Nicolas Chevaugeon

On use of the thick level set method in 3D quasi-static crack simulation of quasi-brittle material

This work demonstrates the 3D capability of the thick level set (TLS) method, first introduced by Moës et al. (Int J Numer Methods Eng 86:358–380, 2011. doi:10.1002/nme.3069) and later in Stolz and Moës (Int J Fract 174(1):49–60, 2012. doi:10.1007/s10704-012-9693-3). The thick level set approach is a non-local damage method embedding fracture mechanics discontinuity. Enhanced numerical implementation for elastic quasi-brittle materials in 2D under quasi-static loading conditions was presented in Bernard et al. (Comput Methods Appl Mech Eng 233–236:11–27, 2012. doi:10.1016/j.cma.2012.02.020). The present work focuses on using this enhanced numerical implementation in a 3D context. This work adds a new way to construct the crack faces by use of a “double cut algorithm”. The regularization computation, part of the non-local feature of the model, is also reviewed to improve its accuracy. As 3D models are computationally intensive, CPU aspects are discussed. Five test cases are presented. The first one illustrates the capability of the method to deal with crack coalescence, which is quite unique for this kind of simulation. Three other cases point out a comparison with literature examples (numerical and experimental) and good agreement is observed. One is a more complex example, which deals with an engineering oriented application. This work confirms good performance of the thick level set method in 3D context. The use of the new “double cut” algorithm is giving well discretized crack path and allows for discontinuous displacement.

The inequality level-set approach to handle contact: membrane case

Background Contact mechanics involves models governed by inequality constraints. Even for the simplest contact problem, inequalities arise from the lack of information on the contact zone position. In addition to increasing the difficulty to solve such problems, an unknown contact zone makes it difficult to use an appropriate mesh and to represent efficiently phenomena on the contact zone boundary. Nevertheless these phenomena are often crucial to have an accurate representation of the problem such as weak discontinuity of the displacement.Methods In this paper, we propose a method specifically designed to solve inequality constraint problems linked to an unknown domain without remeshing. In order to do so, level sets coupled with X-FEM is used to define the unknown domain and take into account the specific behavior at the contact zone boundary. The key idea of the method is to split the problem involving inequality constraints into two problems. In the first problem, the unknown domain is set and therefore it only involves equalities. Nevertheless, the constraints might be violated, meaning the set domain has to be changed. Then, the other problem is a shape optimization of this domain and leads to an updated set domain. These two problems are iterated up to convergence of the algorithm. Moreover, the addition of adhesion to the problem will be considered.Results The studied case in this paper is a membrane in the context of small deformations. First, a 1D example will be given to illustrate the method with and without adhesion. Then 2D cases will be studied. Finally an example with an evolving load will be given. Comparison will be made with a classical active-set method.ConclusionsThe ILS is proved to be an efficient method giving a convincing accuracy for the contact boundary without need of re-meshing. It is also able to naturally handle adhesion.

A Regularized Brittle Damage Model Solved by a Level Set Technique

We consider an elastic brittle damage model in which a degradation front is propagating based on a criteria depending both on the energy along the front and the curvature of the front. This model was introduced about 20 years ago but to our knowledge was not yet exploited numerically. The contribution of this paper is to solve this model using a level set technique coupled to the eXtended Finite Element Method (X-FEM).

Handling Localization in Damage Models With the Thick Level Set Approach (TLS)

In this paper, we discuss a new way to model damage growth in solids. A level set is used to separate the undamaged zone from the damaged zone. In the damaged zone, the damage variable is an explicit function of the level set. This function is a parameter of the model. Beyond a critical length, it is assumed that the material is totally damaged, thus allowing a straightforward transition to fracture. The damage growth is expressed as a level set propagation. The configurational force driving the damage front is non local in the sense that it averages information over the thickness in the wake of the front. Three important theoretical advantages of the proposed approach are as follows: (a) The zone for which the materials is fully damaged is located inside a clearly identified domain (given by an iso-level set). (b) The non-locality steps in gradually in the model. At initiation the model is fully local. At initiation, micro-cracks being absent no length scale should prevail. (c) It is straightforward to prove that dissipation is positive. A numerical experiment of the cracking of a multiply perforated plate is discussed.Copyright