Relaxation and the Computation of Effective Energies and Microstructures in Solid Mechanics

Sören Bartels (), Carsten Carstensen (), Sergio Conti (), Klaus Hackl (), Ulrich Hoppe () and Antonio Orlando ()
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Sören Bartels: Humboldt-Universität zu Berlin, Institut für Mathematik
Carsten Carstensen: Humboldt-Universität zu Berlin, Institut für Mathematik
Sergio Conti: Universität Duisburg-Essen, Campus Duisburg, Fachbereich Mathematik
Klaus Hackl: Ruhr-Universität Bochum, Institut für Mechanik
Ulrich Hoppe: Ruhr-Universität Bochum, Institut für Mechanik
Antonio Orlando: Humboldt-Universität zu Berlin, Institut für Mathematik

A chapter in Analysis, Modeling and Simulation of Multiscale Problems, 2006, pp 197-224 from Springer

Abstract: Summary We address the numerical analysis of relaxed formulations for scalar and vectorial nonconvex variational problems originating from models for solid-solid phase transitions and crystal plasticity.We discuss algorithms for the approximation of the quasiconvex envelope using laminates, rank-one convexity, and polyconvexity, and present some numerical applications to benchmarks problems, and to a model for single-slip crystal plasticity.

Keywords: Young Measure; Convex Envelope; Nodal Interpolation; Quasiconvex Function; Condensed Energy (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-35657-8_8

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DOI: 10.1007/3-540-35657-6_8

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