Related papers: Fundamental solutions for isotropic size-dependent…
The stressed state of flattened thin elastic sheet, as well as that of translationally symmetric 3D solids, are effectively 2D problems. This paper study equilibrium state-of-stress in metrically-incompatible 2D elastic materials. The…
The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method for mixed elasticity. As the name suggests, the tangential component of the displacement vector as well as the normal-normal component of the stress…
Several advances in the theory of space-resolved viscoelasticity of liquids and other amorphous systems are discussed in the present paper. In particular, considering long-time regimes of stress relaxation in liquids we obtain the…
It is stated in the main in essence new approach to mechanics of the stressed state of the solid body from statistically isotropic material and the homogeneous liquid dynamics. The approach essence is in the detected property of the…
In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…
Several different versions of couple stress theory have appeared in the literature, including the indeterminate Mindlin-Tiersten-Koiter couple stress theory (MTK-CST), indeterminate symmetric modified couple stress theory (M-CST) and…
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…
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…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive definite cell centered system. The method is developed on…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
This work concerns the continuum basis and numerical formulation for deformable materials with viscous dissipative mechanisms. We derive a viscohyperelastic modeling framework based on fundamental thermomechanical principles. Since most…
A number of new closed-form fundamental solutions for the generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. These solutions are decomposed into two…
We investigate the possibility to determine the divergence-free displacement $\mathbf{u}$ \emph{independently} from the pressure reaction $p$ for a class of boundary value problems in incompressible linear elasticity. If not possible, we…
A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…
A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time,…
In this paper we derive a line tension model for dislocations in 3d starting from a geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as the amplitude of the Burgers vectors (proportional to the…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
We study the response of granular materials to external stress using experiment, simulation, and theory. We derive an entropic, Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this…