Related papers: 3D mixed finite elements for curved, flat piezoele…
We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects…
We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint.…
In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material…
In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…
We propose and analyze a fully discrete parametric finite element method with minimal deformation rate (MDR) for simulating the mean curvature flow of general closed surfaces in three dimensions. The method is formulated from a coupled…
A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…
We propose a robust simulation method for phospholipid membranes. It is based on a mixed three-field formulation that accounts for tangential fluidity (Boussinesq-Scriven law), bending elasticity (Canham-Helfrich model) and inextensibility.…
In the design of tensegrity structures, traditional form-finding methods utilize kinematic and static approaches to identify geometric configurations that achieve equilibrium. However, these methods often fall short when applied to actual…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…
We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization comes…
Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a…
Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…
We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN…
Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the…
A novel approach was derived to compute the elastic displacement field from a measured elastic deformation field (i.e., deformation gradient or strain). The method is based on integrating the deformation field using Finite Element…
Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…
In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surface force components. As a result the tractions between…
When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the…
Assumed stress hybrid methods are known to improve the performance of standard displacement-based finite elements and are widely used in computational mechanics. The methods are based on the Hellinger-Reissner variational principle for the…