A continuous-discontinuous approach for failure analysis of quasi-brittle materials

Abstract

Quasi-brittle failure is a phenomenon, which is characterized by the development of a nonlinear fracture process zone in front of the crack tip with a finite size compared to the overall structural dimensions. This process zone involves various microscopic activities during a loading process, which categorizes into different stages, such as nucleation and growth of microcracks, localization of these microcracks in a narrow process zone, and at last, the coalescence between the active set of densely distributed microcracks which leads to the formation of a macroscopic stress-free crack front. This material degradation process induces a typical nonlinear response with a small pre-peak hardening region, followed by a softening phase. A wide range of materials exhibits this type of material behavior, such as concrete, rock, bone, ice, and various composites, making failure analysis in quasi-brittle materials an emerging and critical research domain. Various models based on smeared and discrete numerical framework are available in the literature that provides extensive numerical capabilities to address this type of failure phenomenon with some limitations. A smeared or continuous approach to failure introduces an intrinsic internal length scale that smears out the crack over a certain width, limiting their applications to problems requiring an explicit representation of a crack. Conversely, discontinuous or discrete approaches explicitly represent a crack topology but require additional ad-hoc criteria for crack initiation and propagation. This thesis aims to develop a coherent computational framework that combines the advantages of both approaches and uses a continuous-discontinuous failure description to model the complete quasi-brittle failure process in a single FE analysis. The initial focus is to develop an improved gradient-enhanced nonlocal damage framework that captures inelastic material behavior in quasi-brittle solids, which includes crack initiation, crack propagation, and other material instabilities. Some of the key objectives are to obtain regularized solutions with sharp damage profiles with maximum damage in front of the crack tip while addressing the limitations of damage models available in the literature. Two gradient damage models have already been proposed to this contribution, which uses smoothed and micromorphic stress-based anisotropic interaction tensors to govern the spatial diffusive behavior. The damage models are based on a generalized micromorphic approach where fine-scale fluctuations due to interactions within the diffused network of micro-cracks in the fracture process zone are reflected at the macro-scale via incorporating a regularization process using an internal length scale through an additional microforce balance equation. The damage models are tested on various numerical examples and found to circumvent the limitations of conventional damage models by ensuring correct damage bandwidths using low-order finite elements during numerical simulations. The next part of the thesis presents a continuous-discontinuous computational framework that provides a discontinuous character to the quasi-brittle fracture process, modeled in a continuous setting using a gradient-enhanced nonlocal damage framework. The continuous-discontinuous FE framework is developed where the problem field is enhanced using discontinuous interpolation exploiting the local partition of unity via eXtended Finite Element (XFEM) approach, thereby extending the numerical kinematics of the localizing gradient damage framework to provide a continuous-discontinuous failure description. The enhanced kinematics of the proposed continuous-discontinuous formulation helps to successfully eliminate the issue of damage spreading during the final failure stages, with crack paths consistent with the experimental observations. A new path-following arc-length control Newton-Raphson solution scheme based on the internal and dissipated energy rates is developed to trace the nonlinear structural response in the presence of snapbacks. Finally, the last part of this thesis work focuses on applying the developed numerical methodologies to various engineering structural failure problems for materials exhibiting quasi-brittle failure phenomena. Some of the applications include capturing the structural size-effect in concrete structures and modeling anisotropic damage evolution in composite materials. The objective to capture the structural size-effect phenomenon is fulfilled by reproducing the results of experimental investigations using a single set of material and numerical parameters. Whereas, a finite element formulation based on a anisotropic gradient-enhanced continuum damage model is proposed to address anisotropic damage evolution due to progressive intra-laminar fracture in a composite layered materials using distinct damage variables associated with different failure modes. A few benchmark problems are taken from the literature to test the applicability and robustness of the anisotropic damage model.