Localization Study of a Regularized Variational Damage Model

TL;DR

This paper analyzes a regularized damage model's localization behavior, exploring modifications to improve its physical realism and eliminate pathological responses through analytical and numerical methods.

Contribution

It provides a detailed analysis of the model's localization properties and introduces modifications to enhance its realistic response and prevent pathological effects.

Findings

Proper parameter choices yield realistic load-displacement curves.

Modifications can eliminate brittle response and damage zone expansion.

Analytical and numerical studies reveal fundamental model features.

Abstract

The paper presents a detailed analysis and extended formulation of a rate-independent regularized damage model proposed by Mielke and Roub\'i\v{c}ek (2006). Localization properties are studied in the context of a simple one-dimensional problem, but the results reveal the fundamental features of the basic model and of its modified versions. The initial bifurcation from a uniform solution is described analytically while the complete failure process is studied numerically. Modifications of the regularizing term and of the dissipation distance are introduced and their effect on the global response is investigated. It is shown that, with a proper combination of model parameters, a realistic shape of the load-displacement diagram can be achieved and pathological effects such as extremely brittle response or expansion of the damage zone accompanied by stress locking can be eliminated.