Relaxation theorems in nonlinear elasticity

We consider vectorial variational problems in nonlinear elasticity of the form I [u] =´W (Du) dx, where W is continuous on matrices with a positive determinant and diverges to infinity along sequences of matrices whose determinant is positive and tends to zero. We show that, under suitable growth assumptions, the functional´W qc (Du) dx is an upper bound on the relaxation of I , and coincides with the relaxation if the quasiconvex envelope W qc of W is polyconvex and has p-growth from below with p n. This includes several physically relevant examples. We also show how a constraint of incompressibility can be incorporated in our results.

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Relaxation theorems in nonlinear elasticity

Cited by 14 publications

References 7 publications

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Modelling of Thin Martensitic Films with Nonpolynomial Stored Energies

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