Constitutive modeling and thermoviscoplasticity

Development and solution of coupled thermomechanical equations at elevated temperature and/or high strain rates are discussed. Three main considerations are presented: development of the coupled thermomechanical equations by means of the rational theory of thermodynamics, development of a thermoviscoplastic constitutive equation which is congruous with the developed coupled equations, and the applicability of the developed equations to the treatment by the finite element method

Two different fractional Stefan problems which are convergent to the same classical Stefan problem

Two fractional Stefan problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0,1)$ such that in the limit case ($\alpha =1$) both problems coincide with the same classical Stefan problem. For the one and the other problem, explicit solutions in terms of the Wright functions are presented. We prove that these solutions are different even though they converge, when $\alpha \nearrow 1$, to the same classical solution. This result also shows that some limits are not commutative when fractional derivatives are used.Comment: 14 pages, 1 figur

‘‘Cooling by Heating’’- Demonstrating the Significance of the Longitudinal Specific Heat

Heating a solid sphere at its surface induces mechanical stresses inside the sphere. If a finite amount of heat is supplied, the stresses gradually disappear as temperature becomes homogeneous throughout the sphere. We show that before this happens, there is a temporary lowering of pressure and density in the interior of the sphere, inducing a transient lowering of the temperature here. For ordinary solids this effect is small because c_{p}≅c_{V}. For fluent liquids the effect is negligible because their dynamic shear modulus vanishes. For a liquid at its glass transition, however, the effect is generally considerably larger than in solids. This paper presents analytical solutions of the relevant coupled thermoviscoelastic equations. In general, there is a difference between the isobaric specific heat c_{p} measured at constant isotropic pressure and the longitudinal specific heat c_{l} pertaining to mechanical boundary conditions that confine the associated expansion to be longitudinal. In the exact treatment of heat propagation, the heat-diffusion constant contains c_{l} rather than c_{p}. We show that the key parameter controlling the magnitude of the “cooling-by-heating“ effect is the relative difference between these two specific heats. For a typical glass-forming liquid, when the temperature at the surface is increased by 1 K, a lowering of the temperature at the sphere center of the order of 5 mK is expected if the experiment is performed at the glass transition. The cooling-by-heating effect is confirmed by measurements on a glucose sphere at the glass transition

The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation

In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition, into the completely symmetric part S of C plus the reminder A, turns out to be irreducible under the 3-dimensional general linear group. We show that the SA-decomposition is unique, irreducible, and preserves the symmetries of the elasticity tensor. The MN-decomposition fails to have these desirable properties and is such inferior from a physical point of view. Various applications of the SA-decomposition are discussed: the Cauchy relations (vanishing of A), the non-existence of elastic null Lagrangians, the decomposition of the elastic energy and of the acoustic wave propagation. The acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The Cauchy part governs the longitudinal wave propagation. We provide explicit examples of the effectiveness of the SA-decomposition. A complete class of anisotropic media is proposed that allows pure polarizations in arbitrary directions, similarly as in an isotropic medium.Comment: 1 figur

Thermo-mechanical response FEM simulation of ceramic refractories undergoing severe temperature variations

T. K Papathanasiou and F. Dal Corso gratefully acknowledge support from the European Union FP7 project “Mechanics of refractory materials at high–temperature for advanced industrial technologies” under contract number PIAPP–GA–2013–609758. A. Piccolroaz would like to acknowledge financial support from the European Union‟s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement number PITN-GA-2013-606878-CERMAT2