Mechanism-Based Energy Regularization in Numerical Modeling of Quasibrittle Fracture

Brittle heterogenous materials, also known as quasibrittle materials, have been widely used in the design of many engineering structures, such as civil infrastructure, aircraft, automobiles, military armors, and microelectronic devices. Typical examples of quasibrittle materials include concrete, ceramics, fiber and woven composites, rock, and many more brittle materials at the microscale. One salient feature of quasibrittle materials is that they often exhibit a strain-softening constitutive response under many loading scenarios, which eventually leads to localization instability. It is well known that strain localization causes the spurious mesh sensitivity in finite element (FE) simulations, which is one of the fundamental challenges in computational modeling of quasibrittle structure. Previous studies have shown that, for the case of fully localized damage, 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. 

In this talk, we present a generalized energy regularization method that considers the spatial and temporal evolution of damage pattern. The method includes two limiting cases: 1) fully diffused damage in which no energy regularization is needed, and 2) fully localized damage in which regularization is required to preserve the fracture energy. To capture the transition between these two limits, we propose a localization parameter to describe the local damage pattern and govern the regularization of the constitutive model. The present method is cast into an isotropic damage model, and is further extended to rate dependent behavior. For constitutive modeling of rate effect, the energy regularization scheme is incorporated into the kinetics of damage growth. The model is applied to simulate static and dynamic failures of alumina nitride specimens. It is shown that the model recovers the classical crack band model for the case where the structure experiences a purely localized damage pattern. For structures that exhibit a transition from diffused damage to localized damage, the present model outperforms both the crack band model and the diffused damage model in terms of suppressing the spurious mesh sensitivity. In the dynamic spalling test, the specimen exhibits a diffused damage pattern, and the present model is shown to yield a mesh-independent simulation. By contrast, the crack band model grossly underestimates the energy dissipation for large mesh. These different numerical examples clearly demonstrate the essential role of mechanism-based energy regularization of constitutive relation in FE simulations of quasibrittle fracture.