Gmsh is an open-source 3-D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents the overall philosophy, the main design choices and some of the original algorithms implemented in Gmsh. Copyright (C) 2009 John Wiley & Sons, Ltd.

Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

The numerical implementation of the model of brittle fracture developed in Francfort and Marigo (1998. J. Mech. Phys. Solids 46 (8), 1319–1342) is presented. Various computational methods based on variational approximations of the original functional are proposed. They are tested on several antiplanar and planar examples that are beyond the reach of the classical computational tools of fracture mechanics.

Numerical experiments in revisited brittle fracture

In this work we present a new generalization of the geometric mean of positive numbers on symmetric positive‐definite matrices, called Log‐Euclidean. The approach is based on two novel algebraic structures on symmetric positive‐definite matrices: first, a lie group structure which is compatible with the usual algebraic properties of this matrix space; second, a new scalar multiplication that smoothly extends the Lie group structure into a vector space structure. From bi‐invariant metrics on the Lie group structure, we define the Log‐Euclidean mean from a Riemannian point of view. This notion coincides with the usual Euclidean mean associated with the novel vector space structure. Furthermore, this means corresponds to an arithmetic mean in the domain of matrix logarithms. We detail the invariance properties of this novel geometric mean and compare it to the recently introduced affine‐invariant mean. The two means have the same determinant and are equal in a number of cases, yet they are not identical in g...

Geometric means in a novel vector space structure on symmetric positive-definite matrices

The past 20 years have seen substantial work on the modeling of ductile damage and fracture. Several factors explain this interest. (i) There is a growing demand to provide tools which allow to increase the efficiency of structures (reduce weight, increase service temperature or load, etc.) while keeping or increasing safety. This goal is indeed first achieved by using better materials but also by improving design tools. Better tools have been provided which consist (ii) of material constitutive equations integrating a physically-based description of damage processes and (iii) of better numerical tools which allow to use the improved constitutive equations in structural computations which become more and more realistic. This article reviews the material constitutive equations and computational tools, which have been recently developed to simulate ductile rupture.

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Continuum Models of Ductile Fracture: A Review

Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows

Delaunay mesh generation governed by metric specifications. Part I algorithms

An indirect method for meshing parametric surfaces conforming to a user-specifiable size map is presented. First, from this size specification, a Riemannian metric is defined so that the desired mesh is one with unit length edges with respect to the related Riemannian space (the so-called ‘unit mesh’). Then, based on the intrinsic properties of the surface, the Riemannian structure is induced into the parametric space. Finally, a unit mesh is generated completely inside the parametric space such that it conforms to the metric of the induced Riemannian structure. This mesh is constructed using a combined advancing-front—Delaunay approach applied within a Riemannian context. The proposed method can be applied to mesh composite parametric surfaces. Several examples illustrate the efficiency of our approach. Copyright © 2000 John Wiley & Sons, Ltd.

Parametric surface meshing using a combined advancing-front generalized Delaunay approach

The analysis of mechanical structures using the finite element method in the framework of large elasto-plastic strain, needs frequent remeshing of the deformed domain during the computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behaviour of the solution as the plastic strain or the damage fields. This paper gives the necessary steps to remesh a mechanical structure during large elasto-plastic deformations with damage. An important part of this process concerns the geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. After recalling the formulation of the elasto-plastic problem with damage, four types of applications using the proposed adaptive remeshing are given: orthogonal cutting, side-pressing of an infinite cylinder, blanking and backward extrusion with drilling. Copyright © 2005 John Wiley & Sons, Ltd.

Adaptive remeshing in large plastic strain with damage

The BL2D software package is a bidimensional, adaptive and anisotropic mesh generator. Its architecture is very modular. This report is made up of three main parts: a beginner's guide (for users who are new to BL2D), a user's manual (for more experienced users) and a programmer's manual (for developers wishing to add new functionalities).

https://hal.inria.fr/inria-00069977/document

Patrick Laug

Papers

Delaunay mesh generation governed by metric specifications. Part I algorithms

Parametric surface meshing using a combined advancing-front generalized Delaunay approach

Adaptive remeshing in large plastic strain with damage

The BL2D Mesh Generator: Beginner's Guide, User's and Programmer's Manual

Adaptive remeshing for ductile fracture prediction in metal forming