Related papers: Duality arguments for linear elasticity problems w…
The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.
For two-scale homogenization of a general class of asymptotically degenerating %uniformly strongly elliptic symmetric PDE systems with a critically scaled high contrast in periodic coefficients of a small period $\varepsilon$, we derive a…
This paper deals with an elliptic problem with a nonlinear lower order term set in an open bounded cylinder of $R^N$, $N\geq 2$, divided into two connected components by an imperfect rough interface. More precisely, we assume that at 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 carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
In this note, we define material-uniform hyperelastic bodies (in the sense of Noll) containing discrete disclinations and dislocations, and study their properties. We show in a rigorous way that the size of a disclination is limited by the…
We investigate the existence and non-existence of a function-valued strain solution in various models of elastoplasticity from the perspective of the constraint-based ``dual'' formulations. We describe abstract frameworks for linear…
In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…
A linear system of differential equations describing a joint motion of thermo-elastic porous body and incompressible thermo-fluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the…
Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic composites. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip…
A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field $\bi u$ and the lattice velocity ${\bi v}=\p {\bi u}/\p t$. Damping is…
Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more accurate physical analysis and understanding of experimental…
We propose a methodology for the homogenization of periodic elastic lattices that covers the case of unstable lattices, having affine (macroscopic) or periodic (microscopic) mechanisms. The singular cell problems that are encountered when a…
We consider the homogenization of a semilinear elliptic equation where the coefficients of the second-order differential operator may be discontinuous. We establish the existence and uniqueness of the fine-scale solution, followed by an a…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
Plastically deforming crystals exhibit scale-free fluctuations that are similar to those observed in driven disordered elastic systems close to depinning, but the nature of the yielding critical point is still debated. Here, we study the…
A three-dimensional continuum dislocation theory for single crystals containing curved dislocations is proposed. A set of governing equations and boundary conditions is derived for the true placement, plastic slips, and loop functions in…
For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is,…
This paper revisits a well-studied anti-plane shear deformation problem formulated by Knowles in 1976 and analytical solutions in general nonlinear elasticity proposed by Gao since 1998. Based on minimum potential principle, a…