In the second application, the aforementioned max-ent meshfree method outperforms FEM and FFT-based schemes in numerical relaxation of nonconvex energy potentials, which is essential in discovering the effective response and associated energy-minimizing microstructures and patterns. the finite element method (FEM)) are limited due to severe mesh distortions. This scheme is especially suitable for ECAE as the latter falls into the category of severe plastic deformation processes where simulations using mesh-based methods (e.g. In ECAE, the aforementioned enhanced maximum-entropy scheme allows the stable simulation of large deformations at the macroscale. This thesis presents an extensive study of two applications - the modeling of equal-channel angular extrusion (ECAE) based on high-fidelity plasticity models, and the numerical relaxation of nonconvex energy potentials. The improved local maximum-entropy approximation method is of a general construct and has a wide variety of applications. The proposed method achieves robust stability in the updated-Lagrangian setting and fully realizes the potential of meshfree methods in simulating large-deformation mechanics, as shown for benchmark problems of severe elastic and elastoplastic deformations. The proposed method offers an adaptive approximation that addresses the tensile instability which arises in updated-Lagrangian meshfree methods during severe, finite deformations. This presentation will give an overview of major progresses made in the field, the application to many challenging engineering mechanics problems, and the future directions of this research area.This thesis develops an enhanced meshfree method based on the local maximum-entropy (max-ent) approximation and explores its applications. Meshfree collocation methods have also undergone significant development, which also offer a truly meshfree solution. Given the proper treatment, nodal integration can be made accurate and free of spatial instability, making it possible to eliminate the need for a mesh entirely. For instance, essential boundary conditions are almost trivial to enforce by employing the techniques now available, and the need for high order quadrature has been circumvented with the development of advanced techniques, essentially eliminating the previously existing bottleneck of computational expense in meshfree methods. In addition, a significant amount of progress has been made in addressing the major shortcomings that were present in these methods at the early stages of their development. Structural Engineering & Center for Extreme Events Research, University of California, San DiegoĪBSTRACT: In the past two decades, meshfree methods have emerged into a new class of computational methods with considerable success.
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