Multiscale Methods for Fatigue and Dynamic Fracture Failure and High-performance Computing Implementation




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This dissertation presents several multiscale methods for material failure and implementations on high-performance computing (HPC) platforms. The work is motivated by the challenges in fully capturing the mechanics of failure using a single scale method. As such, multiscale approaches that incorporate multiple temporal and spatial scales have been established. To address the high computational costs, efficient algorithms and their implementations on the HPC platform featuring many-core architectures have been developed. Based on the topics being addressed, the dissertation is divided into two parts. First, a multiscale computational framework for high cycle fatigue (HCF) life prediction is established by integrating the Extended Space-Time Finite Element Method (XTFEM) with multiscale fatigue damage models. XTFEM is derived based on the time-discontinuous Galerkin approach, which is shown to be A-stable and high-order accurate. While the robustness of XTFEM has been extensively demonstrated, the associated high computational cost remains a critical barrier for its practical applications. A novel hybrid iterative/direct solver is proposed with a unique preconditioner based on Kronecker product decomposition of the space-time stiffness matrix. XTFEM is further accelerated by utilizing HPC platforms featuring a hierarchy of distributed- and shared-memory parallelisms. A two-scale damage model is coupled with XTFEM to capture nonlinear material behaviors under HCF loading and accelerated by parallel computing using both CPUs and GPUs. Furthermore, an efficient data-driven microstructure-based multiscale fatigue damage model is established by employing the Self-consistent Clustering Analysis, which is a reduced-order method derived from Machine Learning. Robustness and efficiency of the framework are demonstrated through benchmark problems. HCF simulations are conducted to quantify key effects due to mean stress, multiaxial load conditions, and material microstructures. In the second part, a concurrent multiscale method to dynamic fracture is established by coupling Peridynamics (PD) with the classical Continuum Mechanics (CCM). PD is a novel nonlocal generalization of CCM. It is governed by an integro-differential equation of motion, which is free of spatial derivatives. This salient feature makes it attractive for problems with spatial discontinuities such as cracks. However, it generally leads to a much higher computational cost due to its nonlocality. There is a continuing interest to couple PD with CCM to improve efficiency while preserving accuracy in critical regions. In this work, Finite Element (FE) simulation is performed over the entire domain and coexists with a local PD region where crack pre-exists or is expected to initiate. The coupling scheme is accomplished by a bridging-scale projection between the two scales and a class of twoway nonlocal matching boundary conditions that eliminates spurious wave reflections at the numerical interface and transmits waves from the FE domain to the PD region. An adaptive scheme is established so that the PD region is dynamically relocated to track propagating crack. Accuracy and efficiency of the proposed method are illustrated by wave propagation examples. Its effectiveness and robustness in material failure simulation are demonstrated by benchmark problems featuring brittle fracture. Finally, conclusions are drawn from the research work presented and prospective future developments of the established multiscale methods are provided.



Engineering, Mechanical, Applied Mechanics, Mathematics