Existence and uniqueness of dynamic evolutions for a peeling test in dimension one

DOI10.1016/j.jde.2016.07.012zbMath1347.35143OpenAlexW2257900693MaRDI QIDQ738712

Giuliano Lazzaroni, Lorenzo Nardini, Gianni Dal Maso

Publication date: 5 September 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.07.012

zbMATH Keywords

dynamic energy release ratedynamic fractureGriffith's criteriondynamic debondingmaximum dissipation principlewave equation in time-dependent domains

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Thin films (74K35) Wave equation (35L05) Free boundary problems for PDEs (35R35) Existence of solutions of dynamical problems in solid mechanics (74H20) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items

Radial solutions for a dynamic debonding model in dimension two, A comparative review of peridynamics and phase-field models for engineering fracture mechanics, On the approximation of quasistatic evolutions for the debonding of a thin film via vanishing inertia and viscosity, On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding, On the 1d wave equation in time-dependent domains and the problem of debond initiation, The global Lipschitz solution for a peeling model, On the quasistatic limit of dynamic evolutions for a peeling test in dimension one, Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness, Existence, Energy Identity, and Higher Time Regularity of Solutions to a Dynamic Viscoelastic Cohesive Interface Model, Existence and uniqueness of dynamic evolutions for a one-dimensional debonding model with damping, A continuous dependence result for a dynamic debonding model in dimension one, From adhesive to brittle delamination in visco-elastodynamics, A dynamic model for viscoelastic materials with prescribed growing cracks

Cites Work

• Unnamed Item
• Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects
• Nonlinearly coupled thermo-visco-elasticity
• Existence for wave equations on domains with arbitrary growing cracks
• Thermodynamics and analysis of rate-independent adhesive contact at small strains
• Quasistatic crack growth in finite elasticity with Lipschitz data
• Quasistatic crack growth in finite elasticity with non-interpenetration
• Dynamic crack propagation in a 2D elastic body: the out-of-plane case
• Thermomechanics of damageable materials under diffusion: modelling and analysis
• The variational approach to fracture
• Well-posedness results for a model of damage in thermoviscoelastic materials
• Dynamic fracture: An example of convergence towards a discontinuous quasistatic solution
• Damage, gradient of damage and principle of virtual power
• A density result in two-dimensional linearized elasticity, and applications
• A model for the quasi-static growth of brittle fractures: Existence and approximation results
• Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures
• Quasistatic crack growth in nonlinear elasticity
• Revisiting brittle fracture as an energy minimization problem
• Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition
• Rate-independent systems. Theory and application
• On a doubly nonlinear model for the evolution of damaging in viscoelastic materials
• A dynamic evolution model for perfectly plastic plates
• Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
• Thermodynamics of Rate-independent Processes in Viscous Solids at Small Strains
• Epsilon-stable quasi-static brittle fracture evolution
• EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE
• Rate-independent processes in viscous solids at small strains
• Dynamic Fracture Mechanics
• Existence and convergence for quasi-static evolution in brittle fracture
• The Wave Equation on Domains with Cracks Growing on a Prescribed Path: Existence, Uniqueness, and Continuous Dependence on the Data
• Adhesive Contact of Visco-elastic Bodies and Defect Measures Arising by Vanishing Viscosity
• Approximation of dynamic and quasi-static evolution problems in elasto-plasticity by cap models
• Existence of Weak Solutions for a Hyperbolic-Parabolic Phase Field System with Mixed Boundary Conditions on Nonsmooth Domains
• ``Entropic” Solutions to a Thermodynamically Consistent PDE System for Phase Transitions and Damage
• A degenerating PDE system for phase transitions and damage