We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress-strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro-and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.

An extension of the constitutive correspondence framework of peridynamics is proposed. The main motivation is to address unphysical deformation modes which are shown to be permitted in the original constitutive formulation. The specific problem of matter interpenetration observed in numerical discretizations of peridynamics has usually been treated by adding short-range forces between neighboring particles in the discretization. Here, we propose a solution that is rooted directly within the nonlocal theory. The basic approach is to introduce generalized nonlocal peridynamic strain tensors based on corresponding bondlevel Seth-Hill strain measures which inherently avoid violations of the matter interpenetration constraint. Several analytic examples are used to show that the modified theory avoids issues of matter interpenetration in cases where the original theory fails. The resulting extended constitutive correspondence framework supports general classic constitutive laws as originally intended and is also shown to be ordinary.

Peridynamics has gained significant attention as an alternative formulation for problems in solid mechanics. Recent contributions have included initial attempts to include material damage and failure. In this paper, we propose an approach to incorporate classical continuum damage models in the state-based theory of peridynamics. This has the advantage of enabling the description of the damage evolution process in peridynamics according to well-established models. The approach is based on modifying the peridynamic influence function according to the state of accumulated damage. As a result, peridynamic bonds between nonlocal material points are severed in accordance with the damage law. The peridynamic damage formulation proposed is implemented for the particular case of a well established ductile damage model for metals. The model is applied to the simulation of ballistic impact of extruded corrugated aluminum panels and compared with experiments.