Related papers: On anisotropic elasticity and questions concerning…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
We investigate long-range forces between atoms with anisotropic electric polarizability interacting with dielectrics having anisotropic permittivity in the weak-coupling approximation. Unstable configurations in which the force between the…
The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties such as…
We study the sense in which the continuum limit of a broad class of discrete materials with periodic structures can be viewed as a nonlinear elastic material. While we are not the first to consider this question, our treatment is more…
This paper establishes a universal framework for the nonlocal modeling of anisotropic damage at finite strains. By the combination of two recent works, the new framework allows for the flexible incorporation of different established…
Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple…
Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The first, factor proportional to a power of the number of mesh…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
To model ferromagnetic material in finite element analysis a correct description of the constitutive relationship (BH-law) must be found from measured data. This article proposes to use the energy density function as a centrepiece. Using…
We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
Shear transformations (i.e., localised rearrangements of particles resulting in the shear deformation of a small region of the sample) are the building blocks of mesoscale models for the flow of disordered solids. In order to compute the…
Sintering of printed porcelain filaments can be strongly affected by overhang geometry, thin features, and printing-induced anisotropy. These effects are particularly difficult to simulate because they require accurately capturing the…
A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy…
In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime…
The simulation of a short fibre reinforced structure by means of the FEM requires the knowledge of the material behaviour at every Gauss point. In order to obtain such information, a representative volume element (RVE) containing…
The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the…
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…
We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of…
It is proved that elliptically-polarized finite-amplitude inhomogeneous plane waves may not propagate in an isotropic elastic material subject to the constraint of incompressibility. The waves considered are harmonic in time and…