Li, Bo; Luskin, Mitchell Approximation of a martensitic laminate with varying fractions. (English) Zbl 0928.74012 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. Cited in 8 Documents 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 PDF BibTeX XML Cite \textit{B. Li} and \textit{M. Luskin}, M2AN, Math. Model. Numer. Anal. 33, No. 1, 67--87 (1999; Zbl 0928.74012) Full Text: DOI Link EuDML