Related papers: A mixed method for 3D nonlinear elasticity using f…
This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…
A new family of mixed finite element methods$-$compatible-strain mixed finite element methods (CSFEMs)$-$are introduced for three-dimensional compressible and incompressible nonlinear elasticity. A Hu-Washizu-type functional is extremized…
In this paper, we extend the tangential-displacement normal-normal-stress continuous (TDNNS) method from [26] to nonlinear elasticity. By means of the Hu-Washizu principle, the distibutional derivatives of the displacement vector are lifted…
We discuss the Hu-Washizu (HW) variational principle from a geometric standpoint. The mainstay of the present approach is to treat quantities defined on the co-tangent bundles of reference and deformed configurations as primal. Such a…
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…
We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…
Finite element exterior calculus (FEEC) has been developed as a systematical framework for constructing and analyzing stable and accurate numerical method for partial differential equations by employing differential complexes. This paper is…
In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a…
We propose a variational principle combining a phase-field functional for structural topology optimization with a mixed (three-field) Hu-Washizu functional, then including directly in the formulation equilibrium, constitutive, and…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a…
A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
The variational discrete element method developed in [28] for dynamic elasto-plastic computations is adapted to compute the deformation of elastic Cosserat materials. In addition to cellwise displacement degrees of freedom (dofs), cellwise…
We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…