Mesh Dependence of Failure Progression in Continuum Damage Models of Brittle Materials with Size-Dependence and Variability

31 Aug 2022 (modified: 05 May 2023)MPM 2022 Workshop SubmissionReaders: Everyone
Keywords: Continuum Damage, Weibull, Fracture, Failure, Brittle, Size Effects, Mesh Dependence
TL;DR: Mesh dependence of crack propagation after initial damage is achieved through improved seeding of initial strength and an automated crack-tip treatment.
Abstract: In continuum models of brittle material failure, spatially varying material properties can be specified so that the stress associated with initial damage in a domain obeys a Weibull distribution. This approach naturally produces a size effect of strength, and mitigates some effects of mesh resolution in fracture patterns that can arise when modeling homogeneous material properties. However, the stress field around a single damaged MPM particle or grid cell is insufficiently resolved to capture the stress concentration around a critical flaw, and significant mesh dependence of failure progression may occur. Two approaches are found to greatly mitigate this mesh dependence within a continuum damage framework, (i) increasing the length scale of the initial Weibull heterogeneity, so that the stress failure around an initial critical flaw is better resolved, (ii) modifying the crack-tip damage response to create an effective stress concentration that is independent of mesh resolution. These approaches are shown to produce the expected size-dependent and statistically varying failure for a variety of geometries, without the need for explicit tracking of fractures, or sacrificing any of the inherent robustness of an MPM continuum damage solution.
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