Finite Element Analysis of Microstructure for the Cubic to Tetragonal Transformation
SIAM JOURNAL ON NUMERICAL ANALYSIS（2006）
摘要
Martensitic crystals which can undergo a cubic to tetragonal phase transformation have a nonconvex energy density with three symmetry-related, rotationally invariant energy wells. We give estimates for the numerical approximation of a first-order laminate for such martensitic crystals. We give bounds for the L2 convergence of directional derivatives in the "twin" plane, for the L2 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.
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关键词
nonlinear integral,tetragonal transformation,finite element analysis,directional derivative,deformation gradient,rotationally invariant energy well,nonconvex energy density,numerical approximation,l2 convergence,first-order laminate,martensitic crystal,weak convergence,finite element,microstructure,martensitic transformation,microstructures
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