Diego Grandi
University of Bologna
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Publication
Featured researches published by Diego Grandi.
Journal of Mathematical Physics | 2010
Valeria Berti; Mauro Fabrizio; Diego Grandi
By means of the Ginzburg–Landau theory of phase transitions, we study a nonisothermal model to characterize the austenite-martensite transition in shape memory alloys. In the first part of this paper, the one-dimensional model proposed by Berti et al. [“Phase transitions in shape memory alloys: A non-isothermal Ginzburg-Landau model,” Physica D 239, 95 (2010)] is modified by varying the expression of the free energy. In this way, the description of the phenomenon of hysteresis, typical of these materials, is improved and the related stress-strain curves are recovered. Then, a generalization of this model to the three-dimensional case is proposed and its consistency with the principles of thermodynamics is proven. Unlike other three-dimensional models, the transition is characterized by a scalar valued order parameter φ and the Ginzburg–Landau equation, ruling the evolution of φ, allows us to prove a maximum principle, ensuring the boundedness of φ itself.
Nonlinearity | 2011
A. Berti; Valeria Berti; Diego Grandi
We consider a model describing the behaviour of a mixture of two incompressible fluids with the same density under isothermal conditions. The model consists of three balance equations: a continuity equation, a Navier?Stokes equation for the mean velocity of the mixture and a diffusion equation (Cahn?Hilliard equation). We assume that the chemical potential depends on the velocity of the mixture in such a way that an increase in the velocity improves the miscibility of the mixture. We examine the thermodynamic consistence of the model which leads to the introduction of an additional constitutive force in the motion equation. Then, we prove the existence and uniqueness of the solution of the resulting differential problem.
Journal of Intelligent Material Systems and Structures | 2012
Mirko Maraldi; Luisa Molari; Diego Grandi
A phase-field–based model has been employed for numerical tests on the mechanical response of a shape memory alloy. The model consists of a time-dependent Ginzburg–Landau equation for a scalar order parameter describing the local phase of the material (austenite or martensite), coupled with the balance of linear momentum and the heat equations; the mechanical effect of the martensitic phase transition is described in terms of a uniaxial deformation strain along a fixed direction, making the model suited for predictions over monodimensional specimens. A number of numerical simulations under stress-controlled conditions have been performed to investigate the mechanical behaviour of the model; the results obtained are analysed in relation to the experimental evidences available in the literature and previous investigations under strain-controlled conditions.
Siam Journal on Mathematical Analysis | 2017
Diego Grandi; Ulisse Stefanelli
We address a finite-plasticity model based on the symmetric tensor
Journal of Non-Equilibrium Thermodynamics | 2016
Mauro Fabrizio; Diego Grandi; Luisa Molari
P^\top\!P
Acta Materialia | 2012
Diego Grandi; Mirko Maraldi; Luisa Molari
instead of the classical plastic strain
Physica D: Nonlinear Phenomena | 2010
Valeria Berti; Mauro Fabrizio; Diego Grandi
P
Meccanica | 2010
F. Daghia; Mauro Fabrizio; Diego Grandi
. Such a structure arises by assuming that the material behavior is invaria...
Meccanica | 2014
Diego Grandi; Ulisse Stefanelli
Abstract We develop a phase-field model for the liquid–vapor phase transition. The model aims to describe in a thermodynamically consistent way the phase change phenomenon coupled with the macroscopic motion of the fluid. The phase field φ∈[0,1]
Discrete and Continuous Dynamical Systems - Series S | 2014
Diego Grandi; Ulisse Stefanelli
\varphi \in [0, \,1]