Stochastic Computation of Quasibrittle Fracture

Abstract

Continuum finite element (FE) models of quasibrittle structures suffer from the spurious mesh sensitivity, due to strain localization arising from the softening constitutive behavior of quasibrittle materials. Numerical techniques known as the localization limiters, have been developed to mitigate the mesh dependence issue. Some well-known ones include nonlocal formulations and energy regularization schemes such as the crack band model. The crack band model is one of the most computationally efficient methods to address mesh dependence, by scaling the post-peak part of the constitutive law such that the fracture energy is preserved. However, this model can recover mesh-objective global structural response only in cases of failure with damage localization. The present dissertation introduces a mechanism-based energy regularization scheme, which is able to mitigate mesh dependence under various failure mechanisms, overcoming the limitation of the crack band model. Meanwhile, due to material heterogeneity, the response of quasibrittle structures is stochastic. In stochastic FE simulations, the mesh dependence is manifested in the output statistics of structural strength. To address this issue, the size effects on the strength statistics arising due to the failure mechanism of a material element are taken into account. By considering that each finite element represents a material element of finite size, the probability distribution functions (pdf’s) of constitutive properties of the element are formulated according to the prevailing damage pattern. The evolving damage pattern of each finite element is mathematically described based on proposed numerical parameters. These parameters are used to determine the pdf’s of the constitutive properties which could thus be dependent on the mesh size. The same numerical parameters have also been employed in the mechanism-based energy regularization scheme to recover mesh objectivity in the deterministic setting. The efficiency of the proposed model in mitigating mesh dependence is evaluated through its application in deterministic and stochastic FE simulations of quasibrittle structures. Several numerical examples, inducing different failure mechanisms, are considered. It is shown that the present research has introduced a unified and general framework for addressing the mesh dependence of continuum FE simulations of quasibrittle failure, that is efficient in both the deterministic and stochastic settings.