Stiff ceramic platelets (or bricks) that are aligned and bonded to a second ductile phase with low volume fraction (mortar) are a promising pathway to produce stiff, high-toughness composites. For certain ranges of constituent properties, including those of some synthetic analogs to nacre, one can demonstrate that the deformation is dominated by relative brick motions. This paper describes simulations of fracture that explicitly track the motions of individual rigid bricks in an idealized microstructure; cohesive tractions acting between the bricks introduce elastic, plastic and rupture behaviors. Results are presented for the stresses and damage near macroscopic cracks with different brick orientations relative to the loading orientation. The anisotropic macroscopic initiation toughness is computed for small-scale yielding conditions and is shown to be independent of specimen geometry and loading configuration. The results are shown to be in agreement with previously published experiments on synthetic nacre.

Simulation of the nonlinear mechanical response of materials with explicit representation of microstructural features is extremely challenging. These models typically involve a very large number of degrees of freedom, and are prone to convergence difficulties when searching for roots to nonlinear equilibrium equations. We focus on an idealized material model that is motivated by the microstructure of synthetic nacre: individual ‘bricks’ (representing ceramic platelets) interact through nonlinear cohesive springs (representing a small volume fraction of polymer that bonds the platelets). The model simulates composite fracture through rupture of the cohesive springs. The problem is cast in terms of energy minimization and is essentially described by ‘nearest neighbor’ interactions. The principal focus of this paper is to illustrate the computational gains achievable by the strategic marriage of robust, global Monte Carlo minimization algorithms to the graphics processing unit architecture, and to describe how they were realized on the Nvidia GPU. Results comparing the computation times for graphics processing unit and central processing unit implementations demonstrate that a new adaptive version of the simulated annealing algorithm yields a speedup of approximately 5 times, whereas the graphics processing unit implementation yields a speed-up of about 16 times over conventional four-core central processing unit implementations. The resulting speed enhancement for adaptive graphics processing unit minimization of a factor of 80 enables a far broader range of simulations than has previously been possible. Simulations involving as many as 300,000 bricks can be performed in hours, as compared to weeks required by central processing unit implementation. Many aspects of this approach are translatable to other physical problems involving energy minimization in systems with large numbers of degrees of freedom.

This paper examines the effect of non-uniform microstructures on the macroscopic fracture properties of idealized brick and mortar composites, which consist of rigid bricks bonded with elastic-plastic mortar that ruptures at finite strain. A simulation tool that harnesses the parallel processing power of graphics processing units (GPUs) was used to simulate fracture in virtual specimens, whose microstructures were generated by sampling a probability distribution of brick sizes. In the simulations, crack advance is a natural outcome of local ruptures in the cohesive zones bonding the bricks: the macroscopic initiation toughness for small-scale yielding is inferred by correlating the critical load needed to advance a pre-defined crack with an associated far-field energy release rate. Quantitative connections between the statistical parameters defining heterogeneous brick distributions and the statistics of initiation toughness are presented. The nature of crack tip damage and stresses ahead of the crack tip are illustrated as a function of brick size variability. The results offer quantitative insights that can be used to identify microstructural targets for process development, notably specific brick size distributions that still provide macroscopic toughening.