Thermomechanics of damage and fatigue by a phase field model

In the paper we present an isothermal model for describing damage and fatigue by the use of the Ginzburg-Landau (G-L) equation. Fatigue produces progressive damage, which is related with a variation of the internal structure of the material. The G-L equation studies the evolution of the order parameter, which describes the constitutive arrangement of the system and, in this framework, the evolution of damage. The thermodynamic coherence of the model is proved. In the last part of the work, we extend the results of the paper to a non-isothermal system, where fatigue contains thermal effects, which increase the damage of materials.Comment: 21 pages, 4 figure

ALGEBRAIC AND NUMERICAL EXPLORATION OF FREE ENERGIES FOR MATERIALS WITH MEMORY

Abstract. We study the forms of a range of free energy functionals for materials with memory for two types of strain history, namely sinusoidal and ex- ponential behaviours. The work deals with discrete spectrum materials, which are those with relaxation functions given by sums of decaying exponentials

Free Energies in a General Non-Local Theory of a Material with Memory

A general theory of non-local materials, with linear constitutive equations and memory effects, is developed within a thermodynamic framework. Several free energy and dissipation functionals are constructed and explored. These include an expression for the minimum free energy and a functional that is a free energy for important categories of memory kernels and is explicitly a functional of the minimal state. The functionals discussed have a similar general form to the corresponding expressions for simple materials. A number of new results are derived for them, most of which apply equally to both types of material. In particular, detailed formulae are given for these quantities in the case of sinusoidal histories. Read More: http://www.worldscientific.com/doi/abs/10.1142/S021820251350076

Turbulence Phenomena in Magnetohydrodynamic Phase Transitions

The model developed in (Fabrizio in J. Eng. Math., 2023) and (Fabrizio in Int. J. Eng. Sci. 44:529–539, 2006), involving the use of a local Reynolds number, is applied to describe phase transitions in a fluid. Specifically, it is applied in a magnetohydrodynamics context to study the evolution of turbulence in certain phenomena. The relevant equations describing the system are those of Navier-Stokes, Ginzburg-Landau and the magnetohydrodynamic equations, all suitably interconnected

A Mathematical Model for Visco-Ferromagnetic Materials

Visco-ferromagnetic materials represented by non-local constitutive equation are considered in the paper. We use fractional derivatives in order to describe memory and spatial effects. Also, thermodynamic principles are formulated and studied

Free energies for incompressible viscoelastic fluids

In this work we consider some expressions for the free energy, already proposed and studied for viscoelastic solids, in order to adapt them to incompressible viscoelastic fluids. The internal dissipation, corresponding to each of these various forms of the free energy, is also evaluated. In particular, the form of the minimum free energy for the discrete spectrum model is also considered in order to show its equivalence with some classical free energies

On thermodynamic conditions for the stability of a thermoelectromagnetic system

In this note we are concerned with the linear theory of the Thermodynamics of dielectric materials in the presence of memory effects for heat flux. Restrictions imposed on the assumed constitutive equations by Thermodynamics are first determined. Then, we introduce a particular maximal free energy, that allows us to arrive at a domain of dependence. Finally, we confine our attention to a unidimensional model, for which a uniqueness, existence, and asymptotic stability theorem is proved