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- W2157429767 abstract "Aim of this paper is to show that the life-golden rule ‘If you can relax, do it’ applies also to the numerical analysis of microstructures. In broad terms relaxation aims to characterize the weak limits of infimizing sequences with fine scale oscillations of gradients. The latter are identified with the fine-scale microstructure observed in phase transition solids and in inelastic materials in the form of shear bands. An effective density energy is introduced that allows characterization of the admissible microstructure. This equals the least value that the energy of the system can reach among all the microstructures and defines the difficult notion of quasiconvexity. For vector nonconvex energy densities W, the quasiconvex hull Wqc is indeed known only in very few cases, therefore, a numerical relaxation has to be involved. This poses however a computational challenge, because the solution of a nonconvex optimization problem is required. Other notions, such as finite laminates, rank-one convexity, and polyconvexity are introduced and a new class of algorithms for their approximations is introduced. This and other issues will be discussed and illustrated on model examples. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)" @default.
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- W2157429767 date "2006-10-01" @default.
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- W2157429767 title "Computational Microstructures in Phase Transition Solids and Finite-Strain Elastoplasticity" @default.
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- W2157429767 doi "https://doi.org/10.1002/gamm.201490031" @default.
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