Materials with both high strength and high toughness have applications in many areas, including automobiles, aerospace, bridges, buildings, and others. Nacre is a naturally occurring material that consists of calcium carbonate and organic protein, but it has a toughness that is significantly higher than its constituents. Efficient simulations of these composite materials can increase our understanding of their properties and optimize the design of new synthetic materials. We have developed a quasi-static Monte-Carlo based simulation algorithm as well as dynamic implicit/explicit methods for fracture simulations. By utilizing GPU and optimizing the data structures for the GPU architecture, we were able to achieve significant performance improvements. We also developed a high-performance parallel random number generator for GPU using AES that is used in the Monte-Carlo simulation algorithm. We show performance results of our algorithms. In particular, we were able to achieve up to 80x speedup for our Monte-Carlo simulation algorithm and up to 100x for our dynamic implicit/explicit algorithms for problems containing a few hundred thousand elements.