Numerical analysis of a microstructure for a rotationally invariant, double well energy

Mitchell Luskin

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Abstract

The laminated microstructure observed in martensitic crystals can be modeled by energy minimizing sequences of deformations for a rotationally invariant (or frame-indifferent), double well energy density [1, 2, 10]. The deformation gradients of energy minimizing sequences oscillate between energy wells across layers (with width converging to zero) so that the effective energy density becomes the relaxed energy density [2, 12]. We present error estimates for the minimization of the energy ∫Ω φ(▽υ(x)) dx where the energy density φ(A) is a rotationally invariant, double well energy density by a general class of approximation methods for the deformation in L2, the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradient, and the convergence of nonlinear integrals of the deformation gradient.

Original languageEnglish (US)
Pages (from-to)405-408
Number of pages4
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume76
Issue numberSUPPL. 2
StatePublished - Dec 1 1996

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