SISSA PreprintsThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2020-08-03T09:50:10Z2020-08-03T09:50:10ZA Vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlersGidoni, PaoloRiva, Filippohttp://preprints.sissa.it:8180/xmlui/handle/1963/353882020-07-21T23:20:31Z2020-07-21T00:00:00ZA Vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers
Gidoni, Paolo; Riva, Filippo
We study the approximation of quasistatic evolutions, formulated as abstract finite-dimensional rate-independent systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamical solutions to the quasistatic one, employing the concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.
Contents: 1. Introduction and motivation. 2. Setting of the problem and main result.
3. Existence of solutions for the dynamic problem. 4. R-absolutely continuous functions and functions of bounded R-variation. 5. Differential and energetic solutions for the quasistatic problem. 6. Quasistatic limit. 7. Applications and examples. References.
2020-07-21T00:00:00ZOn a Phase-field model of damage for hybrid laminates with cohesive interfacesBonetti, ElenaCavaterra, CeciliaFreddi, FrancescoRiva, Filippohttp://preprints.sissa.it:8180/xmlui/handle/1963/353872020-07-17T23:20:32Z2020-07-17T00:00:00ZOn a Phase-field model of damage for hybrid laminates with cohesive interfaces
Bonetti, Elena; Cavaterra, Cecilia; Freddi, Francesco; Riva, Filippo
In this paper we investigate a rate{independent model for hybrid laminates described by a damage phase field approach on two layers coupled with a cohesive law governing
the behaviour of their interface. For the analysis we adopt the notion of energetic evolution,
based on global minimisation of the involved energy. Due to the presence of the cohesive zone, as already emerged in literature, compactness mathematical issues lead to the introduction of a fictitious variable replacing the physical one which represents the maximal opening of the interface displacement discontinuity reached during the evolution. A new strategy which allows to recover the equivalence between the fictitious and the real variable under general loading-unloading regimes is illustrated. The argument is based on temporal regularity of energetic evolutions. This regularity is achieved by means of a careful balance between the convexity of the elastic energy of the layers and the natural concavity of the cohesive energy of the interface.
2020-07-17T00:00:00ZAtomic decompositions and two stars theorems for non re exive Banach function spacesSbordone, Carlohttp://preprints.sissa.it:8180/xmlui/handle/1963/353862020-07-15T23:20:51Z2020-01-01T00:00:00ZAtomic decompositions and two stars theorems for non re exive Banach function spaces
Sbordone, Carlo
Sbordone, Carlo (University “Federico II” Napoli)
2020-01-01T00:00:00ZSingular perturbations of gradient flows and rate-independent evolutionSavaré, Giuseppehttp://preprints.sissa.it:8180/xmlui/handle/1963/353852020-07-15T23:21:02Z2020-01-01T00:00:00ZSingular perturbations of gradient flows and rate-independent evolution
Savaré, Giuseppe
Savaré, Giuseppe (University of Pavia)
2020-01-01T00:00:00Z