00999nas a2200157 4500008004100000020001400041245014800055210006900203260001500272300000800287490000700295520045600302100001800758700001800776856004700794 2021 eng d a1432-083500aA vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers0 avanishinginertia analysis for finitedimensional rateindependent  c2021/08/03 a1910 v603 a

We study the approximation of finite-dimensional rate-independent quasistatic systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamic solutions to a rate-independent one, employing the variational 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.

1 aGidoni, Paolo1 aRiva, Filippo uhttps://doi.org/10.1007/s00526-021-02067-601183nas a2200145 4500008004100000020001400041245012000055210006900175260001500244300001400259490000700273520069200280100001800972856004700990 2020 eng d a1432-146700aOn the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity0 aApproximation of Quasistatic Evolutions for the Debonding of a T c2020/06/01 a903 - 9510 v303 a

In this paper, we contribute to studying the issue of quasistatic limit in the context of Griffith’s theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate and subjected to a vertical loading. Taking viscosity into account and under suitable assumptions on the toughness of the glue, we prove that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time. We then characterise the size of the jump by means of an asymptotic analysis of the debonding front.

1 aRiva, Filippo uhttps://doi.org/10.1007/s00332-019-09595-800896nas a2200109 4500008004100000245008200041210006900123260001000192520051200202100001800714856005400732 2019 en d00aA continuous dependence result for a dynamic debonding model in dimension one0 acontinuous dependence result for a dynamic debonding model in di bSISSA3 a

In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griffith’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to different natural topologies.

1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3532900945nas a2200109 4500008004100000245010200041210006900143520053000212100002100742700001800763856005400781 2018 en d00aExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping0 aExistence and uniqueness of dynamic evolutions for a one dimensi3 a

In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

1 aNardini, Lorenzo1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/35319