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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 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…
In this paper, we study a hyperbolic-parabolic coupled system arising in nonlinear three-dimensional thermoelasticity. We establish the global well-posedness and asymptotic behavior of solutions. Our main result shows that, a thermoelastic…
In this letter, we develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse grained quantities from simulations of dense disordered…
We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
A geometrically nonlinear continuum mechanical theory is formulated for deformation and failure behaviors of amorphous polymers. The model seeks to capture material response over a range of loading rates, temperatures, and stress states…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
This study presents a comprehensive framework for constitutive modeling of a frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived for…
The topic faced here is the modeling of an axisymmetric multilayer structure. An exact analytical formulation is proposed in the framework of the plane strain problem for a cylinder encircled by annular layers. Isotropic linear…
At low temperature, T -> 0, the yield stress of a perfect crystal is equal to its so called theoretical strength. The yield stress of non-perfect crystals is controlled by the stress threshold of dislocation mobility. A non-crystalline…
In this paper we analyze a PDE system modelling (non-isothermal) phase transitions and damage phenomena in thermoviscoelastic materials. The model is thermodynamically consistent: in particular, no {\em small perturbation assumption} is…
We introduce a one-dimensional stress-rate type nonlinear viscoelastic model for solids that obey the assumptions of the strain-limiting theory. Unlike the classical viscoelasticity theory, the critical hypothesis in the present…
Motivated by the recent experimental and analytical developments enabling high-fidelity material characterization of (heterogeneous) sheet-like solid specimens, we seek to elucidate the constitutive behavior of linear viscoelastic solids…
We investigate numerically the yielding transition of a two dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, that we derive from the full (tensorial) description of…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
Quantum thermodynamics with open systems is often based on the quantum optical weak-coupling master equation or on operational repeated interaction models, whereas early works on thermalisation and on decoherence theory were mostly…
In this work we introduce novel stress-only formulations of linear elasticity with special attention to their approximate solution using weighted residual methods. We present four sets of boundary value problems for a pure stress…
We study closed dense collections of hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (IS) where the density profile is spatially non-uniform but constant in time. The…
This paper presents a new approach to study the effects of temperature on the poro- elastic and viscoelastic behavior of articular cartilage. Biphasic solid-fluid mixture theory is applied to study the poro-mechancial behavior of articular…