Related papers: Shape memory alloys as gradient-polyconvex materia…
We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in divergence form in $\bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.
We show the global existence of smooth solutions of a nonlinear partial differential equation modeling the dynamics of spinodal decomposition in diffusive materials
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian-Sobolev space). Our result covers first-order…
We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint.…
We investigate the variational model for nematic elastomer proposed by Barchiesi and DeSimone with the director field defined on the deformed configuration under general growth conditions on the elastic density. This leads us to consider…
We model a direct solid-state phase transition through a nucleation-and-growth process in which plates have simple, regular shapes - squares, cubes, or square-faced lamellae - and grow homothetically (self-similarly) until they either reach…
A hyperbolic integro-differential equation is considered, as a model problem, where the convolution kernel is assumed to be either smooth or no worse than weakly singular. Well-posedness of the problem is studied in the context of semigroup…
We investigate low energy structures of a lattice with dislocations in the context of nonlinear elasticity. We show that these low energy configurations exhibit in the limit a Cosserat-like behavior. Moreover, we give bounds from above and…
In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…
Stimulus-responsive shape memory materials have attracted tremendous research interests recently, with much effort focused on improving their mechanical actuation. Driven by the needs of nanoelectromechnical devices, materials with large…
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…
We prove existence of globally stable quasistatic evolutions, referred to as energetic solutions, for a model proposed by Marigo and Kazymyrenko in 2019. The behaviour of geomaterials under compression is studied through the coupling of…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming…
Composite materials often exhibit mechanical anisotropy owing to the material properties or geometrical configurations of the microstructure. This makes their inverse design a two-fold problem. First, we must learn the type and orientation…
In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the…
The influence of pre-strain and temperature on the superior properties exhibited by an Nb nanowire embedded in a NiTi shape memory alloy (SMA) are investigated via molecular dynamics simulations. To this end, a new Nb-Ni-Ti ternary…
We demonstrate the existence of unconventional rheological and memory properties in systems of soft-deformable particles whose energy depends on their shape, via numerical simulations. At large strains, these systems experience an…
We consider a model for an incompressible visoelastic fluid. It consists of the Navier-Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature…