相关论文: Viscous corrections of the Time Incremental Minimi…
Visco-Energetic solutions of rate-independent systems are obtained by solving a modified time Incremental Minimization Scheme, where at each step the dissipation is reinforced by a viscous correction, typically a quadratic perturbation of…
This paper focuses on weak solvability concepts for rate-independent systems in a metric setting. Visco-Energetic solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for…
This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of Energetic and Balanced Viscosity solutions. Visco-Energetic solutions have been recently obtained by passing…
We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) non-convex energy and a dissipation potential, which is positively homogeneous of…
In the nonconvex case solutions of rate-independent systems may develop jumps as a function of time. To model such jumps, we adopt the philosophy that rate independence should be considered as limit of systems with smaller and smaller…
This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for…
In this paper we study a rate-independent system for the propagation of damage and plasticity. To construct solutions we resort to approximation in terms of viscous evolutions, where viscosity affects both damage and plasticity with the…
Several mechanical systems are modeled by the static momentum balance for the displacement $u$ coupled with a rate-independent flow rule for some internal variable $z$. We consider a class of abstract systems of ODEs which have the same…
The notion of Inertial Balanced Viscosity (IBV) solution to rate-independent evolutionary processes is introduced. Such solutions are characterized by an energy balance where a suitable, rate-dependent, dissipation cost is optimized at jump…
Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have…
We consider evolutionary PDE inclusions of the form \[ -\lambda \dot{u}_\lambda + \Delta u - \mathrm{D} W_0(u) + f \ni \partial \mathcal{R}_1(\dot{u}) \qquad\text{in $(0,T) \times \Omega$,} \] where $\mathcal{R}_1$ is a positively…
This paper is concerned with an approximation scheme for rate-independent systems governed by a non-smooth dissipation and a possibly non-convex energy functional. The scheme is based on the local minimization scheme introduced in [EM06],…
By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equation of rate-independent type. Approximate solutions are…
Performance-based optimization of energy dissipation devices in structures necessitates massive and repetitive dynamic analyses. In the endurance time method known as a rather fast dynamic analysis procedure, structures are subjected to…
Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for…
Micro- and nano-scale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally…
In this paper we investigate the origin of the Balanced Viscosity solution concept for rate-independent evolution in the setting of a finite-dimensional space. Namely, given a family of dissipation potentials $(\Psi_n)_n$ with superlinear…
We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…
A suitable notion of weak solution to infinite-dimensional rate-independent systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The key feature of such notion is that the energy dissipated at jump discontinuities…
We consider generalized gradient systems with rate-independent and rate-dependent dissipation potentials. We provide a general framework for performing a vanishing-viscosity limit leading to the notion of parametrized and true…