相关论文: Derivation of a von K\'arm\'an plate theory for th…
We derive a new version of the von K\'arm\'an energy and the corresponding Euler-Langrange equations, in the context of thin prestrained plates, under the condition of incompressibility relative to the given prestrain. Our derivation uses…
The equations of linearized viscoelastodynamics in Kelvin-Voigt rheology are rigorously derived from a nonlinear model that satisfies the time-dependent frame indifference in the sense of Antman. Besides showing the convergence of…
A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined…
We derive the time-dependent von K\'arm\'an plate equations from three dimensional, purely atomistic particle models. In particular, we prove that a thin structure of interacting particles whose dynamics is governed by Newton's laws of…
Viscoelastic rate-type fluid models constitute a fundamental framework for the mathematical description of complex materials exhibiting coupled elastic and viscous effects, with a wide range of applications in engineering, biomaterials, and…
We study the asymptotic behaviour, in the sense of $\Gamma$-convergence, of a thin incompressible magnetoelastic plate, as its thickness goes to zero. We focus on the linearized von K\'arm\'an regime. The model features a mixed…
We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary…
This paper investigates a quasilinear parabolic system arising in thermoviscoelasticity of Kelvin-Voigt type with temperature-dependent viscosity and coupled terms. The system, given by \begin{equation*} \begin{cases}…
We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up…
A rectangular plate modeling the deck of a suspension bridge is considered. The plate may widely oscillate, which suggests to consider models from nonlinear elasticity. The von K\'arm\'an plate model is studied, complemented with the action…
A classical 3-D thermoviscoelastic system of Kelvin-Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation…
We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…
This paper aims to study the convergence of solutions in three-dimensional nonlinear elastodynamics for a thin rod as its cross section shrinks to zero for displacements that are comparable to the small radius of the rod. Assuming the…
We propose a model for thermo-elastic beams, consistent with the theory of linear three-dimensional thermo-elasticity and deduced by a suitable version of the Principle of Virtual Powers. Dimensional reduction is achieved by postulating…
An exact result concerning the energy transfers between non-linear waves of thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the F\"oppl-von K\'arm\'an equation for thin…
We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the…
We analyze the stability of the Von K\'arm\'an model for thin plates subject to pure Neumann conditions and to dead loads, with no restriction on their direction. We prove a stability alternative, which extends previous results by…
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…
We derive the variational limiting theory of thin films, parallel to the F\"oppl-von K\'arm\'an theory in the nonlinear elasticity, for films that have been prestrained and whose thickness is a general non-constant function. Using…
The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse…