Effect of a nonuniform distribution of voids on the plastic response of voided materials: a computational and statistical analysis

This study investigates the overall and local response of porous media composed of a perfectly plastic matrix weakened by stress-free voids. Attention is focused on the specific role played by porosity fluctuations inside a representative volume element. To this end, numerical simulations using the Fast Fourier Transform (FFT) are performed on different classes of microstructure corresponding to different spatial distributions of voids. Three types of microstructures are investigated: random microstructures with no void clustering, microstructures with a connected cluster of voids and microstructures with disconnected void clusters. These numerical simulations show that the porosity fluctuations can have a strong effect on the overall yield surface of porous materials. Random microstructures without clusters and microstructures with a connected cluster are the hardest and the softest configurations, respectively, whereas microstructures with disconnected clusters lead to intermediate responses. At a more local scale, the salient feature of the fields is the tendency for the strain fields to concentrate in specific bands. Finally, an image analysis tool is proposed for the statistical characterization of the porosity distribution. It relies on the distribution of the ‘distance function’, the width of which increases when clusters are present. An additional connectedness analysis allows us to discriminate between clustered microstructures

A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

The correspondence principle is customarily used with the Laplace–Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599–1606) have shown the equivalence between the collocation method used to invert Laplace–Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered

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

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