Error estimation and adaptivity for nonlocal damage models

By A. Rodríguez‐Ferran, Antonio Huerta. 2000

62 citations recorded by the source corpus.

Nonlocal damage models are typically used to model failure of quasi-brittle materials. Due to brittleness, the choice of a particular model or set of parameters can have a crucial influence on the structural response. To assess this influence, it is essential to keep finite element discretization errors under control. If not, the effect of these errors on the result of a computation could be erroneously interpreted from a constitutive viewpoint. To ensure the quality of the FE solution, an adaptive strategy based on error estimation is proposed here. It is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. Another important consequence of brittleness is that it leads to structural responses of the snap-through or snap-back type. This requires the use of arc-length control, with a definition of the arc parameter that accounts for the localized nature of quasi-brittle failure. All these aspects are discussed for two particular nonlocal damage models (Mazars and modified von Mises) and for two tests: the Brazilian tensile splitting test and the single-edge notched beam test. For the latter test, the capability of the Mazars model to capture the curved crack pattern observed in experiments – a topic of debate in the literature – is confirmed.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a92c5fd1e8738e4b95282d42ce38b106e37f1abb

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In Mechanics of Materials

Citations in the corpus

Stress-based nonlocal damage model (2011, background): “Evolution of q(x,rprin(s)) during the load Alternatively, more ‘‘local’’ definitions of the arc-length parameter s are needed, such as the maximum strain increment (Pegon and Anthoine, 1997; Rodríguez-Ferran and Huerta, 2000).”
Convergence, adaptive refinement, and scaling in 1D peridynamics (2009, methodology): “Adaptive refinement for other non-local methods applied to damage problems and discretized using the finite element method has appeared in, for example, [20–23].”
Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces (2000, unknown): “…account for the inﬂuence of shear strains in the equivalent strain deﬁnition to obtain this crack path (see, e.g., Peerlings et al., 1998), although Rodriguez-Ferran and Huerta (2000) showed that the necessity to do so may very well be an artifact due to discretization errors For the physically…”
Efficient and Reliable Nonlocal Damage Models (2004, methodology): “The FE discretization errors are kept under control and, thus, the physical significance of the computations is guaranteed [7,6].”