Related papers: Formulation of small-strain magneto-elastic proble…
We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes…
Ferrogels and magnetoelastomers are composite materials obtained by embedding magnetic particles of mesoscopic size in a crosslinked polymeric matrix. They combine the reversible elastic deformability of polymeric materials with the high…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
We show that the dynamic magnetization at the edges of a thin magnetic element with finite lateral size can be described by new effective boundary conditions that take into account inhomogeneous demagnetizing fields near the element edges.…
Magnetic nanoparticles are useful biological probes as well as therapeutic agents. There have been several approaches used to model nanoparticle magnetization dynamics for both Brownian as well as N\'eel rotation. The magnetizations are…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…
We consider the coupled system of the Landau--Lifshitz--Gilbert equation and the conservation of linear momentum law to describe magnetic processes in ferromagnetic materials including magnetoelastic effects in the small-strain regime. For…
In this article we revisit the significance of the often debated structural similarity between the equations of electromagnetism and fluid dynamics. Although the matching of the two sets of equations has successfully been done for…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
A minimalist approach to the linear stability problem in fluid dynamics is developed that ensures efficiency by utilizing only the essential elements required to find the eigenvalues for given boundary conditions. It is shown that the…
We suggest the new definition of the magnetization. For the two - dimensional Ising model with the free boundary conditions we calculate any derivative of this magnetization for zero magnetic field.
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
Magnetic gels are composite materials, consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity…
Time-discrete numerical minimization schemes for simple viscoelastic materials in the large strain Kelvin-Voigt rheology are not well-posed due to non-quasiconvexity of the dissipation functional. A possible solution is to resort into…
In the perspective of developing smart hybrid materials with customized features, ferrogels and magnetorheological elastomers allow a synergy of elasticity and magnetism. The interplay between elastic and magnetic properties gives rise to a…
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…