Related papers: Rectangular finite elements for modeling the mecha…
Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…
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 study the construction of low-degree robust finite element schemes for planar linear elasticity on general triangulations. Firstly, we present a low-degree nonconforming Helling-Reissner finite element scheme. For the…
Results are presented for finding the optimal orientation of an anisotropic elastic material. The problem is formulated as minimizing the strain energy subject to rotation of the material axes, under a state of uniform stress. It is shown…
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 develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
In this paper we study the motion of a finite composite cylindrical annulus made of generalized neo-Hookean solids that is subject to periodic shear loading on the inner boundary. Such a problem has relevance to several problems of…
Rapid prototyping is an emerging technology for the fast make of engineering components. A common technique is to laser cut a two-dimensional (2D) part from polymethyl methacrylate (PMMA) sheet. However, both manufacturing defects and…
The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic elastic body, in a general framework. In particular, the proof…
The complex incremental behavior of granular materials is explored with multi-directional loading probes. An advanced discrete element model (DEM) was used to examine the reversible and irreversible strains for small loading probes, which…
While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial…
This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full…
This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…
Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these…
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first present the functional framework on the example of a linear…
Anisotropy in granular materials arises from both the internal fabric and the directionality of the stress state, yet separating these effects experimentally remains challenging. This study develops a first-order linearisation of the…
In this work we study the rheological features of yield stress materials that exhibit non-homogeneous steady flows and that are subjected to an additional mechanical noise. Using a mesoscale elasto-plastic model accounting for a viscosity…
Manufactured materials usually contain random imperfections due to the fabrication process, e.g., the 3D-printing, casting, etc. These imperfections affect significantly the effective material properties and result in uncertainties in the…
This paper investigates finite-element modeling of a vertically damped free-standing rocking column. The paper first derives the nonlinear equation of motion for the coupled system and then compares the analytical solution with…