Journal Title
Title of Journal: Continuum Mech Thermodyn
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Abbravation: Continuum Mechanics and Thermodynamics
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Publisher
Springer-Verlag
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Authors: D M Kochmann K Hackl
Publish Date: 2010/11/03
Volume: 23, Issue: 1, Pages: 63-85
Abstract
The analysis and simulation of microstructures in solids has gained crucial importance virtue of the influence of all microstructural characteristics on a material’s macroscopic mechanical behavior In particular the arrangement of dislocations and other lattice defects to particular structures and patterns on the microscale as well as the resultant inhomogeneous distribution of localized strain results in a highly altered stress–strain response Energetic models predicting the mechanical properties are commonly based on thermodynamic variational principles Modeling the material response in finite strain crystal plasticity very often results in a nonconvex variational problem so that the minimizing deformation fields are no longer continuous but exhibit smallscale fluctuations related to probability distributions of deformation gradients to be calculated via energy relaxation This results in fine structures that can be interpreted as the observed microstructures In this paper we first review the underlying variational principles for inelastic materials We then propose an analytical partial relaxation of a NeoHookean energy formulation based on the assumption of a firstorder laminate microstructure thus approximating the relaxed energy by an upper bound of the rankoneconvex hull The semirelaxed energy can be employed to investigate elastoplastic models with a single as well as multiple active slip systems Based on the minimization of a Lagrange functional consisting of the sum of energy rate and dissipation potential we outline an incremental strategy to model the timecontinuous evolution of the laminate microstructure then present a numerical scheme by means of which the microstructure development can be computed and show numerical results for particular examples in single and doubleslip plasticity We discuss the influence of hardening and of slip system orientations in the present model In contrast to many approaches before we do not minimize a condensed energy functional Instead we incrementally solve the evolution equations at each time step and account for the actual microstructural changes during each time step Results indicate a reduction in energy when compared to those theories based on a condensed energy functional
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