相关论文: Consistent polynomial expansions of stored energy …

The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…

Shape memory alloys are remarkable 'smart' materials used in a broad spectrum of applications, ranging from aerospace to robotics, thanks to their unique thermomechanical coupling capabilities. Given the complex properties of shape memory…

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.

This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87…

High-order CFD is gathering a broadening interest as a future industrial tool, with one such approach being Flux Reconstruction (FR). However, due to the need to mesh complex geometries if FR is to displace current, lower order methods, FR…

Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic…

This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…

While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. Until now, it has not…

We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts:…

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…

This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…

Recently the materials possessing structure of molecular and supramolecular matrix are more and more actively studied. They are relative to many polymeric materials of a technological origin, such as rubber, and living biological tissues.…

We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…

Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the…

In this work, we review and analyze both the theoretical and numerical aspects of strongly and weakly coupled thermoelastic systems. By employing spectral analysis techniques and establishing uniform resolvent estimates, we derive uniform…

In layered materials, a common mode of deformation involves buckling of the layers under tensile deformation in the direction perpendicular to the layers. The instability mechanism, which operates in elastic materials from geological to…

Differentiable physics modeling combines physics models with gradient-based learning to provide model explicability and data efficiency. It has been used to learn dynamics, solve inverse problems and facilitate design, and is at its…

In a recent work [10], we have introduced a pressure-robust Hybrid High-Order method for the numerical solution of the incompressible Navier-Stokes equations on matching simplicial meshes. Pressure-robust methods are characterized by error…