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Variational Approaches and Methods for Dissipative Material Models with Multiple Scales

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Analysis and Computation of Microstructure in Finite Plasticity

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 78))

Abstract

In a first part we consider evolutionary systems given as generalized gradient systems and discuss various variational principles that can be used to construct solutions for a given system or to derive the limit dynamics for multiscale problems via the theory of evolutionary Gamma-convergence. On the one hand we consider a family of viscous gradient system with quadratic dissipation potentials and a wiggly energy landscape that converge to a rate-independent system. On the other hand we show how the concept of Balanced-Viscosity solution arise in the vanishing-viscosity limit.

As applications we discuss, first, the evolution of laminate microstructures in finite-strain elastoplasticity and, second, a two-phase model for shape-memory materials, where H-measures are used to construct the mutual recovery sequences needed in the existence theory.

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  1. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

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  1. Alexander Mielke
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  1. Inst. für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Sergio Conti

  2. Lehrstuhl für Mechanik - Materialtheorie, Ruhr-Universität Bochum, Bochum, Nordrhein-Westfalen, Germany

    Klaus Hackl

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Mielke, A. (2015). Variational Approaches and Methods for Dissipative Material Models with Multiple Scales. In: Conti, S., Hackl, K. (eds) Analysis and Computation of Microstructure in Finite Plasticity. Lecture Notes in Applied and Computational Mechanics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-18242-1_5

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  • DOI: https://doi.org/10.1007/978-3-319-18242-1_5

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