A weak approach to finite elasticity,

On the ground of four axioms we define the kinematics of perfectly elastic bodies and in particular the notion of weak deformations of a perfectly elastic body. Weak deformations turn out to agree with weak diffeomorphisms introduced in [10], a class of rectifiable currents which enjoys good closure and compactness properties. Defining the dynamics of perfectly elastic bodies in terms of two constitutive conditions on the stored energy function, we can therefore prove existence of stable equilibrium weak deformations for mixed boundary value problems, which moreover satisfy equilibrium and conservation equations.