A modular approach based on graph transformation to simulate tearing and fractures on various mechanical models

Abstract

This paper introduces an extension of a general framework that allows the simulation of various mechanical models (discrete or continuous ones, for different kinds of meshes, in any dimension). This framework relies on a topological model and a rule-based language, that performs sub-graph matching and, possibly, transformations. This extension allows topological modifications such as tearing and fractures for all the implemented physical models. A general process has been used to simulate fractures and tearing: the topological transformation is described using the provided rule-based language and its application is triggered when a selected criterion is verified. Several criteria are proposed, that depend upon the strain or stress generated by a single or a set of interactions. This method raises the question of the link between the location where a criterion is applied and the mesh elements involved in a modification. This question has motivated us to design new criteria which are closely related to the mesh modification. Using this method, a minimal number of mechanical data need to be updated after a transformation and any interaction relying on mesh features (vertex, edge, face, volume) that are suppressed or split can be automatically ignored