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Approximation of a laminated microstructure for a rotationally invariant, double well energy density. (English) Zbl 0874.73060
Summary: We give error estimates for the approximation of a laminated microstructure which minimizes the energy \(\int_\Omega\phi(\nabla v(x))dx\) for a rotationally invariant, double well energy density \(\phi(A)\). We present error estimates for the convergence of the deformation in \(L^2\), the convergence of directional derivatives of the deformation in the “twin planes”, the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient.

MSC:
74A60 Micromechanical theories
74M25 Micromechanics of solids
74B20 Nonlinear elasticity
74E30 Composite and mixture properties
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
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