Work

Wave dispersion and bifurcation analyses of eikonal gradient-enhanced isotropic damage models

Year: 2025

Type: article

Abstract: Often used to describe material degradation , local continuum damage models inevitably lead to an ill-posed problem. In quasi-static analysis, the singularity of the acoustic tensor implies the loss of ellipticity of the boundary value problem . In dynamics, the hyperbolic equilibrium equations become elliptic, which defines the loss of hyperbolicity, and waves cannot propagate in a local medium experiencing strain-softening. Classic gradient-enhanced damage models are known to preserve the well-posedness of the initial value problem, and waves can propagate in such a medium in a dispersive way. This paper addresses the question of wave dispersion and localization analysis in a gradient-enhanced medium with evolving non-local interactions. Particular attention is given to the gradient-enhanced Eikonal continuum, where damage-dependent interactions are considered. The regularization properties of the model are first studied through a one-dimensional problem of dispersive wave propagation . The analysis is completed by a three-dimensional bifurcation study based on a geometric representation, which generalizes the wave dispersion results. It is shown analytically that the gradient-enhanced Eikonal model preserves the localization-limiting character of non-local approaches and exhibits an intrinsic re-localizing nature for high initial damage levels. Like classic non-local approaches, loading waves propagate and can be transformed into a unique stationary harmonic localization wave, associated with a critical wavelength .

Source: European Journal of Mechanics - A/Solids

DOI: 10.1016/j.euromechsol.2025.105643

Authors: Breno Ribeiro Nogueira, Giuseppe Rastiello, Cédric Giry, Fabrice Gatuingt