### Modelli di transizione di fase con movimenti microscopici

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This note deals with a class of abstract quasivariational evolution problems that may include some memory effects. Under a suitable monotonicity framework, we provide a generalized existence result by means of a fixed point technique in ordered spaces. Finally, an application to the modeling of generalized kinematic hardening in plasticity is discussed.

We investigate a global-in-time variational approach to abstract evolution by means of the functionals proposed by Mielke and Ortiz [ (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization. Applications of the...

This work deals with some abstract equations, either linear or nonlinear, arising from the so-called mixed formulation of PDEs of elliptic and parabolic type. This class of variational formulations turns out to be particularly relevant in connection with the development of finite elements approximations. We prove the well-posedness of both the stationary and the evolution problems.

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via $\Gamma $-convergence for rate-independent processes that energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique strong solution of linearized elastoplasticity.

We address a global-in-time variational approach to semilinear PDEs of either parabolic or hyperbolic type by means of the so-called Weighted Inertia-Dissipation-Energy (WIDE) functional. In particular, minimizers of the WIDE functional are proved to converge, up to subsequences, to weak solutions of the limiting PDE. This entails the possibility of reformulating the limiting differential problem in terms of convex minimization. The WIDE formalism can be used in order to discuss parameters asymptotics...

We present a model of the full thermo-mechanical evolution of a shape memory body undergoing a uniaxial tensile stress. The well-posedness of the related quasi-static thermo-inelastic problem is addressed by means of hysteresis operators techniques. As a by-product, details on a time-discretization of the problem are provided.

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