A model scaling approach for fracture and size effect simulations in solids: Cohesive zone, smeared crack band and phase-field models

Abstract

Despite many noteworthy contributions, the computational modeling of arbitrary fracture configurations and in particular, the quantification of size effect in quasi-brittle solids, still remains a challenging issue. In this work we proposed a model scaling approach for fracture and size effect simulations in solids. It employs only the geometric transformation relations and thus applies to any material model for fracture. Those popular models, i.e., the cohesive zone model, the smeared crack model and the phase-field cohesive zone model, are considered. With the geometric scaling factor intrinsically incorporated in the formulation, the resulting scaled models are able to predict the energetic size effect of a series of geometrically similar structures by parametric numerical simulations of the reference one. The 1-D analytical results of all the three scaled models are coincident with those from the underlying unscaled counterparts, validating the proposed model scaling approach. As it is independent of the mesh discretization and insensitive to the length scale, the scaled phase-field cohesive zone model (PF-CZM) is adopted for application to several representative benchmark tests of concrete and ice with mode-I and mixed I+II failure modes. The numerical results demonstrate that, owing to the strength-based crack nucleation criterion, the energy-based crack propagation criterion and the variational principle based path chooser, as well as the geometric scaling factor, are all incorporated into a standalone framework, the scaled PF-CZM is able to predict both the type II size effect law of pre-cracked quasi-brittle structures and the type I size effect law of intact ones. Moreover, those laborious manual manipulations in the numerical modeling of a large size range of geometrically similar structures, e.g., spatial discretization, enforcement of loading and boundary conditions, postprocessing of output data, etc., need to be done only once on the reference structure. These advantages make the scaled PF-CZM rather promising in the quantification of size effect in quasi-brittle structures.