Related papers: Deformation gradient averaging regularization for …
The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact…
The third medium contact has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, the third medium contact introduces a third medium between two…
This work presents a comprehensive three-dimensional third-medium contact framework for modeling complex contact interactions in hyperelastic solids and pneumatically actuated systems. The proposed third-medium formulation embeds a…
Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single…
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These…
This paper presents a unified variational framework that integrates phase-field fracture (PFF) and third-medium contact (TMC) within finite deformation hyperelasticity. The key idea is that both crack and contact are treated through…
I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
We propose and analyze a new stabilized cut finite element method for the Laplace-Beltrami operator on a closed surface. The new stabilization term provides control of the full $\mathbb{R}^3$ gradient on the active mesh consisting of the…
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 objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…
This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…
We introduce a novel regularization for localizing an elastic-energy-driven deformation to only those regions being manipulated by the user. Our local deformation features a natural region of influence, which is automatically adaptive to…
The development of higher order finite elements methods has become an active research area. The deformation method for mesh generation has achieved a prescribed positive Jacobian determinant constraint and it has been a useful method for…
This work aims to provide standard formulations for direct minimization approaches on various types of static problems of continuum mechanics. Particularly, form-finding problems of tension structures are discussed in the first half and the…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…