A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation

Abstract

In the framework of continuum damage mechanics, a computational model for quasi-brittle crack modelling is proposed. The proposed model has significant mesh-objectivity and accuracy advantages over existing methods for modeling quasi-brittle crack. These stem from the combination of the local crack tracking algorithm, the new calculation of crack bandwidth and the non-local treatment regarding strain field. Resorting to the implementation of local crack tracking algorithm, it is desirable that the spurious dependence of conventional continuum damage mechanics-based model on mesh bias can be effectively addressed. The new estimation of the real-time crack bandwidth can be not only depending on the element size and pattern, but also on the physical crack path within each consolidate cracked element. Thus, the energy dissipation during crack propagation can be characterized in a more accurate, physically based manner. The non-local averaging regarding the strain field in the course of failure evolution is carried out within an elliptical domain, the configuration of which is related to finite element and crack trajectory obtained by the local crack track algorithm. With this combined technique, it is expected that a more accurate crack evolution course can be achieved numerically, which allows engineers to adopt relatively coarse unstructured discretizations without sacrificing solution accuracy. By numerical examples, the proposed model, empowered by the combined techniques, demonstrates significant improvements in the prediction of crack propagating of quasi-brittle materials. This model may provide engineers a more reliable tool in practical application of computational material failure.

On a Computational Approach to Micro- and Macro-modelling of Damage in Brittle and Quasi-brittle Materials

“…in (7). This seems to be supported by the discrete formulation (12), containing the 2nd time differences, corresponding to the 2nd time derivatives in (22), naturally. Nevertheless, one cannot guarantee any reasonable convergence of the sequences of 2nd differences to u ∈ W 1,2,2 (I, V, V ), suffering from the lack of information onü: we have only u,u ∈ L 2 (I, V ) here.…”

“…, which is the desired formula for the step-by-step evaluation of u m s . Now we shall exploit (12) to derive some a priori bounds for all sequences…”

“…Here we shall apply namely the engineering computational approach of [13] to demonstrate the possibility of effective numerical simulations; the discussion of computational techniques for numerical quadrature on relevant adaptive meshes can be found in [54]. Much more references to the advances in XFEM strategies in the last decade are contained in [63], [64], [12] and [65]; especially for some inverse problems of identification of material characteristics including sensitivity analysis see [66] and for the potential coupling of XFEM with BEM, i. e. the boundary element method, utilizing some knowledge of (semi-)analytical solutions, cf. [67].…”

“…One of possible ways is to adopt a discontinuous-like finite element approach to the lattice model by [8]. An alternative approach refers to special constitutive relations, inspired by continuum mechanics, where crack opening and contact surface sliding are included into the model of plastic damage, using smeared cracking by [9], [10] or [11], together with mesh objective strain localization due to material softening, referring to the thermodynamically irreversible continuum damage mechanics by [12], in particular that leading to a smeared representation of the crack path by [13]. At least for the practically significant application of self-compacting concrete, supported by both experimental methods and numerical simulations, smeared cracking can be combined with Monte Carlo simulations, which results in the variational multiscale cohesive method by [14], whose various implementations differs in the choice of basis functions.…”

Safety analysis of existing masonry arch bridges by nonlinear finite element simulations

“…Other advantages of simulating the cracking process are the opportunities to formulate failure criteria based on crack lengths and to directly consider pre-existing cracks in the model. In the present investigation, the smeared crack approach, which is widely used for describing the mechanical behavior of concrete (Li and Wu, 2018;Li et al, 2019), was adopted. The analysis assumptions are explained in the following section, and a concept for the safety evaluation of existing masonry arch bridges is proposed.…”