Related papers: Existence results in large-strain magnetoelasticit…
We study a variational model of magnetoelasticity both in the static and in the quasistatic setting. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed configuration in the actual…
We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference…
We consider a variational model for magnetoelastic solids in the large-strain setting with the magnetization field defined on the unknown deformed configuration. Through a simultaneous linearization of the deformation and sharp-interface…
We investigate the problem of dimension reduction for plates in nonlinear magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed set in the actual space. We consider…
Starting from a model of nonlinear magnetoelasticity where magnetization is defined in the Eulerian configuration while elastic deformation is in the Lagrangean one, we rigorously derive a linearized model that coincides with the standard…
Despite of the topical engineering need and all scientific investments, the mathematical formulation of modeling elastic deformations in magnetic systems is not yet fully established. Often, especially in electrical engineering…
We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…
We investigate the existence of minimizers of variational models with Eulerian-Lagrangian formulations. We consider energy functionals depending on the deformation of a body, defined on its reference configuration, and an Eulerian map…
We evaluate the conditions for surface stability of a layered magnetoelastic half-space subjected to large deformations and a magnetic field. After reviewing the fundamental measures of deformation and summarizing the magnetostatic…
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…
We analyze a model of the evolution of a (solid) magnetoelastic material. More specifically, the model we consider describes the evolution of a compressible magnetoelastic material with a non-convex energy and coupled to a gradient flow…
This paper deals with the mathematical modelling of large strain magneto-viscoelastic deformations. Energy dissipation is assumed to occur both due to the mechanical viscoelastic effects as well as the resistance offered by the material to…
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…
The theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous…
We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the…
Modeling microstructural evolution at large strains requires mechanical formulations that remain thermodynamically consistent while capturing significant lattice rotations and transformation-induced stresses. However, most existing…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total…
We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is…
We perform a simultaneous homogenization and linearization analysis for a magnetoelastic energy functional featuring a mixed Eulerian-Lagrangian structure. Neglecting Zeeman and anisotropic contributions, we characterize the asymptotic…