145 research outputs found
From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination
Get PDFWe revisit the weak, energetic-type existence results obtained in [Rossi/Thomas-ESAIM-COCV-21(1):1-59,2015] for a system for rate-independent, brittle delamination between two visco-elastic, physically nonlinear bulk materials and explain how to rigorously extend such results to the case of visco-elastic, linearly elastic bulk materials. Our approximation result is essentially based on deducing the Mosco-convergence of the functionals involved in the energetic formulation of the system. We apply this approximation result in two different situations: Firstly, to pass from a nonlinearly elastic to a linearly elastic, brittle model on the time-continuous level, and secondly, to pass from a time-discrete to a time-continuous model using an adhesive contact approximation of the brittle model, in combination with a vanishing, super-quadratic regularization of the bulk energy. The latter approach is beneficial if the model also accounts for the evolution of temperature
Well-posedness and asymptotic analysis for a Penrose-Fife type phase field system
No full textIn this paper, an asymptotic analysis of the (non-conserved)
Penrose-Fife phase field system for two vanishing time relaxation parameters
and is developed. Although formally the
singular limits for and for
emph{and} are, respectively, the viscous Cahn-Hilliard
equation and the Cahn-Hilliard equation, it turns out that the Penrose-Fife
system is indeed a emph{bad} approximation for these equations. Therefore,
we consider an alternative approximating phase field system, which could be
viewed as a generalization of the classical Penrose-Fife phase field system,
featuring a double nonlinearity given by two maximal monotone graphs. A
well-posedness result is proved for such a system, and it is shown that the
solutions converge to the unique solution of the viscous Cahn-Hilliard
equation as , and of the Cahn-Hilliard equation as emph{and}
Asymptotic analysis of the Caginalp phase-field model for two vanishing time relaxation parameters
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On two classes of generalized viscous Cahn-Hilliard equations
No full textThis paper investigates two classes of generalized viscous
Cahn-Hilliard equations, featuring two different laws for the mobility,
which is assumed to depend on the chemical potential. Both equations can be
framed in the new derivation of equations of Cahn-Hilliard type proposed by
M.E. Gurtin. Approximation and compactness tools allow to prove well-posedness
and, in one case, regularity results for the systems obtained supplementing
each equation with initial and suitable boundary conditio
Existence and approximation results for general rate-independent problems via a variable time-step discretization scheme
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A Temperature-Dependent Phase-Field Model for Phase Separation and Damage
No full textIn this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature concerning phase separation and damage processes in elastic media, in our model we encompass thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More particularly, we prove the existence of “entropic weak solutions”, resorting to a solvability concept first introduced in Feireisl (Comput Math Appl 53:461–490, 2007) in the framework of Fourier–Navier–Stokes systems and then recently employed in Feireisl et al. (Math Methods Appl Sci 32:1345–1369, 2009) and Rocca and Rossi (Math Models Methods Appl Sci 24:1265–1341, 2014) for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme
Coupling rate-independent and rate-dependent processes: Existence results
No full textWe address the analysis of an abstract system coupling a rate-independent process with a rate-dependent nonlinear evolution equation. We propose suitable weak solution concepts and obtain existence results by passing to the limit in carefully devised time-discretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rate-independent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rate-independent processes in viscoelastic solids with inertia, and to a recently proposed model for damage with plasticity
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