4,863 research outputs found
Irreversible thermodynamics of creep in crystalline solids
We develop an irreversible thermodynamics framework for the description of
creep deformation in crystalline solids by mechanisms that involve vacancy
diffusion and lattice site generation and annihilation. The material undergoing
the creep deformation is treated as a non-hydrostatically stressed
multi-component solid medium with non-conserved lattice sites and
inhomogeneities handled by employing gradient thermodynamics. Phase fields
describe microstructure evolution which gives rise to redistribution of vacancy
sinks and sources in the material during the creep process. We derive a general
expression for the entropy production rate and use it to identify of the
relevant fluxes and driving forces and to formulate phenomenological relations
among them taking into account symmetry properties of the material. As a simple
application, we analyze a one-dimensional model of a bicrystal in which the
grain boundary acts as a sink and source of vacancies. The kinetic equations of
the model describe a creep deformation process accompanied by grain boundary
migration and relative rigid translations of the grains. They also demonstrate
the effect of grain boundary migration induced by a vacancy concentration
gradient across the boundary
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
The aim of this paper is to compare a hyperelastic with a hypoelastic model
describing the Eulerian dynamics of solids in the context of non-linear
elastoplastic deformations. Specifically, we consider the well-known
hypoelastic Wilkins model, which is compared against a hyperelastic model based
on the work of Godunov and Romenski. First, we discuss some general conceptual
differences between the two approaches. Second, a detailed study of both models
is proposed, where differences are made evident at the aid of deriving a
hypoelastic-type model corresponding to the hyperelastic model and a particular
equation of state used in this paper. Third, using the same high order ADER
Finite Volume and Discontinuous Galerkin methods on fixed and moving
unstructured meshes for both models, a wide range of numerical benchmark test
problems has been solved. The numerical solutions obtained for the two
different models are directly compared with each other. For small elastic
deformations, the two models produce very similar solutions that are close to
each other. However, if large elastic or elastoplastic deformations occur, the
solutions present larger differences.Comment: 14 figure
Distinguished rheological models in the framework of a thermodynamical internal variable theory
We present and analyze a thermodynamical theory of rheology with single
internal variable. The universality of the model is ensured as long as the
mesoscopic and/or microscopic background processes satisfy the applied
thermodynamical principles, which are the second law, the basic balances and
the existence of an additional-tensorial-state variable. The resulting model,
which we suggest to call the Kluitenberg-Verh\'as body, is the
Poynting-Thomson-Zener body with an additional inertial element, or, in other
words, is the extension of Jeffreys model to solids. We argue that this
Kluitenberg-Verh\'as body is the natural thermodynamical building block of
rheology. An important feature of the presented methodology is that nontrivial
inequality-type restrictions arise for the four parameters of the model. We
compare these conditions and other aspects to those of other known
thermodynamical approaches, like Extended Irreversible Thermodynamics or the
original theory of Kluitenberg.Comment: 16 pages, 1 figure, revise
Relativistic viscoelastic fluid mechanics
A detailed study is carried out for the relativistic theory of
viscoelasticity which was recently constructed on the basis of Onsager's linear
nonequilibrium thermodynamics. After rederiving the theory using a local
argument with the entropy current, we show that this theory universally reduces
to the standard relativistic Navier-Stokes fluid mechanics in the long time
limit. Since effects of elasticity are taken into account, the dynamics at
short time scales is modified from that given by the Navier-Stokes equations,
so that acausal problems intrinsic to relativistic Navier-Stokes fluids are
significantly remedied. We in particular show that the wave equations for the
propagation of disturbance around a hydrostatic equilibrium in Minkowski
spacetime become symmetric hyperbolic for some range of parameters, so that the
model is free of acausality problems. This observation suggests that the
relativistic viscoelastic model with such parameters can be regarded as a
causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting
parameters to various values, this theory can treat a wide variety of materials
including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a
nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus
we expect the theory to be the most universal description of single-component
relativistic continuum materials. We also show that the presence of strains and
the corresponding change in temperature are naturally unified through the
Tolman law in a generally covariant description of continuum mechanics.Comment: 52pages, 11figures; v2: minor corrections; v3: minor corrections, to
appear in Physical Review E; v4: minor change
Elastic, thermal expansion, plastic and rheological processes - theory and experiment
Rocks are important examples for solid materials where, in various
engineering situations, elastic, thermal expansion, rheological/viscoelastic
and plastic phenomena each may play a remarkable role. Nonequilibrium continuum
thermodynamics provides a consistent way to describe all these aspects in a
unified framework. This we present here in a formulation where the kinematic
quantities allow arbitrary nonzero initial (e.g., in situ) stresses and such
initial configurations which - as a consequence of thermal or remanent stresses
- do not satisfy the kinematic compatibility condition. The various
characteristic effects accounted by the obtained theory are illustrated via
experimental results where loaded solid samples undergo elastic, thermal
expansion and plastic deformation and exhibit rheological behaviour. From the
experimental data, the rheological coefficients are determined, and the
measured temperature changes are also explained by the theory.Comment: 15 pages, to appear in Period. Polytech. Civil En
- âŠ