Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics

The peridynamic equation of motion is considered for a large class of nonlinear pairwise force functions modelling isotropic microelastic material. Existence of Young-measure-valued solutions to the peridynamic equation of motion is proven if the underlying basic function space is L^p. Moreover, if the underlying basic function space is W^{σ, p} (0 < σ < 1), existence of weak solutions is shown. The choice of the function space depends on the singularity of the pairwise force function. The results do not rely upon any convexity assumption whatsoever. (paper)