Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting

Numerical Meth Engineering

Guilbaud

et al. 2016

116

International audienceIn this contribution we propose a dynamic gradient damage model as a phase-field approach for studying brutal fracture phenomena in quasi-brittle materials under impact-type loading conditions. Several existing approaches to account for the tension-compression asymmetry of fracture behavior of materials are reviewed. A better understanding of these models is provided through a uniaxial traction experiment. We then give an efficient numerical implementation of the model in an explicit dynamics context. Simulations results obtained with parallel computing are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture

Section: Simulation Resultsmentioning

confidence: 99%

Gradient damage modeling of brittle fracture in an explicit dynamics context

Numerical Meth Engineering

Guilbaud

et al. 2016

116

“…An interesting challenge is to give a theoretical proof of this global property of periodicity and even to give a method for calculating the period in terms of the parameters of the problem. We expect that it will be achieved by considering second order stability conditions like in Benallal and Marigo (2007), Pham et al (2011) and Pham and Marigo (2012b).…”

mentioning

confidence: 99%

From Gradient Damage Laws to Griffith’s Theory of Crack Propagation

Sicsic

2012

J Elast

This paper is devoted to the comparison of the evolution of damage governed by a gradient damage model with the evolution of a crack predicted by Griffith's law. The analysis is made in a two-dimensional setting, assuming that damage is concentrated inside thin bands whose width is proportional to the internal length of the material. Taking advantage of the variational formulation based on the three principles of irreversibility, stability and energy balance, one introduces a generalized Rice path integral which contains terms involving the gradient of damage. Assuming that the internal length of the material is small by comparison with the dimension of the body, a separation of scales is achieved. Owing to the energy balance and the stability condition, one first proves some properties of this path integral with respect to the path. Then, one shows that the evolution of the damage zone is governed by Griffith's law, the dissipated surface energy being given by the energy dissipated in the damage process zone.

“…where the constitutive function E(α) represents the Young modulus of the material and is supposed to be sufficiently smooth and decreasing with α up to zero [57]. Accordingly, the stress is defined as…”

Section: State Variables and Basic Energetic Quantitiesmentioning

confidence: 99%

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Alessi

International Journal of Mechanical Sciences

Maurini

et al. 2018

107

Plasticity and damage are two fundamental phenomena in nonlinear solid mechanics associated to the development of inelastic deformations and the reduction of the material stiffness. Alessi et al. [4] have recently shown, through a variational framework, that coupling a gradient-damage model with plasticity can lead to macroscopic behaviours assimilable to ductile and cohesive fracture. Here, we further expand this approach considering specific constitutive functions frequently used in phase-field models of brittle fracture. A numerical solution technique of the coupled elastodamage-plasticity problem, based on an alternate minimisation algorithm, is proposed and tested against semi-analytical results. Considering a one-dimensional traction test, we illustrate the properties of four different regimes obtained by a suitable tuning of few key constitutive parameters. Namely, depending on the relative yield stresses and softening behaviours of the plasticity and the damage criteria, we obtain macroscopic responses assimilable to (i) brittle fracturè a la Griffith, (ii) cohesive fractures of the Barenblatt or Dugdale type, and (iii) a sort of cohesive fracture including a depinning energy contribution. The comparisons between numerical and analytical results prove the accuracy of the proposed numerical approaches in the considered quasi-static time-discrete setting, but they also emphasise some subtle issues occurring during time-discontinuous evolutions.