Development of GPU-based Strategies for Finite Element Simulation of Elastoplastic Problems

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Elastoplasticity is a phenomenon in which materials deform elastically up to a certain load limit and plastically afterwards. The elastic deformation is recoverable, but plastic deformation is permanent. The elastoplastic behaviour is commonly observed in materials of practical interest like metals, concrete, soils, rocks, biological tissues, etc., that yield when subjected to loads high enough. The design and optimization of such materials depend strongly on the elastoplastic analysis for the prediction of displacement and stress. However, elastoplastic analysis is computationally expensive and often requires the use of parallel computers in real-world applications like metal forming and crashworthiness. This thesis presents a parallel computing framework for finite element analysis of elastoplastic problems using massively parallel Graphics Processing Unit (GPU) processor. Considering assembly-based approach, GPU-based parallel algorithms are proposed for all expensive steps in elastoplastic analysis, namely the computation of elemental matrices and their assembly, the computation of stress using the well-known radial-return method and the computation of internal force vectors and their assembly. Since GPUs have limited memory, assembly is done directly into a sparse storage format that can be seamlessly integrated with a GPU-based linear solver. In order to further accelerate the linear solver step in elastoplastic analysis, matrix-free iterative solvers have been proposed. Matrix-free solvers never assemble large sparse global tangent matrix and perform computations with small dense elemental matrices, reducing the storage requirement and avoiding the use of expensive sparse storage formats. For problems using unstructured mesh, a novel matrix-free strategy is developed that uses only symmetric part of elemental tangent matrices to compute sparse matrix-vector product (SpMV) by following element-by-element technique. For problems using voxel-based structured mesh, single kernel and improved split kernel strategies are proposed to efficiently handle branching issues due to the presence of both elastic and plastic states. For GPU implementation, node-based, degree-of-freedom-based and element-by-element matrix-free strategies have been used with suitable modifications. The performance of the proposed strategies are demonstrated by solving a number of benchmark examples from elastoplasticity. Compared with single-core CPU implementation, speedups of several orders of magnitude are achieved. When compared with existing GPU-based strategies from literature, the proposed strategies show significant speedups and occupy lesser memory space.
Supervisors: Sharma, Deepak and Gautam, Sachin Singh