A second strain gradient damage model with a numerical implementation for quasi-brittle materials with micro-architectures

Abstract

In this paper, a quasi-brittle damage model for micro-architectural materials is presented within the framework of isogeometric analysis to exploit the high-order continuity of the non-uniform B-spline basis functions. The constitutive relation depends not only on the strain field, but also on their first and second strain gradient terms. The simplified second-gradient elasticity formulation from Mindlin’s theory is employed with corresponding micro-architecture-related length scales to capture the material nonlocality and size effects. The strain-based damage is modelled by a nonlocal independent field coupled to the displacement field. Influences of the two types of nonlocalities (manufactured micro-architectures and damage-induced micro-defects) on the response of structures, as well as the damage initiation and propagation, are analysed through numerical experiments. A formula to determine the micro-defect-related length scale from macroscopic measurements is proposed, boosting the accuracy and applicability of the model. In addition, relevant open problems and further developments of this damage model are discussed.

On the Kachanov-Rabotnov continuum damage model

“…It is well known that using an integral type non-local constitutive equation or inclusion of higher order spatial displacement gradients, as well as damage gradients, brings the desired length-scale into the material model, see e.g. [6,15,18,19,20,21,23]. However, the damage evolution equation is then a partial differential equation and extra boundary conditions are required.…”

“…For the second model use of eqs. (18) and choices (20) results in the following constitutive equations…”

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

“…Quasi-brittle materials, including high-strength steels, play a crucial role in many aerospace and aircraft applications. A reliable prediction of the failure for quasi-brittle materials has become a subject of interest in experimental studies and computational mechanics [165,166]. A novel coupling between the Total Lagrangian (TL) and Eulerian formulations of the SPH method has been presented by Young et al [167].…”

Research perspective on multiphysics and multiscale materials: a paradigmatic case

“…Some solutions for the last specific problem can be found in [4,41,86]. More generally, one can try to get targeted materials basing, for instance, the demands: (i) on the mechanical properties of granular materials as done in [71]; (ii) by requiring some particular properties when damage occurs as in [73,79,87];…”