Numéro thématique des Comptes Rendus Mécanique en lʼhonneur dʼAndré Zaoui

La Mécanique des Matériaux a connu, en France et dans le monde, un développement spectaculaire au cours des dernières décennies, rendu à la fois nécessaire par les besoins d’innovation et de sûreté de secteurs industriels comme l’énergie et les transports, et possible par les avancées contemporaines en Physique et en Mécanique des Milieux Continus. Tout matériau est, par nature, hétérogène à une et souvent plusieurs échelles. La prise en compte, à une échelle pertinente, de cette hétérogénéité gouvernant les interactions entre mécanismes élémentaires est bien souvent la clef de la compréhension et de la prédiction du comportement mécanique des matériaux à leur échelle macroscopique d’usage. La Micromécanique des Matériaux, à laquelle ce numéro thématique des Comptes Rendus Mécanique est consacré, a précisément pour objet d’aborder ces problèmes de transition d’échelles. Ce numéro thématique est tout naturellement l’occasion d’honorer l’un des acteurs emblématiques du domaine, André Zaoui, qui a contribué de façon essentielle à l’établissement de la démarche micro–macro sur des bases théoriques rigoureuses validées par une approche expérimentale ambitieuse. Par ses travaux personnels, par la création, en avance sur son temps, d’une équipe de recherche dédiée aux expériences micromécaniques, par ses enseignements et ses actions de structuration de la recherche, André Zaoui a initié, puis constamment encouragé,ce domaine en France, l’ancrant solidement dans un dialogue fructueux entre expériences à petite échelle et modélisation

Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space

Characterization of Generalized Young Measures Generated by Symmetric Gradients

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer\ue2\u80\u93Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The \ue2\u80\u9clocal\ue2\u80\u9d proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti\ue2\u80\u99s rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences

Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models

Mineralized collagen fibrils have been usually analyzed like a two phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that, when Halpin-Tsai equations are applied to estimate elastic constants from typical constituent properties, not all crystal dimensions yield a model that satisfy thermodynamic restrictions. We provide the ranges of platelet dimensions that lead to positive definite stiffness matrices. On the other hand, a finite element model of a mineralized collagen fibril unit cell under periodic boundary conditions is analyzed. By applying six canonical load cases, homogenized stiffness matrices are numerically calculated. Results show a monoclinic behavior of the mineralized collagen fibril. In addition, a 5-layer lamellar structure is also considered where crystals rotate in adjacent layers of a lamella. The stiffness matrix of each layer is calculated applying Lekhnitskii transformations and a new finite lement model under periodic boundary conditions is analyzed to calculate the homogenized 3D anisotropic stiffness matrix of a unit cell of lamellar bone. Results are compared with the rule-of-mixtures showing in general good agreement.The authors acknowledge the Ministerio de Economia y Competitividad the financial support given through the project DPI2010-20990 and the Generalitat Valenciana through the Programme Prometeo 2012/023. The authors thank Ms. Carla Gonzalez Carrillo by her help in the development of some of the numerical models.Vercher Martínez, A.; Giner Maravilla, E.; Arango Villegas, C.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ. (2014). Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models. 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Fin Spine Bone Resorption in Atlantic Bluefin Tuna, Thunnus thynnus, and Comparison between Wild and Captive-Reared Specimens

Bone resorption in the first spine of the first dorsal fin of Atlantic bluefin tuna (ABFT) has long been considered for age estimation studies. In the present paper spine bone resorpion was assessed in wild (aged 1 to 13 years) and captive-reared (aged 2 to 11 years) ABFT sampled from the Mediterranean Sea. Total surface (TS), solid surface (SS) and reabsorbed surface (RS) were measured in spine transverse sections in order to obtain proportions of SS and RS. The spine section surface was found to be isometrically correlated to the fish fork length by a power equation. The fraction of solid spine bone progressively decreased according to a logarithmic equation correlating SS/TS to both fish size and age. The values ranged from 57% in the smallest examined individuals to 37% in the largest specimens. This phenomenon was further enhanced in captive-reared ABFT where SS/TS was 22% in the largest measured specimen. The difference between the fraction of SS of wild and captive-reared ABFT was highly significant. In each year class from 1- to 7-year-old wild specimens, the fraction of spine reabsorbed surface was significantly higher in specimens collected from March to May than in those sampled during the rest of the year. In 4-year-old fish the normal SS increase during the summer did not occur, possibly coinciding with their first sexual maturity. According to the correlations between SS/TS and age, the rate of spine bone resorption was significantly higher, even almost double, in captive-reared specimens. This could be attributed to the wider context of systemic dysfunctions occurring in reared ABFT, and may be related to a number of factors, including nutritional deficiencies, alteration of endocrine profile, cortisol-induced stress, and loss of spine functions during locomotion in rearing conditions.Versión del editor4,411

Ecological impacts of non-native Pacific oysters (Crassostrea gigas) and management measures for protected areas in Europe

Pacific oysters are now one of the most ‘globalised’ marine invertebrates. They dominate bivalve aquaculture production in many regions and wild populations are increasingly becoming established, with potential to displace native species and modify habitats and ecosystems. While some fishing communities may benefit from wild populations, there is now a tension between the continued production of Pacific oysters and risk to biodiversity, which is of particular concern within protected sites. The issue of the Pacific oyster therefore locates at the intersection between two policy areas: one concerning the conservation of protected habitats, the other relating to livelihoods and the socio-economics of coastal aquaculture and fishing communities. To help provide an informed basis for management decisions, we first summarise evidence for ecological impacts of wild Pacific oysters in representative coastal habitats. At local scales, it is clear that establishment of Pacific oysters can significantly alter diversity, community structure and ecosystem processes, with effects varying among habitats and locations and with the density of oysters. Less evidence is available to evaluate regional-scale impacts. A range of management measures have been applied to mitigate negative impacts of wild Pacific oysters and we develop recommendations which are consistent with the scientific evidence and believe compatible with multiple interests. We conclude that all stakeholders must engage in regional decision making to help minimise negative environmental impacts, and promote sustainable industry development

Effective anisotropic elastic constants of bimaterial interphases: comparison between experimental and analytical techniques

The effective elastic constants of a bimaterial composite were experimentally measured with the goal of validating the numerical predications of these constants made by homogenization theory. Secondly, solutions predicted by homogenization theory were compared to predictions made with more standard composite theories. Composite specimens consisting of titanium and epoxy were developed to mimic a porous titanium/tissue interphase. Tensile and shear tests (ASTM D3983) measured the stiffness along the porous coating/epoxy interphase ( E L ), across the interphase ( E T ) and in shear ( G LT ). No significant differences in moduli were found between the experimental measurements and predictions made with homogenization theory, nor between the experimental measurements and Hashin-Shtrikman estimates. Homogenization theory predicted results usually within 20% of Hashin-Shtrikman estimates, but typically more than 50% different from what is predicted by the rule of mixtures. However, homogenization theory allows calculation of anisotropic stiffness estimates and local strains, neither of which is possible using Hashin-Shtrikman estimates. With this experimental validation, the accuracy of homogenization theory for use in implant/tissue interface mechanics applications is confirmed. Since the composite interphase is anisotropic and more compliant in the transverse direction, with stiffness an order of magnitude lower across the interphase, local mechanics, tissue ingrowth and remodeling may be strongly directional dependent.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46748/1/10856_2004_Article_BF00058722.pd