Related papers: Variational models with Eulerian-Lagrangian formul…

We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…

This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to potential damages, balancing construction costs against the…

We investigate variational problems in large-strain magnetoelasticity, both in the static and in the quasistatic setting. The model contemplates a mixed Eulerian-Lagrangian formulation: while deformations are defined on the reference…

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…

This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…

We present a construction of the action, in the framework of the calculus of variations and Sobolev spaces, describing deformations and the oscillations of a uniformly rotating, elastic and self-gravitating earth. We establish the…

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…

After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…

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…

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…

Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…

A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…

Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the…

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…

We develop a variationally consistent mesoscopic extension of Cosserat elasticity motivated by the breakdown of compatibility in classical formulations. By admitting compatibility-breaking perturbations, the classical theory ceases to…

Accretion and ablation, i.e. the addition and removal of mass at the surface, is important in a wide range of physical processes including solidification, growth of biological tissues, environmental processes, and additive manufacturing.…

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…

The above comment http://dx.doi.org/10.1088/0953-8984/22/42/428001 and a previous letter by the same author reveal a great misunderstanding of what Eulerian and Lagrangian quantities are, and a confusion between the deformation of an…

A relation between variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It is shown that for a system of differential equations in Eulerian variables corresponding Lagrangian…

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…