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Finite element analysis of microstructure for the cubic to tetragonal transformation. (English) Zbl 0919.49020
Martensitic crystals which can undergo a cubic to tetragonal phase transformation have a nonconvex energy density with three symmetry-related, rotationally invariant energy wells. The authors give estimates for the numerical approximation of a first-order laminate for such martensitic crystals. He gives bounds for the $$L^2$$-convergence of directional derivatives in the “twin” plane, for the $$L^2$$-convergence of the deformation, for the weak convergence of the deformation gradient, for the convergence of the microstructure, and for the convergence of nonlinear integrals of the deformation gradient.

##### MSC:
 49M15 Newton-type methods 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65C20 Probabilistic models, generic numerical methods in probability and statistics 74B20 Nonlinear elasticity 74E30 Composite and mixture properties
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