On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the C1-continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of C1-continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for C-continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these C1-continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates. © 2021, The Author(s)

Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved

A Three-Dimensional Analysis of Symmetric Composite Laminates with Damage

Damage behavior of a symmetric composite laminate without an initial im perfection or macro-crack is analyzed based on a three-dimensional lamination theory under multi-axial loading. The global response of the laminate during the damaging pro cess is determined from the individual response of its constituent plies and their mutual relations. Some specific results are presented to illustrate the damage characteristics of several typical composite laminates when they are subjected to proportional loading. The application of the method to characterize damage initiation and growth in more complex structures is also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67341/2/10.1177_105678959300200304.pd

A three-scale domain decomposition method for the 3D analysis of debonding in laminates

The prediction of the quasi-static response of industrial laminate structures requires to use fine descriptions of the material, especially when debonding is involved. Even when modeled at the mesoscale, the computation of these structures results in very large numerical problems. In this paper, the exact mesoscale solution is sought using parallel iterative solvers. The LaTIn-based mixed domain decomposition method makes it very easy to handle the complex description of the structure; moreover the provided multiscale features enable us to deal with numerical difficulties at their natural scale; we present the various enhancements we developed to ensure the scalability of the method. An extension of the method designed to handle instabilities is also presented

A Virtual Testing Approach for Laminated Composites Based on Micromechanics

International audienceThe chapter deals with a crucial question for the design of composite structures: how can one predict the evolution of damage up to and including final fracture? Virtual testing, whose goal is to drastically reduce the huge number of industrial tests involved in current characterization procedures, constitutes one of today’s main industrial challenges. In this work, one revisits our multiscale modeling answer through its practical aspects. Some complements regarding identification, kinking, and crack initiation are also given. Finally, the current capabilities and limits of this approach are discussed, as well as the computational challenges that are inherent to “Virtual Structural Testing.

Analysis of Inelasticity Effect Due to Damage on Stress Distributions in Composite Laminates

A damage mechanics model characterizing damage behavior of composite materials proposed earlier by the authors is employed to analyze the damage effects on stress field near the free edge in symmetrically laminated graphite/epoxy composites of finite dimensions under umaxial tension. A quasi-three-dimensional finite element analy sis is developed for the present investigation. The results from the damaged and undam aged stress distributions of [0/90°]s, [90/0°]s, and [±45°] s laminates are compared and examined. The processes of initiation and development of damage zone in these composite laminates are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68869/2/10.1177_073168449301200805.pd

A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics

We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No \textit{a priori} knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture.Comment: Submitted for publication in CMAM

The Forest behind the Tree: Phylogenetic Exploration of a Dominant Mycobacterium tuberculosis Strain Lineage from a High Tuberculosis Burden Country

BACKGROUND: Genotyping of Mycobacterium tuberculosis isolates is a powerful tool for epidemiological control of tuberculosis (TB) and phylogenetic exploration of the pathogen. Standardized PCR-based typing, based on 15 to 24 mycobacterial interspersed repetitive unit-variable number of tandem repeat (MIRU-VNTR) loci combined with spoligotyping, has been shown to have adequate resolution power for tracing TB transmission and to be useful for predicting diverse strain lineages in European settings. Its informative value needs to be tested in high TB-burden countries, where the use of genotyping is often complicated by dominance of geographically specific, genetically homogeneous strain lineages. METHODOLOGY/PRINCIPAL FINDINGS: We tested this genotyping system for molecular epidemiological analysis of 369 M. tuberculosis isolates from 3 regions of Brazil, a high TB-burden country. Deligotyping, targeting 43 large sequence polymorphisms (LSPs), and the MIRU-VNTRplus identification database were used to assess phylogenetic predictions. High congruence between the different typing results consistently revealed the countrywide supremacy of the Latin-American-Mediterranean (LAM) lineage, comprised of three main branches. In addition to an already known RDRio branch, at least one other branch characterized by a phylogenetically informative LAM3 spoligo-signature seems to be globally distributed beyond Brazil. Nevertheless, by distinguishing 321 genotypes in this strain population, combined MIRU-VNTR typing and spoligotyping demonstrated the presence of multiple distinct clones. The use of 15 to 24 loci discriminated 21 to 25% more strains within the LAM lineage, compared to a restricted lineage-specific locus set suggested to be used after SNP analysis. Noteworthy, 23 of the 28 molecular clusters identified were exclusively composed of patient isolates from a same region, consistent with expected patterns of mostly local TB transmission. CONCLUSIONS/SIGNIFICANCE: Standard MIRU-VNTR typing combined with spoligotyping can reveal epidemiologically meaningful clonal diversity behind a dominant M. tuberculosis strain lineage in a high TB-burden country and is useful to explore international phylogenetical ramifications