Macroscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strains |
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Authors: | M Brünig |
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Affiliation: | 1. Lehrstuhl für Baumechanik-Statik, Universit?t Dortmund, D-44221, Dortmund, Germany
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Abstract: | The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the macroscopic rate-independent
and rate-dependent analysis of micromechanics of metal single crystals undergoing finite elastic-plastic deformations which
is based on the assumption that inelastic deformation is solely due to crystallographic slip. The formulation relies on a
multiplicative decomposition of the material deformation gradient into incompressible elastic and plastic as well as a scalar
valued volumetric part. Furthermore, the crystal deformation is described as arising from two distinct physical mechanisms,
elastic deformation due to distortion of the lattice and crystallographic slip due to shearing along certain preferred lattice
planes in certain preferred lattice directions. Macro- and microscopic stress measures are related to Green’s macroscopic
strains via a hyperelastic constitutive law based on a free energy potential function, whereas plastic potentials expressed
in terms of the generalized Schmid stress lead to a normality rule for the macroscopic plastic strain rate. Estimates of the
microscopic stress and strain histories are obtained via a highly stable and very accurate semi-implicit scalar integration
procedure which employs a plastic predictor followed by an elastic corrector step, and, furthermore, the development of a
consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also
be discussed. Finally, the numerical simulation of finite strain elastic-plastic tension tests is presented to demonstrate
the efficiency of the algorithm. |
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