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The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…

Materials Science · Physics 2026-01-01 Juan Michael Sargado , Joachim Mathiesen

Irreversible evolution is one of the central concepts as well as implementation challenges of both the variational approach to fracture by Francfort and Marigo (1998) and its regularized counterpart by Bourdin, Francfort and Marigo (2000,…

Numerical Analysis · Mathematics 2019-07-24 Tymofiy Gerasimov , Laura De Lorenzis

We prove existence of globally stable quasistatic evolutions, referred to as energetic solutions, for a model proposed by Marigo and Kazymyrenko in 2019. The behaviour of geomaterials under compression is studied through the coupling of…

Analysis of PDEs · Mathematics 2021-09-20 Vito Crismale

The isothermal quasistatic (i.e.\ acceleration neglected) hardening-free plasticity at large strains is considered, based on the standard multiplicative decomposition of the total strain and the isochoric plastic distortion. The Eulerian…

Analysis of PDEs · Mathematics 2022-06-01 Tomáš Roubíček

Important physical observations in rupture dynamics such as static fault friction, short-slip, self-healing, and supershear phenomenon in cracks are studied. A continuum model of rupture dynamics is developed using the field dislocation…

Materials Science · Physics 2023-12-18 Abhishek Arora , Amit Acharya

Developing a unified theory describing both ductile and brittle yielding constitutes a fundamental challenge of non-equilibrium statistical physics. Recently, it has been proposed that the nature of the yielding transition is controlled by…

Soft Condensed Matter · Physics 2024-11-22 Jack T. Parley , Peter Sollich

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…

Analysis of PDEs · Mathematics 2020-01-08 Filippo Riva

In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme…

Numerical Analysis · Mathematics 2019-03-07 Stefano Almi , Sandro Belz

We present a non-linear stability analysis of quasi-static slip in a spring-block model. The sliding interface is governed by rate- and state-dependent friction, with an intermediate state evolution law that spans between aging and slip…

Geophysics · Physics 2024-07-25 Federico Ciardo , Robert C. Viesca

We prove the stability of a large class of unilateral minimality properties which arise naturally in the theory of crack propagation proposed by Francfort and Marigo in [Revisiting brittle fractures as an energy minimization problem. J.…

Analysis of PDEs · Mathematics 2007-05-23 Alessandro Giacomini , Marcello Ponsiglione

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…

Biological Physics · Physics 2017-05-16 Shakti N. Menon , Cameron L. Hall , Scott W. McCue , D. L. Sean McElwain

We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\epsilon$-gradient flow of the energy functional, as the "viscosity" parameter $\epsilon$ tends to zero.

Analysis of PDEs · Mathematics 2007-05-23 Rodica Toader , Chiara Zanini

A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…

Optimization and Control · Mathematics 2014-11-19 L. Adam , J. V. Outrata , T. Roubicek

We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two…

Statistical Mechanics · Physics 2013-09-23 Jonathan Barés , Luc Barbier , Daniel Bonamy

Through experiments, we idealise a plant leaf as a flexible, thin, rectangular plate clamped at the midpoint and positioned perpendicular to an airflow. Flexibility of the structure is considered as an advantage at moderate flow speed…

Fluid Dynamics · Physics 2024-03-05 Maryam Boukor , Augustin Choimet , Éric Laurendeau , Frédérick P. Gosselin

In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\ge1$, with a quasiconvex bulk…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Gilles A. Francfort , Rodica Toader

This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect…

Analysis of PDEs · Mathematics 2022-02-16 Jean-François Babadjian , Randy Llerena

The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a…

Analysis of PDEs · Mathematics 2025-03-24 Eleonora Maggiorelli , Filippo Riva , Edoardo Giovanni Tolotti

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…

Optimization and Control · Mathematics 2026-01-09 Stefano Almi , Massimo Fornasier , Jona Klemenc , Alessandro Scagliotti

In this paper we derive a new model for visco-elasticity with large deformations where the independent variables are the stretch and the rotation tensors which intervene with second gradients terms accounting for physical properties in the…

Analysis of PDEs · Mathematics 2024-10-21 Abramo Agosti , Pierluigi Colli , Michel Frémond