Related papers: Linear viscoelasticity: Mechanics, analysis and ap…
A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate…
Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel,…
This paper proves that the linear elastic behavior of the material with inhomogeneous pre-stresses can be described by the Willis equations. In this case, the additional terms in the Willis equations, compared with the classical linear…
We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of…
It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…
This work concerns the continuum basis and numerical formulation for deformable materials with viscous dissipative mechanisms. We derive a viscohyperelastic modeling framework based on fundamental thermomechanical principles. Since most…
This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $\beta$, the existence of a finite/infinite…
In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…
The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…
Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Understanding the origins of such rheologic behaviors is crucial to find proper technological applications. Using an elastic…
An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…
For solving the longstanding materials science problem of correlating elastic properties of a solid material to the formation of cracks we present a new general concept. This concept is applied to the technologically most important cracks…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…