This paper presents a modified regularized formulation of the Ambrosio–Tortorelli type to introduce the crack non-interpenetration condition in the variational approach to fracture mechanics proposed by Francfort and Marigo [1998. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (8), 1319–1342]. We focus on the linear elastic case where the contact condition appears as a local unilateral constraint on the displacement jump at the crack surfaces. The regularized model is obtained by splitting the strain energy in a spherical and a deviatoric parts and accounting for the sign of the local volume change. The numerical implementation is based on a standard finite element discretization and on the adaptation of an alternate minimization algorithm used in previous works. The new regularization avoids crack interpenetration and predicts asymmetric results in traction and in compression. Even though we do not exhibit any gamma-convergence proof toward the desired limit behavior, we illustrate through several numerical case studies the pertinence of the new model in comparison to other approaches.

Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

A consistent model coupling adhesion, friction, and unilateral contact

https://my.vanderbilt.edu/mcml/files/2011/09/Oskay-Fish-CMAME-2007.pdf

Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials

This study reviews seismograms from 10 rock-fall events recorded between 1992 and 2001 by the permanent seismological network Sismalp in the French Alps. A new seismic magnitude scale was defined, which allowed us to compare and classify g round-motion vibrations generated by these Alpine rock-falls. Each rock-fall has also been cha racterized by its ground-motion duration t30 at an epicentral distance of 30 km. No relation was found between rock-fall parameters (fall height, runout distance, volume, potential energy) and rock-fall s eismic magnitudes derived from seismogram amplitudes. On the other hand, the signal duration t30 shows a rough correlation with the potential energy and the runout distance, highlighting the co ntrol of the propagation phase on the signal length . The signal analysis suggests the existence of at le ast two distinct seismic sources: one corresponding to the initial rupture associated with an elastic r ebound during the detachment and the other one generated by the rock impact on the slope. Although the fall phenomenon includes other complex processes (fragmentation of the block, interaction with topography, plastic deformation during and after impact) 2D finite-element simulations of thes e two seismic sources are able to retrieve the main seismogram characteristics.

https://hal-insu.archives-ouvertes.fr/insu-00355126/document

Analysis of Rock-Fall and Rock-Fall Avalanche Seismograms in the French Alps

Determination of the size of the representative volume element for random quasi-brittle composites

This paper is concerned with a continuum thermodynamic and mathematical formulation of an interface law including unilateral contact, adhesion and friction. The model is based on the notion of material boundary associated to the interface and its derivation follows from the principle of virtual power and the principles of thermodynamics (Cangemi et al., 1996 a). Adhesion and friction are strongly coupled and adhesion is characterized by a new variable, the intensity of adhesion β introduced by Premond. We consider a quasistatic unilateral contact problem for which we present a variational formulation. A time discretization is adopted and we prove that if the friction coefficient is sufficiently small then the incremental formulation that can be derived from this discretization has a unique solution. Finally an application to an indentation problem is mentioned.

M. Raous

Papers

A consistent model coupling adhesion, friction, and unilateral contact

Approximation Results for a Class of Quasistatic Contact Problems Including Adhesion and Friction