Approximation of a martensitic laminate with varying fractions. (English) Zbl 0928.74012

Li, Bo; Luskin, Mitchell

M2AN, Math. Model. Numer. Anal. 33, No. 1, 67-87 (1999).

Summary: We give results on the approximation of a laminate with varying volume fractions for multi-well energy minimization problems modeling martensitic crystals that can undergo either an orthorhombic to monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfy the corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energy for the approximation of the limiting macroscopic deformation and the simply laminated microstructure. Finally, we give results for the corresponding finite element approximation of the laminate with varying volume fractions.

MSC:

74A40	Random materials and composite materials
74N15	Analysis of microstructure in solids
74E30	Composite and mixture properties
74E15	Crystalline structure
74S05	Finite element methods applied to problems in solid mechanics

Keywords:

orthorhombic to monoclinic transformation; multi-well energy minimization; martensitic crystals; cubic to tetragonal transformation; energy minimizing sequences; error bounds; finite element approximation