## 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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