On the impossibility of arbitrary deformations in nonlinear elasticity

摘要

We employ partly Sobolev classes to obtain a necessary condition for mappings of W-1,W- p-class to be deformations of nonlinearly elastic bodies that can be induced by L-q-forces, 1 = p, q infinity. This condition is useful for studying continuous deformations of non- homogeneous materials and for obtaining stable numerical methods for nonlinear elasticity.