Preconditioning of nonsymmetric saddle point systems as arising in modelling of viscoelastic problems.
Quasistatic frictional problems for elastic and viscoelastic materials
We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational...
Rayleigh waves in a viscoelastic half-space under initial hydrostatic stress in the presence of the temperature field.
Recovering a time- and space-dependent kernel in a hyperbolic integro-differential equation from a restricted Dirichlet-to-Neumann operator.
Rheologies quasi wave number independent in a sphere and splitting the spectral line
The solution of the equations which govern the slow motions (for which the inertia forces are negligible) in an elastic sphere is studied for a great variety of rheological models and surface tractions with rotational symmetry (Caputo 1984a). The solution is expressed in terms of spherical harmonics and it is shown that its time dependent component is dependent on the order of the harmonic. The dependence of the time component of the solution on the order of the harmonic number is studied. The problem...
Sulla nozione di stato per materiali viscoelastici di tipo «rate»
Si considera un materiale viscoelastico lineare in cui la funzione di rilassamento è la somma di esponenziali. Lo stato di questi sistemi non è necessariamente assegnato dalla storia passata di , ma è sufficiente fornire il valore iniziale del tensore di deformazione , del tensore degli sforzi e delle sue derivate. Infine per questi materiali abbiamo ottenuto una espressione dell'energia libera come una funzione dello stato di dimensione finita .
Sull'espressione analitica di alcune grandezze termodinamiche nei materiali con memoria
Thick obstacle problems with dynamic adhesive contact
In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the Kelvin-Voigt type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...
Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey
2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into...