@article {2021, title = {A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers}, volume = {60}, year = {2021}, month = {2021/08/03}, pages = {191}, abstract = {

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.

}, isbn = {1432-0835}, url = {https://doi.org/10.1007/s00526-021-02067-6}, author = {Paolo Gidoni and Filippo Riva} } @article {2020, title = {On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity}, volume = {30}, year = {2020}, month = {2020/06/01}, pages = {903 - 951}, abstract = {

In this paper, we contribute to studying the issue of quasistatic limit in the context of Griffith{\textquoteright}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.

}, isbn = {1432-1467}, url = {https://doi.org/10.1007/s00332-019-09595-8}, author = {Filippo Riva} } @article {2019, title = {A continuous dependence result for a dynamic debonding model in dimension one}, number = {SISSA;05/2019/MATE}, year = {2019}, institution = {SISSA}, abstract = {

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{\textquoteright}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.

}, url = {http://preprints.sissa.it/xmlui/handle/1963/35329}, author = {Filippo Riva} } @article {2018, title = {Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping}, number = {SISSA;28/2018/MATE}, year = {2018}, abstract = {

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{\textquoteright}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{\textquoteright}s criterion.

}, url = {http://preprints.sissa.it/xmlui/handle/1963/35319}, author = {Lorenzo Nardini and Filippo Riva} }