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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.

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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