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Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, convergence, and stability of such schemes. Employing an FE…
The first part of the cumulative thesis contains the numerical analysis of different $hp$-finite element discretizations related to two different weak formulations of a model problem in elastoplasticity with linearly kinematic hardening.…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
Quantitative characterization of tissue properties, known as elasticity imaging, can be cast as solving an ill-posed inverse problem. The finite element methods (FEMs) in magnetic resonance elastography (MRE) imaging are based on solving a…
This paper addresses an important issue raised for the clinical relevance of Computer-Assisted Surgical applications, namely the methodology used to automatically build patient-specific Finite Element (FE) models of anatomical structures.…
We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between plastic dynamics and the structure of a particle's…
Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…
Ductile fracture of metallic materials typically involves the elastoplastic deformation and associated damaging process. The nonlocal lattice particle method (LPM) can be extended to model this complex behavior. Recently, a distortional…
We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…
We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…
Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a…
The paper presents an innovative methodology based on the use of a new predictive algorithm created by the researchers capable of obtaining the elastic modulus of a plastic material manufactured with MEX and its mechanical behaviour in the…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the…
The local geometrical randomness of metal foams brings complexities to the performance prediction of porous structures. Although the relative density is commonly deemed as the key factor, the stochasticity of internal cell sizes and shapes…
In this paper, a reliable a posteriori error estimator for a model problem of elastoplasticity with linear kinematic hardening is derived, which satisfies some (local) efficiency estimates. It is applicable to any discretization that is…
We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…