Mechanism-Based Energy Regularization in Computational Modeling of Quasibrittle Fracture

Quasibrittle materials are featured by a strain-softening constitutive behavior under many loading scenarios, which could eventually lead to localization instability. It has long been known that strain localization would result in spurious mesh sensitivity in finite element (FE) simulations. Previous studies have shown that, for the case of fully localized damage, the mesh sensitivity can be mitigated through energy regularization of the material constitutive law. However, depending on the loading configuration and structural geometry, quasibrittle structures could exhibit a complex damage process, which involves both localized and diffused damage patterns at different stages of loading. This study presents a generalized energy regularization method that considers the spatial and temporal evolution of damage pattern. The method introduces a localization parameter, which describes the local damage pattern. The localization parameter governs the energy regularization of the constitutive model, which captures the transition from diffused to localized damage during the failure process. The method is cast into an isotropic damage model, and is further extended to rate-dependent behavior. The energy regularization scheme is directly incorporated into the kinetics of damage growth. The model is applied to simulate static and dynamic failures of ceramic specimens. It is shown that the present model is able to effectively mitigate the spurious mesh sensitivity in FE simulations of both types of failure. The present analysis demonstrates the essential role of mechanism-based energy regularization of constitutive relation in FE simulations of quasibrittle fracture.

A Probabilistic Crack Band Model for Quasibrittle Fracture

This paper presents a new crack band model (CBM) for probabilistic analysis of quasibrittle fracture. The model is anchored by a probabilistic treatment of damage initiation, localization, and propagation. This model regularizes the energy dissipation of a single material element for the transition between damage initiation and localization. Meanwhile, the model also takes into account the probabilistic onset of damage localization inside the finite element (FE) for the case where the element size is larger than the crack band width. The random location of the localization band is related to the random material strength, whose statistics is described by a finite weakest link model. The present model is applied to simulate the probability distributions of the nominal strength of different quasibrittle structures. It is shown that for quasibrittle structures direct application of the conventional CBM for stochastic FE simulations would lead to mesh-sensitive results. To mitigate such mesh dependence, it is essential to incorporate the strain localization mechanism into the formulation of the sampling distribution functions of material constitutive parameters.