Zusammenfassung
We consider vectorial variational problems in nonlinear elasticity of the form , 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 is an upper bound on the relaxation of I, and coincides with the relaxation if the ...
Zusammenfassung
We consider vectorial variational problems in nonlinear elasticity of the form , 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 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 . This includes several physically relevant examples. We also show how a constraint of incompressibility can be incorporated in our results.
Altmetric