Nonlocal constitutive model for simulating localized damage and fracture of viscoplastic solids under high energy impacts

Developing and applying theoretical and computational models that guide the development of design criteria and fabrication processes of high impact/ballistic-resistant material are essential. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening (localization) and the finite element computations are considerably affected by the mesh size and alignment and gives non-physical descriptions of the damaged regions and failure of solids. This study is concerned with the development of a novel coupled thermo-hypoelasto, thermo-viscoplastic, and thermo-viscodamage constitutive model within the laws of thermodynamics in which implicit and explicit intrinsic material length scale parameters are incorporated through the nonlocal gradient-dependent viscoplasticity and viscodamage constitutive equations. In this current model, the Laplacian of the effective viscoplastic strain rate and its coefficient, which introduces a missing length scale parameter, enter the constitutive equations besides the local effective viscoplastic strain. It is shown through simulating plugging fracture in ballistic penetration of high-strength steel circular plates by hardened blunt-nose cylindrical steel projectiles that the Laplacian coefficient parameter plays the role of a localization limiter during the penetration and perforation processes allowing one to obtain meaningful values for the ballistic limit velocity (or perforation resistance) independent of the finite element mesh density. For the corresponding local model, on the other hand, the ballistic limit continuously decreases as the mesh density increases and does not converge even for the finest mesh.