373 research outputs found
A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis
The theory of elastic magnets is formulated under possible diffusion and heat
flow governed by Fick's and Fourier's laws in the deformed (Eulerian)
configuration, respectively. The concepts of nonlocal nonsimple materials and
viscous Cahn-Hilliard equations are used. The formulation of the problem uses
Lagrangian (reference) configuration while the transport processes are pulled
back. Except the static problem, the demagnetizing energy is ignored and only
local non-selfpenetration is considered. The analysis as far as existence of
weak solutions of the (thermo)dynamical problem is performed by a careful
regularization and approximation by a Galerkin method, suggesting also a
numerical strategy. Either ignoring or combining particular aspects, the model
has numerous applications as ferro-to-paramagnetic transformation in elastic
ferromagnets, diffusion of solvents in polymers possibly accompanied by
magnetic effects (magnetic gels), or metal-hydride phase transformation in some
intermetalics under diffusion of hydrogen accompanied possibly by magnetic
effects (and in particular ferro-to-antiferromagnetic phase transformation),
all in the full thermodynamical context under large strains
Thermodynamics and analysis of rate-independent adhesive contact at small strains
We address a model for adhesive unilateral frictionless Signorini-type
contact between bodies of heat-conductive viscoelastic material, in the linear
Kelvin-Voigt rheology, undergoing thermal expansion. The flow-rule for
debonding the adhesion is considered rate-independent and unidirectional, and a
thermodynamically consistent model is derived and analysed as far as the
existence of a weak solution is concerned
Thermomechanics of hydrogen storage in metallic hydrides: modeling and analysis
A thermodynamically consistent mathematical model for hydrogen adsorption in
metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for
phase transformation accompanied by hysteresis, swelling, temperature and heat
transfer, strain, and stress. We prove existence of solutions of the ensuing
system of partial differential equations by a carefully-designed, semi-implicit
approximation scheme. A generalization for a drift-diffusion of multi-component
ionized "gas" is outlined, too
A simple and efficient BEM implementation of quasistatic linear visco-elasticity
A simple, yet efficient procedure to solve quasistatic problems of special
linear visco-elastic solids at small strains with equal rheological response in
all tensorial components, utilizing boundary element method (BEM), is
introduced. This procedure is based on the implicit discretisation in time (the
so-called Rothe method) combined with a simple "algebraic" transformation of
variables, leading to a numerically stable procedure (proved explicitly by
discrete energy estimates), which can be easily implemented in a BEM code to
solve initial-boundary value visco-elastic problems by using the Kelvin
elastostatic fundamental solution only. It is worth mentioning that no inverse
Laplace transform is required here. The formulation is straightforward for both
2D and 3D problems involving unilateral frictionless contact. Although the
focus is to the simplest Kelvin-Voigt rheology, a generalization to Maxwell,
Boltzmann, Jeffreys, and Burgers rheologies is proposed, discussed, and
implemented in the BEM code too. A few 2D and 3D initial-boundary value
problems, one of them with unilateral frictionless contact, are solved
numerically
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