A critical comparison of gradient and integral nonlocal damage models: Formulation, numerical predictions and computational aspects

Abstract

This contribution provides a comparative numerical assessment of the two main classes of nonlocal damage models: gradient-enhanced and integral-type strategies. Particular focus is placed on their formulations, mechanical predictions and computational aspects. A constitutive model for finite strain elastoplasticity, coupled with isotropic damage, is adopted in both cases. In-depth descriptions of both nonlocal models are included, encompassing their theoretical framework and numerical treatment. The integral approach introduces nonlocality explicitly, with a given nonlocal operator establishing the relations between neighbouring points, which impact the structure of the stiffness matrix. The gradient strategy treats nonlocality in an implicit fashion, through the addition of a damage diffusion equation in the global equilibrium system. In this paper, a strongly coupled staggered solution scheme is adopted to solve the mechanical and damage problems separately. Three numerical examples showcase the distinct predictions and computational aspects of the two nonlocal models, revealing their fundamental differences. For small nonlocal lengths, in contrast with its integral counterpart, the gradient model circumvents excessive localisation even in the presence of sharp notches. In general, the gradient approach yields more diffuse damage zones and reduced damage magnitudes. These observations are associated with the different formulations of nonlocality, the role of the nonlocal characteristic parameter, and their practical implications. The gradient model also shows advantages in terms of computational efficiency, mesh independence, and implementation simplicity, making it a compelling choice for most engineering applications.