Abstract
The delayed damage model has been introduced by Allix and Deü [] as a way to overcome spurious mesh dependency in failure analysis involving damage and dynamic loading. The damage rate is bounded through a time scale which, combined with the wave speed, introduces implicitly a length scale. In this paper, the delayed damage model is analyzed through numerical experiments on three different loading cases of a bar: a slow loading leading to a dynamic failure, pulses and impact. We observe and discuss the load level needed for failure (and the dependence of this load level with respect to the loading rate), as well as the dissipation and extent of the fully damaged zone at failure. Observations lead to the following conclusions. First, the delayed damage model has no regularization effect for a dynamic failure initiating from rest. Second, for pulse loadings, the loading rate has no influence on the minimal load level needed for failure (even though the delayed damage model is a time-dependent model), and beyond this minimal load level for failure, the extent of the fully damage zone rises, proportionally to the length scale. Third, regarding the impact, the velocity needed to reach failure depends only the time-independent parameters of the models, and not the ones linked to the delayed damage.
Highlights
Damage growth simulation up to failure presents many challenges among which the need to introduce a length scale in the material model to avoid spurious mesh dependency even in the case of dynamic loading
We find different types of approaches in this category as the non-local approach [4, 5] in which the damage growth at a point depends on the average of some quantity at some distance around the point
The delayed damage model is an appealing approach to avoid spurious localization in damage analysis leading to failure
Summary
Damage growth simulation up to failure presents many challenges among which the need to introduce a length scale in the material model to avoid spurious mesh dependency even in the case of dynamic loading. More recent works as the phase-field approach emanating from the physics community [11], the variational approach to fracture [12] and the thick level set approach [13] Another way to introduce a length scale in problems involving inertia effect is to rely on a time scale. The three sections deal with one after the other the three scenarii, starting with the sudden rupture of pre-loaded bar, followed by the bar subjected to symmetrical tension pulses, and, the impact scenario.
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