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DCDS-S

Viscoelastic solids in Kelvin-Voigt rheology at small strains
exhibiting also stress-driven Prandtl-Reuss perfect plasticity
are considered quasistatic (i.e. inertia neglected)
and coupled with heat-transfer equation
through dissipative heat production by viscoplastic effects
and through thermal expansion and corresponding adiabatic effects.
Enthalpy transformation is used and existence of a weak solution is
proved by an implicit suitably regularized time discretisation.

DCDS-S

A general-topological construction of limits of inverse systems
is applied to convex compactifications and furthermore to
special convex compactifications of Lebesgue-space-valued
functions parameterized by time. Application to relaxation of
quasistatic evolution in phase-change-type problems is outlined.

DCDS-B

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.

PROC

Existence of a solution to the thermo-visco-elasto-"plastic-type" system involving also higher capillarity/viscosity terms and describing thermodynamics of activated martensitic transformation at large strains is proved by a careful successive passage to a limit in a suitably regularized Galerkin
approximation.

DCDS-S

The quasistatic rate-independent evolution of delamination in the
so-called mixed-mode, i.e. distinguishing opening (mode I) from
shearing (mode II), devised in [45], is described in detail and
rigorously analysed as far as existence of the so-called energetic
solutions concerns.
The model formulated at small strains uses a delamination parameter of
Frémond's type combined with a concept of interface plasticity,
and is associative in the sense that the dissipative force
driving delamination has a potential
which depends in a 1-homogeneous way only on rates of internal
parameters. A sample numerical simulation documents that this
model can really produce mode-mixity-sensitive delamination.

DCDS-S

The model of brittle cracks in elastic solids at small strains is approximated by the Ambrosio-Tortorelli functional and then extended into evolution situation to an evolutionary system, involving viscoelasticity, inertia, heat transfer, and coupling with Cahn-Hilliard-type diffusion of a fluid due to Fick's or Darcy's laws. Damage resulting from the approximated crack model is considered rate independent. The fractional-step Crank-Nicolson-type time discretisation is devised to decouple the system in a way so that the energy is conserved even in the discrete scheme. The numerical stability of such a scheme is shown, and also convergence towards suitably defined weak solutions. Various generalizations involving plasticity, healing in damage, or phase transformation are mentioned, too.

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