Mindlin, in his celebrated papers of
Arch. Rat. Mech. Anal. 16, 51–78, 1964 and
Int. J. Solids Struct. 1, 417–438, 1965, proposed two enhanced strain gradient elastic theories to describe linear ...elastic behavior of isotropic materials with micro-structural effects. Since then, many works dealing with strain gradient elastic theories, derived either from lattice models or homogenization approaches, have appeared in the literature. Although elegant, none of them reproduces entirely the equation of motion as well as the classical and non-classical boundary conditions appearing in Mindlin theory, in terms of the considered lattice or continuum unit cell. Furthermore, no lattice or continuum models that confirm the second gradient elastic theory of Mindlin have been reported in the literature. The present work demonstrates two simple one dimensional models that conclude to first and second strain gradient elastic theories being identical to the corresponding ones proposed by Mindlin. The first is based on the standard continualization of the equation of motion taken for a sequence of mass-spring lattices, while the second one exploits average processes valid in continuum mechanics. Furthermore, Mindlin developed his theory by adding new terms in the expressions of potential and kinetic energy and introducing intrinsic micro-structural parameter without however providing explicit expressions that correlate micro-structure with macro-structure. This is accomplished in the present work where in both models the derived internal length scale parameters are correlated to the size of the considered unit cell.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Analytical wave propagation studies in gradient elastic solids and structures are presented. These solids and structures involve an infinite space, a simple axial bar, a Bernoulli–Euler flexural beam ...and a Kirchhoff flexural plate. In all cases wave dispersion is observed as a result of introducing microstructural effects into the classical elastic material behavior through a simple gradient elasticity theory involving both micro-elastic and micro-inertia characteristics. It is observed that the micro-elastic characteristics are not enough for resulting in realistic dispersion curves and that the micro-inertia characteristics are needed in addition for that purpose for all the cases of solids and structures considered here. It is further observed that there exist similarities between the shear and rotary inertia corrections in the governing equations of motion for bars, beams and plates and the additions of micro-elastic (gradient elastic) and micro-inertia terms in the classical elastic material behavior in order to have wave dispersion in the above structures.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Data-driven techniques have recently drawn significant interest in the predictive modeling of subcutaneous (s.c.) glucose concentration in type 1 diabetes. In this study, the s.c. glucose prediction ...is treated as a multivariate regression problem, which is addressed using support vector regression (SVR). The proposed method is based on variables concerning: 1) the s.c. glucose profile; 2) the plasma insulin concentration; 3) the appearance of meal-derived glucose in the systemic circulation; and 4) the energy expenditure during physical activities. Six cases corresponding to different combinations of the aforementioned variables are used to investigate the influence of the input on the daily glucose prediction. The proposed method is evaluated using a dataset of 27 patients in free-living conditions. Tenfold cross validation is applied to each dataset individually to both optimize and test the SVR model. In the case, where all the input variables are considered, the average prediction errors are 5.21, 6.03, 7.14, and 7.62 mg/dl for 15-, 30-, 60-, and 120-min prediction horizons, respectively. The results clearly indicate that the availability of multivariable data and their effective combination can significantly increase the accuracy of both short-term and long-term predictions.
The gradient theory of elasticity with damping is successfully employed to explain the experimentally observed shift in resonance frequencies during forced harmonic torsional vibration tests of ...columns made of fine-grained material from their theoretically computed values on the basis of the classical theory of elasticity with damping. To this end, the governing equation of torsional vibrations of a column with circular cross-section is derived both by the lattice theory and the continuum gradient elasticity theory with damping, with consideration of micro-stiffness and micro-inertia effects. Both cases of a column with two rotating masses attached at its top and bottom, and of a column fixed at its base carrying a rotating mass at its free top, are considered. The presence of both micro-stiffness and micro-inertia effects helps to explain the observed natural frequency shift to the left or to the right of the classical values depending on the nature of interparticle forces (repulsive or attractive) due to particle charge. A method for using resonance column tests to determine not only the shear modulus but also the micro-stiffness and micro-inertia coefficients of gradient elasticity for fine-grained materials is proposed.
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•The performance of etched FBGs as refractive index sensors is studied both theoretically and experimentally.•The etching process is modeled and analytic expressions for the heating and etching rates ...are provided.•The etched FBGs are utilized as liquid level sensors for liquids with lower and higher RI than that of the fiber core.•In both cases, analytic expressions are provided which enable the direct calculation of the submersion length.
In this work, a theoretical and experimental study of the effect of the etching process on the properties of fiber Bragg gratings (FBGs) used as refractive index sensors is presented. The theoretical study addresses the dependence of the effective refractive index on the cladding thickness of the etched FBG. The results of this study show that as the cladding thickness is reduced, the effective refractive index decreases exponentially. Based on this result, a simple analytic expression between the effective refractive index and the radius of the etched FBG was developed. Thus, the radius of the FBG after the etching process can be determined directly from the shift of the Bragg wavelength, without the need of extensive numerical simulations. Also, the sensitivity of the FBG sensor in characteristic environments of practical interest has been calculated as a function of the fiber radius, and found to be described by simple analytic functions. The time evolution of the Bragg wavelength during the etching process has also been investigated, both experimentally and theoretically. By means of detailed theoretical analysis of the experimental results, the heating and the etching rate of the FBG was calculated. Finally, the etched FBGs have been used as liquid level sensors for water and oil, having refractive indices lower and higher than the fiber core respectively. The analysis of the experimental results was based on the shift of the diffracted wavelength in the case of water and on the reduction of the reflected power in the case of oil.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Most of the mechnoregulatory computational models appearing so far in tissue engineering for bone healing predictions, utilize as regulators for cell differentiation mainly the octahedral volume ...strains and the interstitial fluid velocity calculated at any point of the fractured bone area and controlled by empirical constants concerning these two parameters. Other stimuli like the electrical and chemical signaling of bone constituents are covered by those two regulatory fields. It is apparent that the application of the same mechnoregulatory computational models for bone healing predictions in scaffold-aided regeneration is questionable since the material of a scaffold disturbs the signaling pathways developed in the environment of bone fracture. Thus, the goal of the present work is to evaluate numerically two fields developed in the body of two different compressed scaffolds, which seem to be proper for facilitating cell sensing and improving cell viability and cell seeding efficiency. These two fields concern the surface octahedral strains that the cells attached to the scaffold can experience and the internal strain gradients that create electrical pathways due to flexoelectric phenomenon. Both fields are evaluated with the aid of the Boundary Element Method (BEM), which is ideal for evaluating with high accuracy surface strains and stresses as well as strain gradients appearing throughout the analyzed elastic domain.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
CERN is currently investigating the feasibility of a future collider - the Future Circular Collider (FCC) - as a potential successor of the Large Hadron Collider (LHC), providing scientists with a ...powerful discovery tool in the field of high energy physics. INFN developed the main 16 T Nb 3 Sn dipole of the FCC based on the cos-theta coil design. The baseline design of the superconducting magnet adopts the bladder-and-key concept and includes 4-layered asymmetric coils, an aluminum shell and a welded stainless-steel skin. The scope of this collaborative work between INFN, CERN, UPATRAS and FEAC, is to validate and further study the baseline design. This paper describes the design concept and the fully parametric multi-physics finite and boundary element (FEM and BEM) model. The baseline assembly parameters are presented while the study of geometrical, material and assembly parameters, unveils the optimized structure.
The issues of surface crack depth determination and the evaluation of repair effectiveness are not trivial for concrete engineers. In the present paper, surface waves are applied on concrete blocks ...with artificial slots to correlate wave parameters with crack depth. To simulate crack repair with an injected material, epoxy is applied to the slots in the laboratory and quantification of the filling percentage is attempted. Simultaneously, a frequency domain boundary element method is employed for the numerical simulation of transient pulses interacting with surface breaking cracks. Experimental results compare well with the numerical ones, showing that the repair effectiveness, which so far can be evaluated only by destructive techniques, is possible by simple surface wave measurements.
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An advanced Boundary Element method (BEM) accelerated via Adaptive Cross Approximation (ACA) and Hierarchical Matrices (HM) techniques is presented for the solution of large-scale elastostatic ...problems with multi-connected domains like in fiber reinforced composite materials. Although the proposed ACA/ BEM is demonstrated for two-dimensional (2D) problems, it is quite general and it can be used for 3D problems. Different forms of ACA technique are employed for exploring their efficiency when they combined with a BEM code. More precisely, the fully and partially pivoted ACA with and without recompression are utilized, while the solution of the final linear system of equations is accelerated via an iterative GMRES solver. The proposed methodology is demonstrated with the solution of large scale, plane strain elastic problems dealing with the bending of unidirectional fiber composite plates with large numbers of periodically or randomly distributed cylindrical elastic fibers embedded in a matrix medium.
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