Related papers: A Unified Variational Framework for Planar Elastic…
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…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
We revisit the classical problem of the planar Euler \emph{elastica} with applied forces and moments, and present a classification of the shapes in terms of tangentially conserved quantities associated with spatial and material symmetries.…
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…
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…
A rigorous unified perspective of cohesive zone models is presented, including and comparing potential-based and non potential-based formulations, and encompassing known examples studied in literature. The main novelty of the work consists…
A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with…
We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known…
In order to clarify common assumptions on the form of energy and momentum in elasticity, a generalized conservation format is proposed for finite elasticity, in which total energy and momentum are not specified a priori. Velocity, stress,…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
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,…
In this work we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model…
Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field…
This paper establishes a unified element-based framework for formation control by introducing the concept of the deformation gradient from continuum mechanics. Unlike traditional methods that rely on geometric constraints defined on graph…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based…
We present a geometric formulation of classical Cosserat elasticity in which the coframe and rotational connection are treated as independent variational fields. In contrast to conventional metric-based approaches, this formulation makes…
The purpose of this paper is to provide analytical and numerical solutions of the formation and evolution of the localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. An energy-based variational approach is…
Under suitable regularity assumptions the $p$-elastic energy of a planar set $E\subset\mathbb{R}^2$ is defined to be $\int_{\partial E} 1 + |k_{\partial E}|^p \,\, d\mathcal{H}^1,$ where $k_{\partial E}$ is the curvature of the boundary…