相关论文: Weakly symmetric stress equilibration for hyperela…
The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a…
Hypo-elastoplasticity is a framework suitable for modeling the mechanics of many hard materials that have small elastic deformation and large plastic deformation. In most laboratory tests for these materials the Cauchy stress is in…
We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a…
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric…
We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…
A posteriori error estimates are constructed for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure. The discretization under focus is the…
The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The…
In this work we introduce novel stress-only formulations of linear elasticity with special attention to their approximate solution using weighted residual methods. We present four sets of boundary value problems for a pure stress…
Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…
Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite elasticity and examine its geometric, constitutive, and…
This study presents an analytical investigation of stress distributions in square-shaped elastic bodies subjected to concentrated compressive loads under uniaxial and biaxial conditions. By employing the Airy stress function method, we…
In the fiber melt spinning of semi-crystalline polymers, the degree of crystallization can be non-homogeneous over the cross-section of the fiber, affecting the properties of the end product. For simulation-based process design, the…
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…
For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu:…
The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…
This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a…
Superconvergence and a posteriori error estimators of recovery type are analyzed for the 4-node hybrid stress quadrilateral finite element method proposed by Pian and Sumihara (Int. J. Numer. Meth. Engrg., 1984, 20: 1685-1695) for linear…
We re-examine the notion of stress in peridynamics. Based on the idea of traction we define two new peridynamic stress tensors $\mathbf{P}^{\mathbf{y}}$ and $\mathbf{P}$ which stand, respectively, for analogues of the Cauchy and 1st…