UC Santa Barbara

Computer simulation of fracture in materials with nonlinear mechanical response can be computationally expensive. These simulations often require a large number of degrees of freedom, and the nonlinearity in the problem can pose difficulties when computing solutions. This work focuses on two material models. The first model consists of rigid bricks interacting through nonlinear cohesive springs. Fracture in the material occurs through the rupture of the cohesive springs. The second, more complicated, model consists of deformable elements interacting through nonlinear cohesive springs.

In the first model, we assume the bricks are under a quasi-static loading scenario. With this assumption, the problem can be solved using a global Monte Carlo minimization algorithm to minimize the energy of the system. The energy in the system comes from the deformation and rupture of the nonlinear cohesive springs. Since these simulations have a high computational cost, we have developed a GPU-based (Graphics Processing Unit) Monte Carlo minimization algorithm that offers a significant speedup compared to a conventional multithreaded CPU-based algorithm.

With the second model, we have dynamic simulations with explicit time discretization. In this case we compute the force, acceleration, velocity, and position explicitly. The force in the system comes from both the deformation of the elements as well as the deformation of the nonlinear cohesive springs. We have developed explicit, CPU-based methods and implicit-explict methods on both CPUs and GPUs. Our implicit-explict GPU-based method achieves substantial performance improvement compared to the explicit, CPU-based method.

We present our GPU-based implementation of AES (Advanced Encryption Standard), which is used in the Monte Carlo minimization algorithm to generate random numbers. Our implementation is substantially faster than CPU-based implementation of AES. It is also faster than previous GPU implementations of AES.