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.
This paper investigates the effect of strain rate on the scaling behavior of dynamic tensile strength of quasibrittle structures. The theoretical framework is anchored by a rate-dependent finite weakest link model. The model involves a rate-dependent length scale, which captures the transition from localized damage to diffused damage with an increasing strain rate. As a result, the model predicts a rate- and size-dependent probability distribution function of the nominal tensile strength. The transitional behavior of the strength distribution directly leads to the rate and size effects on the mean and standard deviation of the tensile strength. The model is verified by a series of stochastic discrete element simulations of dynamic fracture of aluminum nitride specimens. The simulations involve a set of geometrically similar specimens of various sizes subjected to a number of different strain rates. Both random microstructure geometry and fracture properties are considered in these simulations. The simulated damage pattern indicates that an increase in the strain rate results in a more diffusive cracking pattern, which supports the theoretical formulation. The simulated rate and size effects on the mean and standard deviation of the nominal tensile strength agree well with the predictions by the rate-dependent finite weakest link model.
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