Nonsmooth dynamics of extrinsic cohesive models for fracture
Abstract
Cohesive zone models are an effective tool for simulating fracture in solids. They are generally differentiated between intrinsic models, which have an elasticity of their own at the interface, and extrinsic models, which behave as rigid interfaces prior to the initiation of fracture. The main problems with intrinsic models are as follows: they substantially modify the global elasticity of the materials, the interface elasticity is difficult to measure experimentally and they lead to stiff numerical systems involving strong constraints on the choice of time–integration schemes and the size of time steps.
In this work [1,2], we propose an extrinsic cohesive zone model that contains one-sided contact and Coulomb dry friction as residual behaviour at fracture. In order to model an extrinsic model, it is necessary to be able to write set-valued non-smooth models, i.e. models that take a set of possible values for a given displacement of the interface. What is fairly standard for unilateral contact and friction is therefore extended to the cohesive part with damage using the tools of convex and variational analysis.
In the spirit of M. Frémond’s work, the model is written from thermodynamic principles in order to guarantee energy consistency. A time integration scheme for the dynamics preserves its properties in discrete time. The discrete system solved at each time step is a well-posed linear complementarity problem, guaranteeing the existence of solutions and uniqueness in the frictionless case where it is just a convex quadratic program.
We will end this presentation by emphasising the fact that this framework, which makes it possible to model softening behaviour using non-convex interface energies, leads to well-posed convex or co-positive models. This is mainly due to the presence of inertia, which enables the problem to be well defined and solved efficiently.
[1] Nicholas Anton Collins-Craft, Franck Bourrier, Vincent Acary. On the formulation and implementation of extrinsic cohesive zone models with contact. Computer Methods in Applied Mechanics and Engineering, 2022, 400, pp.115545. 〈10.1016/j.cma.2022.115545〉. 〈hal-03371667v5〉
[2] Nicholas Anton Collins-Craft, Franck Bourrier, Vincent Acary. On the formulation and implementation of mixed mode I and mode II extrinsic cohesive zone models with contact and friction. 2024. 〈hal-04447397〉
Short bio
Vincent Acary is a research director at INRIA, Grenoble-Alpes University Centre. He is head of the TRIPOP team, which specialises in the modelling, analysis, simulation and control of non-smooth dynamical systems. He is particularly interested in the development of numerical methods and simulation codes, in particular for unilateral contact with friction, plasticity, impacts and fracture mechanics. The most important application of this work in recent years has been in the field of natural gravity hazards in mountainous areas. More details at https://tripop.inrialpes.fr/people/acary/
Sandwiches are offered at the end of the seminar.
Cohesive zone models are an effective tool for simulating fracture in solids. They are generally differentiated between intrinsic models, which have an elasticity of their own at the interface, and extrinsic models, which behave as rigid interfaces prior to the initiation of fracture. The main problems with intrinsic models are as follows: they substantially modify the global elasticity of the materials, the interface elasticity is difficult to measure experimentally and they lead to stiff numerical systems involving strong constraints on the choice of time–integration schemes and the size of time steps.
In this work [1,2], we propose an extrinsic cohesive zone model that contains one-sided contact and Coulomb dry friction as residual behaviour at fracture. In order to model an extrinsic model, it is necessary to be able to write set-valued non-smooth models, i.e. models that take a set of possible values for a given displacement of the interface. What is fairly standard for unilateral contact and friction is therefore extended to the cohesive part with damage using the tools of convex and variational analysis.
In the spirit of M. Frémond’s work, the model is written from thermodynamic principles in order to guarantee energy consistency. A time integration scheme for the dynamics preserves its properties in discrete time. The discrete system solved at each time step is a well-posed linear complementarity problem, guaranteeing the existence of solutions and uniqueness in the frictionless case where it is just a convex quadratic program.
We will end this presentation by emphasising the fact that this framework, which makes it possible to model softening behaviour using non-convex interface energies, leads to well-posed convex or co-positive models. This is mainly due to the presence of inertia, which enables the problem to be well defined and solved efficiently.
[1] Nicholas Anton Collins-Craft, Franck Bourrier, Vincent Acary. On the formulation and implementation of extrinsic cohesive zone models with contact. Computer Methods in Applied Mechanics and Engineering, 2022, 400, pp.115545. 〈10.1016/j.cma.2022.115545〉. 〈hal-03371667v5〉
[2] Nicholas Anton Collins-Craft, Franck Bourrier, Vincent Acary. On the formulation and implementation of mixed mode I and mode II extrinsic cohesive zone models with contact and friction. 2024. 〈hal-04447397〉
Short bio
Vincent Acary is a research director at INRIA, Grenoble-Alpes University Centre. He is head of the TRIPOP team, which specialises in the modelling, analysis, simulation and control of non-smooth dynamical systems. He is particularly interested in the development of numerical methods and simulation codes, in particular for unilateral contact with friction, plasticity, impacts and fracture mechanics. The most important application of this work in recent years has been in the field of natural gravity hazards in mountainous areas. More details at https://tripop.inrialpes.fr/people/acary/
Sandwiches are offered at the end of the seminar.
Practical information
- Informed public
- Free
Organizer
- Prof. Olga Fink (IMOS), Prof. Alexandre Alahi (VITA), Prof. Dusan Licina (HOBEL), Prof. Alain Nussbaumer (RESSLab)
Contact
- Guillaume Anciaux