A Fourier-series-based virtual fields method for the identification of three-dimensional stiffness distributions and its application to incompressible materials

We present an inverse method to identify the spatially varying stiffness distributions in 3 dimensions. The method is an extension of the classical Virtual Fields Method—a numerical technique that exploits information from full-field deformation measurements to deduce unknown material properties—in the spatial frequency domain, which we name the Fourier-series-based virtual fields method (F-VFM). Three-dimensional stiffness distributions, parameterised by a Fourier series expansion, are recovered after a single matrix inversion. A numerically efficient version of the technique is developed, based on the Fast Fourier Transform. The proposed F-VFM is also adapted to deal with the challenging situation of limited or even non-existent knowledge of boundary conditions. The three-dimensional F-VFM is validated with both numerical and experimental data. The latter came from a phase contrast magnetic resonance imaging experiment containing material with Poisson's ratio close to 0.5; such a case requires a slightly different interpretation of the F-VFM equations, to enable the application of the technique to incompressible materials

A Fourier-series-based virtual fields method for the identification of three-dimensional stiffness distributions and its application to incompressible materials

This is the peer reviewed version of the following article: Nguyen, TT and Huntley, JM and Ashcroft, IA and Ruiz, PD and Pierron, F (2017) A Fourier-series-based virtual fields method for the identification of three-dimensional stiffness distributions and its application to incompressible materials. Strain, 53 (5). e12229-e12229 which has been published in final form at 10.1111/str.12229 This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving." We present an inverse method to identify the spatially varying stiffness distributions in 3 dimensions. The method is an extension of the classical Virtual Fields Method—a numerical technique that exploits information from full-field deformation measurements to deduce unknown material properties—in the spatial frequency domain, which we name the Fourier-series-based virtual fields method (F-VFM). Three-dimensional stiffness distributions, parameterised by a Fourier series expansion, are recovered after a single matrix inversion. A numerically efficient version of the technique is developed, based on the Fast Fourier Transform. The proposed F-VFM is also adapted to deal with the challenging situation of limited or even non-existent knowledge of boundary conditions. The three-dimensional F-VFM is validated with both numerical and experimental data. The latter came from a phase contrast magnetic resonance imaging experiment containing material with Poisson's ratio close to 0.5; such a case requires a slightly different interpretation of the F-VFM equations, to enable the application of the technique to incompressible materials

Fourier-series-based Virtual Fields Method for the identification of 2-D stiffness distributions

The Virtual Fields Method (VFM) is a powerful technique for the calculation of spatial distributions of material properties from experimentally-determined displacement fields. A Fourier-series-based extension to the VFM (the F-VFM) is presented here, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM. We summarise here the theory of the F-VFM for the case of elastic isotropic thin structures with known boundary conditions. An efficient numerical algorithm based on the 2-D Fast Fourier Transform reduces the computation time by 3-4 orders of magnitude compared to a direct implementation of the F-VFM for typical experimental dataset sizes. Reconstruction of stiffness distributions with the FVFM has been validated on several stiffness distribution scenarios, one of which is presented here, in which a difference of about 0.5% was achieved between the reference and recovered stiffness distributions

A Fourier-series-based Virtual Fields Method for the Identification of 2-D Stiffness and Traction Distributions

The virtual fields method (VFM) allows spatial distributions of material properties to be calculated from experimentally determined strain fields. A numerically efficient Fourier-series-based extension to the VFM (the F-VFM) has recently been developed, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM. However, the boundary conditions for the F-VFM are assumed to be well-defined, whereas in practice, the traction distributions on the perimeter of the region of interest are rarely known to any degree of accuracy. In the current paper, we therefore consider how the F-VFM theory can be extended to deal with the case of unknown boundary conditions. Three different approaches are proposed; their ability to reconstruct normalised stiffness distributions and traction distributions around the perimeter from noisy input strain fields is assessed through simulations based on a forward finite element analysis. Finally, a practical example is given involving experimental strain fields from a diametral compression test on an aluminium disc

Interlaminar Fracture Toughness Evaluation in Glass/Epoxy Composites Using Acoustic Emission and Finite Element Methods

© 2014, ASM International. Delamination is one of the most common modes of failure in laminated composites and it leads to the loss of structural strength and stiffness. In this paper, mode I, mode II, and mixed of these pure modes were investigated using mechanical data, Finite Element Method (FEM) and Acoustic Emission (AE) signals. Experimental data were obtained from insitu monitoring of glass/epoxy laminated composites with different lay-ups when subjected to different modes of failure. The main objective was to investigate the behavior of delamination propagation and to evaluate the critical value of the strain energy which is required for onset of the delamination (GC). For the identification of interlaminar fracture toughness of the specimens, four methods were used: (a) ASTM standard methods, (b) FEM analysis, (c) AE method, and (d) sentry function method which is a function of mechanical and AE behaviors of the specimens. The results showed that the GC values obtained by the sentry function method and FEM analysis were in a close agreement with the results of nonlinearity methods which is recommended in the ASTM standards. It was also found that the specimens under different loading conditions and various lay-up have different GC values. These differences are related to different stress components distribution in the specimens which induce various damage mechanisms. Accordingly, stress components distribution obtained from FEM analyses were in agreement with SEM observations of the damaged surfaces of the specimens

Aging Alters Functionally Human Dermal Papillary Fibroblasts but Not Reticular Fibroblasts: A New View of Skin Morphogenesis and Aging

Understanding the contribution of the dermis in skin aging is a key question, since this tissue is particularly important for skin integrity, and because its properties can affect the epidermis. Characteristics of matched pairs of dermal papillary and reticular fibroblasts (Fp and Fr) were investigated throughout aging, comparing morphology, secretion of cytokines, MMPs/TIMPs, growth potential, and interaction with epidermal keratinocytes. We observed that Fp populations were characterized by a higher proportion of small cells with low granularity and a higher growth potential than Fr populations. However, these differences became less marked with increasing age of donors. Aging was also associated with changes in the secretion activity of both Fp and Fr. Using a reconstructed skin model, we evidenced that Fp and Fr cells do not possess equivalent capacities to sustain keratinopoiesis. Comparing Fp and Fr from young donors, we noticed that dermal equivalents containing Fp were more potent to promote epidermal morphogenesis than those containing Fr. These data emphasize the complexity of dermal fibroblast biology and document the specific functional properties of Fp and Fr. Our results suggest a new model of skin aging in which marked alterations of Fp may affect the histological characteristics of skin

Rapid Insulinotropic Action of Low Doses of Bisphenol-A on Mouse and Human Islets of Langerhans: Role of Estrogen Receptor β

Bisphenol-A (BPA) is a widespread endocrine-disrupting chemical (EDC) used as the base compound in the manufacture of polycarbonate plastics. It alters pancreatic β-cell function and can be considered a risk factor for type 2 diabetes in rodents. Here we used ERβ−/− mice to study whether ERβ is involved in the rapid regulation of KATP channel activity, calcium signals and insulin release elicited by environmentally relevant doses of BPA (1 nM). We also investigated these effects of BPA in β-cells and whole islets of Langerhans from humans. 1 nM BPA rapidly decreased KATP channel activity, increased glucose-induced [Ca2+]i signals and insulin release in β-cells from WT mice but not in cells from ERβ−/− mice. The rapid reduction in the KATP channel activity and the insulinotropic effect was seen in human cells and islets. BPA actions were stronger in human islets compared to mouse islets when the same BPA concentration was used. Our findings suggest that BPA behaves as a strong estrogen via nuclear ERβ and indicate that results obtained with BPA in mouse β-cells may be extrapolated to humans. This supports that BPA should be considered as a risk factor for metabolic disorders in humans

Investigation of the effect of relative humidity on polymers by depth sensing indentation

This article was published in the serial, Journal of Materials Science [© Springer]. The definitive version is available from: http://www.springerlink.com/content/y2g413h8h2l6044m/Stereolithography (SL) resins absorb varying amounts of moisture dependent on the relative humidities, which can significantly affect the mechanical properties. In this work, the influence of relative humidity (RH) on the mechanical behaviour of an SL resin is investigated using depth sensing indentation (DSI). The samples were conditioned by two methods. In the first method, samples were pre-conditioned at 33.5, 53.8, 75.3 and 84.5% RH using saturated salt solutions. These preconditioned samples were tested at 33.5% RH, using a humidity control unit (HCU) to control RH in the DSI system. In the second method, samples were conditioned and tested at 33.5, 53.8, 75.3 and 84.5% RH by regulating humidity in the DSI system using the HCU. Temperature was kept constant at 22.5 C for the conditioning and DSI testing. It was seen that hardness and modulus decreased with increasing RH and conditioning time but recovered significantly when tested after drying. This study demonstrates that RH needs to be taken into account during the DSI testing of polymers

Sensing the fuels: glucose and lipid signaling in the CNS controlling energy homeostasis

The central nervous system (CNS) is capable of gathering information on the body’s nutritional state and it implements appropriate behavioral and metabolic responses to changes in fuel availability. This feedback signaling of peripheral tissues ensures the maintenance of energy homeostasis. The hypothalamus is a primary site of convergence and integration for these nutrient-related feedback signals, which include central and peripheral neuronal inputs as well as hormonal signals. Increasing evidence indicates that glucose and lipids are detected by specialized fuel-sensing neurons that are integrated in these hypothalamic neuronal circuits. The purpose of this review is to outline the current understanding of fuel-sensing mechanisms in the hypothalamus, to integrate the recent findings in this field, and to address the potential role of dysregulation in these pathways in the development of obesity and type 2 diabetes mellitus