material laws analyzing inhomogeneous mechanical fields. Generally, the constitutive model under consideration represents a system of differential and algebraic equations. It distinguishes itself by a strictly thermodynamically consistent foundation, and an identical structure in case of small as well as finite deformations. Different rules for the evolution of internal variables describing various hardening effects are proposed. The nonlinear inverse problem of the identification of material parameters is solved with deterministic optimization methods. Basically, the least squares type objective function contains several local and global variables for the comparison of experimental and numerical data. Within this context, the numerical values of the comparative quantities are calculated either using the local integration of the initial value problem at suitably chosen material points or analyzing the entire initial‐boundary value problem (e.g. with the Finite Element Method). In order to obtain the gradient of the objective function within the framework of a sensitivity analysis a semianalytical approach based on the implicit differentiation of the equilibrium conditions and the discretized constitutive relations is presented. The numerical algorithms for the direct as well as the inverse problem are implemented into in‐house Finite Element codes. Some examples based on real and numerical experiments analyzing selected constitutive approaches are presented. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)