A note on topological properties of volumes constructed from surfaces

Converting surfaces into a volume has a long interest in several communities, e.g. the computational mechanics community. This process involves having specific surfaces which can be converted into a solid, i.e., a volume. This paper presents in a clear and brief manner the topological properties conserved during surface to volume transformation. We state the limits of this approach if a specific volume structure is required. Volume structures can be a coarse volume organization or meshes. For that purpose, surface manifolds are mathematically turned into a volume manifold. Topological tools are presented to understand which properties are transmitted to the volume and which ones are unset. Developments are submitted both for continuous and discrete manifolds using CW-complexes

Mixed-mode stress intensity factors for graded materials

AbstractIn this paper, we present a general method for the calculation of the various stress intensity factors in a material whose constitutive law is elastic, linear and varies continuously in space. The approach used to predict the stress intensity factors is an extension of the interaction integral method. For this type of material, we also develop a systematic method to derive the asymptotic displacement fields and use it to achieve better-quality results. A new analytical asymptotic field is given for two special cases of graded materials. Numerical examples focus on materials with space-dependent Young modulus

Modélisation par la méthode X-FEM de la propagation de fissure sur des structures minces, soumises à des sollicitations intenses et rapides

 Dans l'industrie navale, les méthodes classiques pour analyser la tenue des structures sous des chargements extrêmes sont très dépendantes de la taille de maille du modèle. De plus, la propagation sur de grandes longueurs avec des modèles volumiques demande une puissance de calcul importante, souvent inaccessible dans ce cadre. Face à ces problématiques et compte tenu de la géométrie des structures à étudier, un couplage entre les éléments finis de coque et l'utilisation de la méthode des éléments finis étendus utilisant un critère de propagation adapté est proposé

One-step deposition of nano-to-micron-scalable, high-quality digital image correlation patterns for high-strain in-situ multi-microscopy testing

Digital Image Correlation (DIC) is of vital importance in the field of experimental mechanics, yet, producing suitable DIC patterns for demanding in-situ mechanical tests remains challenging, especially for ultra-fine patterns, despite the large number of patterning techniques in the literature. Therefore, we propose a simple, flexible, one-step technique (only requiring a conventional deposition machine) to obtain scalable, high-quality, robust DIC patterns, suitable for a range of microscopic techniques, by deposition of a low melting temperature solder alloy in so-called 'island growth' mode, without elevating the substrate temperature. Proof of principle is shown by (near-)room-temperature deposition of InSn patterns, yielding highly dense, homogeneous DIC patterns over large areas with a feature size that can be tuned from as small as 10nm to 2um and with control over the feature shape and density by changing the deposition parameters. Pattern optimization, in terms of feature size, density, and contrast, is demonstrated for imaging with atomic force microscopy, scanning electron microscopy (SEM), optical microscopy and profilometry. Moreover, the performance of the InSn DIC patterns and their robustness to large deformations is validated in two challenging case studies of in-situ micro-mechanical testing: (i) self-adaptive isogeometric digital height correlation of optical surface height profiles of a coarse, bimodal InSn pattern providing microscopic 3D deformation fields (illustrated for delamination of aluminum interconnects on a polyimide substrate) and (ii) DIC on SEM images of a much finer InSn pattern allowing quantification of high strains near fracture locations (illustrated for rupture of a Fe foil). As such, the high controllability, performance and scalability of the DIC patterns offers a promising step towards more routine DIC-based in-situ micro-mechanical testing.Comment: Accepted for publication in Strai

X-FEM in isogeometric analysis for linear fracture mechanics

The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X-FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X-FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X-FEM with conventional finite elements of equal degree, the NURBS-based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree

A generalized finite element formulation for arbitrary basis functions : from isogeometric analysis to XFEM

Many of the formulations of cm-rent research interest, including iosogeometric methods and the extended finite element method, use nontraditional basis functions. Some, such as subdivision surfaces, may not have convenient analytical representations. The concept of an element, if appropriate at all, no longer coincides with the traditional definition. Developing a new software for each new class of basis functions is a large research burden, especially, if the problems involve large deformations, non-linear materials, and contact. The objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file. Elements ranging from a traditional linear four-node tetrahedron through a higher-order element combining XFEM and isogeometric analysis may be specified entirely through an input file without any additional programming. Examples of this framework to applications with Lagrange elements, isogeometric elements, and XFEM basis functions for fracture are presented

Isogeometric analysis: an overview and computer implementation aspects

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. The open source Matlab code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bezier extraction concept that allows FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA

A stable and optimally convergent LaTIn-CutFEM algorithm for multiple unilateral contact problems

In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of the interacting solids, which can be arbitrarily complex. The key novelty of the approach is the combination of elements of the CutFEM technology, namely the enrichment of the solution field via the definition of overlapping fictitious domains with a dedicated penalty-type regularisation of discrete operators, and the LaTIn hybrid-mixed formulation of complex interface conditions. Furthermore, the novel P1-P1 discretisation scheme that we propose for the unfitted LaTIn solver is shown to be stable, robust and optimally convergent with mesh refinement. Finally, the paper introduces a high-performance 3D level-set/CutFEM framework for the versatile and robust solution of contact problems involving multiple bodies of complex geometries, with more than two bodies interacting at a single point