Vorosweep: a fast generalized crystal growing Voronoi diagram generation algorithm

We propose a new algorithm for generating quickly approximate generalized Voronoi diagrams of point sites associated to arbitrary convex distance metric in the Euclidian plane. This algorithm produces connected cells by emulating the growth of crystals starting at the point sites, in order to reduce the complexity of the diagram. The main practical contribution is the Vorosweep package which is the reference implementation of the algorithm. Experimental results and benchmarks are given to demonstrate the versatility of this approach.WIST 3 grant 1017074 DOMHEX (Dominant Hexahedral Mesh Generation

Simulation of contact on crack lips and its influence on fatigue life prediction

his work is dedicated to evaluate the influence of the contact on crack lips on crack path and crack growth rate under multi-axial loading conditions. An important part is dedicated to algorithmic robustness when handling contact in the context of XFEM in presence of crack tip enrichment functions. Crack path predictions as well as crack growth rate are also strongly influenced by the partial contact so that expressions classically used in the context of uniaxial loading without contact must be adapted. Preliminary simulations of a cracked cylinder submitted to four points bending under multiaxial loading conditions are presented and will be compared to experimental results

Semi-implicit representation of sharp features with level sets

The present contribution enriches the nowadays “classical” level set implicit representation of geometries with topological information in order to correctly represent sharp features. For this, sharp features are classified according to their positions within elements of the level set support. Based on this additional information, sub-elements and interface-mesh used in a finite element context for integration and application of boundary conditions are modified to match exactly to the sharp features. In order to analyze evolving geometries, Boolean operations on these semi-implicit representations are derived so that the minimal additional information to represent correctly the new geometry is stored. This approach has been successfully applied to complex two-dimensional geometries. It computes in a robust way numerous Boolean operations and guarantees the precision and the convergence rate of the numerical simulations.Integrating Numerical Simulation and Geometric Design Technology (INSIST

Embedded solids of any dimension in the X-FEM. Part II - Imposing Dirichlet boundary conditions

peer reviewedThis paper focuses on the design of a stable Lagrange multiplier space dedicated to enforce Dirichlet boundary conditions on embedded boundaries of any dimension. It follows a previous paper in a series of two, on the topic of embedded solids of any dimension within the context of the extended finite element method. While the first paper is devoted to the design of a dedicated P1 function space to solve elliptic equations defined on manifolds of codimension one or two (curves in 2D and surfaces in 3D, or curves in 3D), the general treatment of Dirichlet boundary conditions, in such a setting, remains to be addressed. This is the aim of this second paper. A new algorithm is introduced to build a stable Lagrange multiplier space from the traces of the shape functions defined on the background mesh. It is general enough to cover: (i) boundary value problems investigated in the first paper (with, for instance, Dirichlet boundary conditions defined along a line in a 3D mismatching mesh); but also (ii) those posed on manifolds of codimension zero (a domain embedded in a mesh of the same dimension) and already considered in Béchet et al. 2009. In both cases, the compatibility between the Lagrange multiplier space and that of the bulk approximation (the dedicated P1 function space used in (i), or classical shape functions used in (ii)) — resulting in the inf–sup condition — is investigate through the numerical Chapelle-Bath test. Numerical validations are performed against analytical and finite element solutions on problems involving 1D or 2D boundaries embedded in a 2D or 3D background mesh. Comparisons with Nitsche’s method and the stable Lagrange multiplier space proposed in Hautefeuille et al. 2012, when they are feasible, highlight good performance of the approach

Embedded solids of any dimension in the X-FEM. Part I - Building a dedicated P1 function space

peer reviewedThis paper focuses on the design of a dedicated P1 function space to model elliptic boundary value problem on a manifold embedded in a space of higher dimension. Using the traces of the linear P1 shape functions, it introduces an algorithm to reduce the function space into an equivalent space having the same properties than a P1 Lagrange approximation. Convergence studies involving problems of codimension one or two embedded in 2D or 3D show good accuracy with regard to classical finite element and analytical solutions. The effects of the relative position of the domain with respect to the mesh are studied in a sensitivity analysis; it illustrates how the proposed solution allows to keep the condition number bounded. A comparative study is performed with the method introduced by Olshanskii et al. 2009 on a closed surface to validate our approach. The robustness of the proposed approach is investigated with regard to their method and that of Burman et al. 2016. This paper is the first in a series of two, on the topic of embedded solids of any dimension within the context of the extended finite element method. It investigates problems involving borderless domains or domains with boundary subject to Dirichlet constraint defined only on the boundaries of the bulk mesh, while the forthcoming paper overcomes this limitation by introducing a new stable Lagrange multiplier space for Dirichlet boundary condition (and more generally stiff condition), that is valid for every combination of the background mesh and manifold dimensions. The combination of both algorithms allows to handle any embedding i.e. 1D, 2D and 3D problems embedded in 2D or 3D background meshes

Digital twin for tool wear monitoring and compensation in turning

In mass production of manufactured goods using conventional milling and turning, tool wear is reflected in the drift of quality control measurements. Methods have been developed to correct this drift and compensate the wear. With the possibilities offered by the digital twin concept, a new method of tool wear compensation was proposed including a digital twin of the tool and a digital twin of the lathe, based on the measurements of the parts. This digital twin solution provides useful functionalities such as a heritage process between the digital twin of old tools and the one of the tool being used.Interreg EMR Digital Twin Academy12. Responsible consumption and productio

Identifying a problem and solving it with a digital twin idea

Interreg EMR Digital Twin Academ

Application of the X-FEM to the fracture of piezoelectric materials

Materials exhibiting a strong piezoelectric effect may be used in many applications, where they serve as sensors, actuators or transducers. These applications range from for sub-millimeter length scales in MEMs (Micro-Electro-Mechanical Systems) up to large scales in the the design of smart wings in the aerospace industry. As for regular materials subjected to high mechanical stresses, the knowledge of fracture behavior for these smart materials is often crucial within the design of parts under high electrical and mechanical loading. The Extended Finite Element Method [1] has been originally designed for crack growth analysis in isotropic elastic materials. In association with level-sets [2] as a mean for representing the crack geometry, it is a powerful way to get rid of the costly constrained remeshing needed with conventional techniques. Under certain circumstances, this method is also able to achieve regular convergence rates in the energy error even for a cracked domain [3]. Piezoelectric materials exhibit an transversely isotropic mechanical characteristic, as well as a coupling between mechanical and electrical variables. This leads to different near-crack tip mechanical fields and the presence of singularities in the electrical variables [4][5]. To treat this new problem in the X-FEM, specific crack analysis tools and changes in the enrichment functions are needed which allows to represent the crack- both in the mechanical and electrical functional spaces. In this work, we will present these techniques and perform a convergence analysis to ensure that the crack tip behavior is accurately taken into account. Finally, we suggest a simple propagation model for crack growth

Exact Representation of Interfaces Using Enriched Level-Set Technique

This work aims to improve implicit representation of complex industrial work-pieces by reducing the existing gap between Computer Aided Design (CAD) and Computer Aided Engineering (CAE). The proposed approach is based on the level-set technique [1]. Limitations of the latter technique results in the miss-capturing of corners lying on the interface (iso-0 level-set) and other sharp features. These limitations also have a significant impact on surrounding elements. In order to avoid undesired over-smoothing to the sharp features, especially corners, an enhanced representation is proposed that is based on level sets method is introduced. This technique, referred in what follows by “level-set+” ,enriches the classical level-set by using data related to the corner points. This is done by automatically detecting geometrical points and using this information in the implicit representation. Elements containing these geometrical points and surrounding elements will be re-subdivided according to the updated iso-contour. This technique helps to employ classical level set and preserve current data structure for most of the creation of the iso-0 level set. Although the method is general enough to handle most possible configurations in terms of the corner locations, there are still limitations which have been handled in such a way to prevent computational failure. Also, the technique is effective at reducing the memory requirements by automatically erasing sharp features that are no longer existing after e.g. boolean operations. Some novel results illustrates accurate implicit representations of boundaries including the exact capture of sharp features in 2D and 3D. All the developments are implemented in our in-house finite element software Morfeo. There are numerous applications which can benefit from the above mentioned developments including crack propagation with the X-FEM method and transient machining simulations