Related papers: Complex Eigenvalue Analysis for Structures with Vi…
Mathematical models describing the behavior of viscoelastic materials are often based on evolution equations that measure the change in stress depending on its material parameters such as stiffness, viscosity or relaxation time. In this…
We study a variant of the well known Maxwell model for viscoelastic fluids, namely we consider the Maxwell fluid with viscosity and relaxation time depending on the pressure. Such a model is relevant for example in modelling behaviour of…
The rigorous tools of convex analysis are used to examine various serial and parallel combinations of linear viscosity and perfect plasticity. Nonlinear viscosities are also considered. The general aim is to synthesize a single convex…
Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft…
It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. At the longest length…
Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, the…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in $L^2$ norm. The proof is based on an error representation formula using a…
The present paper introduces the analysis of the eigenvalue problem for the elasticity equations when the so called Navier-Lam\'e system is considered. Such a system introduces the displacement, rotation and pressure of some linear and…
Eigenvalue analysis is widely used for linear instability analysis in both external and internal aerodynamics. It typically involves finding the steady state, linearizing around it to obtain the Jacobian, and then solving for its…
An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow property with respect to a viscoelastic energy. Based on the…
In this paper we present a theoretical and experimental study aimed at characterizing the hysteretic properties of viscoelastic materials. In the last decades viscoelastic materials have become a reference for new technological…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
Maxwell's models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But rigorous proofs are lacking. The present note is a…
In this work, we present a high-throughput first-principles study of elastic properties of bulk and monolayer materials mainly using the vdW-DF-optB88 functional. We discuss the trends on the elastic response with respect to changes in…
When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic…
The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the…
We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of…
In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. This paper concerns resolvent…
Exact relaxation times and eigenfunctions for a simple mechanical model of polymer dynamics are obtained using supersymmetry methods of quantum mechanics. The model includes the finite extensibility of the molecule and does not make use of…