Related papers: Low-Mach-number--slenderness limit for elastic Cos…
The equations for the equilibrium of a thin elastic ribbon are derived by adapting the classical theory of thin elastic rods. Previously established ribbon models are extended to handle geodesic curvature, natural out-of-plane curvature,…
We introduce a nonlinear, one-dimensional bending-twisting model for an inextensible bi-rod that is composed of a nematic liquid crystal elastomer. The model combines an elastic energy that is quadratic in curvature and torsion with a…
In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic…
State estimation of robotic systems is essential to implementing feedback controllers, which usually provide better robustness to modeling uncertainties than open-loop controllers. However, state estimation of soft robots is very…
We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear…
In this paper, we study a particular class of solutions to the Rayleigh--Boltzmann equation, known in the nonlinear setting as \emph{homoenergetic solutions}. These solutions take the form $ g(x, v, t) = f(v - L(t)x, t),$ where the matrix…
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…
We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical…
We consider a heterogeneous elastic structure which is stratified in some direction. We derive the limit problem under the assumption that the Lam\'e coefficients and their inverses weakly* converge to Radon measures. Our method applies…
Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear $k$-mers (also denoted in the literature as rigid rods, needles, sticks) on…
A rope laid on the ground with one end subjected to time-dependent forcing is proposed as a prototypical elastic dynamical contact problem, which we study analytically, numerically, and experimentally. The dynamics is governed by an…
A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.
We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the thickness of these…
We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter $\ep \to 0$ and the fluid is confined to an exterior spatial domain $\Omega_\ep$ that may vary with…
In this paper, we consider the isotropic-nematic phase transition with anisotropic elasticity governed by the Landau-de Gennes dynamics of liquid crystals. For $-\frac{3}{2}< L<0,$ we rigorously justify the limit from the Landau-de Gennes…
In this paper we consider a family of three-dimensional problems in thermoelasticity for linear elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero.We fully characterize with strong…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the…
We present a hybrid Eulerian-Lagrangian method for the direct simulation of three-dimensional, heterogeneous structures made of soft fibers and immersed in incompressible viscous fluids. Fiber-based organization of matter is pervasive in…
We present a reduced order theory of locally impenetrable elastic tubes. The constraint of local impenetrability -- an inequality constraint on the determinant of the 3D deformation gradient -- is transferred to the Frenet curvature of the…