Related papers: On the planar elastica, stress, and material stres…
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…
We study the elastic deformations that appear due to tidal and centrifugal forces acting on an elastic sphere in helical motion in a spherically symmetric gravitational field, where gravity is considered to be given by either a Newtonian or…
A short review of the problems which arise in the generalization of the Lifshitz theory of van der Waals force in the case of forces inside dielectric media is presented, together with some historical remarks. General properties of the…
Developing a macroscopic theory of elasto-plasticity in amorphous solids calls for (i) identifying the relevant macro state-variables and (ii) discriminating the different time-scales which characterize these variables. In current theories…
We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field…
The topic faced here is the modeling of an axisymmetric multilayer structure. An exact analytical formulation is proposed in the framework of the plane strain problem for a cylinder encircled by annular layers. Isotropic linear…
We construct explicit solutions for scalar, vector and tensor perturbations in a less known setting, a flat universe filled by an isotropic elastic solid with pressure and shear modulus proportional to energy density. The solutions…
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…
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…
During planar motion, contact surfaces exhibit a coupling between tangential and rotational friction forces. This paper proposes planar friction models grounded in the LuGre model and limit surface theory. First, distributed planar extended…
In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…
This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of equations of motion, viewing motion as a curve in an infinite-dimensional Banach space of embeddings of a body manifold…
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…
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…
In a previous paper, we have introduced a new unified description of the main equations of the gravitational and of the electromagnetic field, in terms of tidal tensors and connections on the tangent bundle TM of the space-time manifold. In…
We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we…
Expressions are obtained for force and couple densities and stress tensors in macroscopic models for nematic liquid crystals subjected to electric fields. The coupling between the liquid crystal orientational properties and the electric…
The use of global displacement basis functions to solve boundary-value problems in linear elasticity is well established. No prior work uses a global stress tensor basis for such solutions. We present two such methods for solving stress…
We consider a system of partial differential equations, of interest to plasma physics, and provide all its Lie point symmetries, with their respective invariant solutions. We also discuss some of its conditional and partial symmetries. We…