Elena Bonetti

A PHASE FIELD MODEL WITH THERMAL MEMORY GOVERNED BY THE ENTROPY BALANCE

We introduce a thermomechanical model describing dissipative phase transitions with thermal memory in terms of the entropy balance and the principle of virtual power written for microscopic movements. The thermodynamical consistence of this model is verified and existence of solutions is proved for a related initial and boundary value problem.

On a model for phase separation in binary alloys driven by mechanical effects

This work is concerned with the mathematical analysis of a system of partial differential equations modeling the effect of phase separation driven by mechanical actions in binary alloys like tin/lead solders. The system combines the (quasistationary) balance of linear momentum with a fourth order evolution equation of Cahn\_Hilliard type for the phase separation, and it is highly nonlinearly coupled. Existence and uniqueness results are shown. TEL:: 0382505631 EMAIL:: bonetti@dimat.unipv.it

Thermal effects in adhesive contact: modelling and analysis

In this paper, we consider a contact problem with adhesion between a viscoelastic body and a rigid support, taking thermal effects into account. The PDE system we deal with is derived within the modelling approach proposed by Fremond and, in particular, includes the entropy balance equations, describing the evolution of the temperatures of the body and of the adhesive material. Our main result shows the existence of global in time solutions (to a suitable variational formulation) of the related initial and boundary value problem.

Damage theory: microscopic effects of vanishing macroscopic motions

This paper deals with a mechanical model describing the evolution of damage in elastic and viscoelastic materials. The state variables are macroscopic deformations and a microscopic phase parameter, which is related to the quantity of damaged material. The equilibrium equations are recovered by refining the principle of virtual powers including also microscopic forces. After proving an existence and uniqueness result for a regularized problem, we investigate the behavior of solutions, in the case when a vanishing sequence of external forces is applied. By use of a rigorous asymptotics analysis, we show that macroscopic deformations can disappear at the limit, but their damaging effect remains in the equation describing the evolution of damage at a microscopic level. Moreover, it is proved that the balance of the energy is satisfied at the limit.

Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system

We have investigated a dynamic thermoviscoelastic system (2003), establishing existence and uniqueness results for a related initial and boundary values problem. The aim of the present paper is to study the asymptotic behavior of the solution to the above problem as the power of the acceleration forces goes to zero. In particular, well-posedness and regularity results for the limit (quasistatic) problem are recovered.

Global existence and uniqueness for a thermomechanical model for shape memory alloys with partition of the strain

This paper investigates an initial and boundary value problem describing the thermomechanical behavior of shape memory alloys. In the strain tensor an elastic contribution is combined with a phase transformation term, for which only one of the phases turns out to be responsible. In particular, the solid-solid phase transition between the austenite phase and the martensites is described by two functionals, the free energy and the pseudo-potential of dissipation. A global existence and uniqueness result is stated by use of a fixed point argument and contracting estimates technique.

A non-smooth regularization of a forward–backward parabolic equation

In this paper, we introduce a model describing diffusion of species by a suitable regularization of a “forward–backward” parabolic equation. In particular, we prove existence and uniqueness of solu...

Entropy balance versus energy balance Application to the heat equation and to phase transitions

In these notes we are concerned with heat conduction described by using the entropy balance. The main advantage of this approach consists in recovering the positivity of the absolute temperature, necessary to prove thermodynamical consistency, directly by solving the equation. We introduce the model and discuss its thermomechanical consistency. Then, we investigate from the analytical and mechanical point of view, the Stefan problem written in terms of the entropy balance and using a generalized version of the principle of virual power including the effects of microscopic forces, responsible for the phase transition process. We prove existence of a solution in a fairly general physical framework, accounting for possible thermal memory effects and local interactions between the phases. Uniqueness is proved in the case no thermal memory nor local interactions are considered.

A phase transition model for the helium supercooling

We build a predictive theory for the evolution of mixture of helium and supercooled helium at low temperature. The absolute temperature θ and the volume fraction β of helium, which is dominant at temperature larger than the phase change temperature, are the state quantities. The predictive theory accounts for local interactions at the microscopic level, involving the gradient of β. The nonlinear heat flux in the supercooled phase results from a Norton-Hoff potential. We prove that the resulting set of partial differential equations has solutions within a convenient analytical frame.

A nonlinear model for marble sulphation including surface rugosity: theoretical and numerical results

We consider an evolution system describing the phenomenon of marble sulphation of a monument, accounting of the surface rugosity. We first prove a local in time well posedness result. Then, stronger assumptions on the data allow us to establish the existence of a global in time solution. Finally, we perform some numerical simulations that illustrate the main feature of the proposed model.