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1
Savoia, Marco, and Nerio Tullini. "Beam theory for strongly orthotropic materials." International Journal of Solids and Structures 33, no. 17 (July 1996): 2459–84. http://dx.doi.org/10.1016/0020-7683(95)00163-8.
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Kellermann, D. C., T. Furukawa, and D. W. Kelly. "Strongly orthotropic continuum mechanics and finite element treatment." International Journal for Numerical Methods in Engineering 76, no. 12 (December 17, 2008): 1840–68. http://dx.doi.org/10.1002/nme.2379.
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Amir, S. "Orthotropic patterns of visco-Pasternak foundation in nonlocal vibration of orthotropic graphene sheet under thermo-magnetic fields based on new first-order shear deformation theory." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 233, no. 2 (September 22, 2016): 197–208. http://dx.doi.org/10.1177/1464420716670929.
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In the present research, vibration and instability of orthotropic graphene sheet subjected to thermo-magnetic fields are investigated. Orthotropic visco-Pasternak foundation is considered to analyze the influences of orthotropy angle, damping coefficient, normal and shear modulus. New first-order shear deformation theory is utilized due to accuracy of its polynomial functions compared to other theories of plate. Motion equations are obtained by means of Hamilton’s principle and then solved analytically. Influences of various parameters such as small scale, magnetic field, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of single layer graphene sheet on the vibration characteristics of nanoplate are discussed in detail. The results indicate that the stability of single layer graphene sheet is strongly dependent on applied magnetic field. Therefore, the mechanical behavior of single layer graphene sheet can be improved by applying magnetic field. The results of this investigation can be used in design and manufacturing of micro/nano mechanical systems.
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Sobota, P. M., and K. A. Seffen. "Bistable polar-orthotropic shallow shells." Royal Society Open Science 6, no. 8 (August 2019): 190888. http://dx.doi.org/10.1098/rsos.190888.
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We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in order to enhance morphing structures. The material law causes stress singularities when the circumferential stiffness is smaller than the radial stiffness ( β < 1), requiring a careful choice of the trial functions in our Ritz approach, which employs a higher-order geometrically nonlinear analytical model. Bistability is found to strongly depend on the orthotropic ratio, β , and the in-plane support conditions. An investigation of their interaction offers a new perspective on the effect of the hoop stiffness on bistability: while usually perceived as promoting, it is shown to be only stabilizing insofar as it prevents radial expansions; however, if in-plane supports are present, it becomes a redundant feature. Closed-form approximations of the bistable threshold are then provided by single-curvature-term approaches. For significantly stiffer values of the radial stiffness, a strong coupling of the orthotropic ratio and the support conditions is revealed: while roller-supported shells are monostable, fixed-pinned ones are most disposed to stable inversions; insight is given by comparing to a simplified beam model. Eventually, we show that cutting a central hole is a suitable method to deal with stress singularities: while fixed-pinned shells are barely affected by a hole, the presence of a hole strongly favours bistable inversions in roller-supported shells.
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Zarandi, Somayeh, Hsiang-Wei Lai, Yun-Che Wang, and Sergey Aizikovich. "Residual Stress Analysis of an Orthotropic Composite Cylinder under Thermal Loading and Unloading." Symmetry 11, no. 3 (March 4, 2019): 320. http://dx.doi.org/10.3390/sym11030320.
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Elastoplastic analysis of a composite cylinder, consisting of an isotropic elastic inclusion surrounded by orthotropic matrix, is conducted via numerical parametric studies for examining its residual stress under thermal cycles. The matrix is assumed to be elastically and plastically orthotropic, and all of its material properties are temperature-dependent (TD). The Hill’s anisotropic plasticity material model is adopted. The interface between the inclusion and matrix is perfectly bonded, and the outer boundary of the cylinder is fully constrained. A quasi-static, uniform temperature field is applied to the cylinder, which is analyzed under the plane-strain assumption. The mechanical responses of the composite cylinder are strongly affected by the material symmetry and temperature-dependent material properties. When the temperature-independent material properties are assumed, larger internal stresses at the loading phase are predicted. Furthermore, considering only yield stress being temperature dependent may be insufficient since other TD material parameters may also affect the stress distributions. In addition, plastic orthotropy inducing preferential yielding along certain directions leads to complex residual stress distributions when material properties are temperature-dependent.
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Fink, Marcel, Olaf Andersen, Torsten Seidel, and André Schlott. "Strongly Orthotropic Open Cell Porous Metal Structures for Heat Transfer Applications." Metals 8, no. 7 (July 19, 2018): 554. http://dx.doi.org/10.3390/met8070554.
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For modern thermal applications, open cell porous metals provide interesting opportunities to increase performance. Several types of cellular metals show an anisotropic morphology. Thus, using different orientations of the structure can boost or destroy the performance in thermal applications. Examples of such cellular anisotropic structures are lotus-type structures, expanded sheet metal, and metal fiber structures. Lotus-type structures are made by casting and show unidirectional pores, whereas expanded sheet metal structures and metal fiber structures are made from loose semi-finished products that are joined by sintering and form a fully open porous structure. Depending on the type of structure and the manufacturing process, the value of the direction-dependent heat conductivity may differ by a factor of 2 to 25. The influence of the measurement direction is less pronounced for the pressure drop; here, the difference varies between a factor of 1.5 to 2.8, depending on the type of material and the flow velocity. Literature data as well as own measurement methods and results of these properties are presented and the reasons for this strongly anisotropic behavior are discussed. Examples of advantageous applications, for example a latent heat storage device and a heat exchanger, where the preferential orientations are exploited in order to gain the full capacity of the structure’s performance, are introduced.
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A., Jayantha Pasdunkorale, and Ian W. Turner. "Generalised finite volume strategies for simulating transport in strongly orthotropic porous media." ANZIAM Journal 44 (April 1, 2003): 443. http://dx.doi.org/10.21914/anziamj.v44i0.690.
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Kunte, M. V., and Venkata R. Sonti. "Asymptotic wavenumber expansions of a strongly orthotropic fluid-filled circular cylindrical shell." Wave Motion 50, no. 3 (April 2013): 402–14. http://dx.doi.org/10.1016/j.wavemoti.2012.10.003.
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Filiou, C., and C. Soutis. "Approximate Biaxial Stress Solution for Orthotropic Open-Hole Composite Laminates." Advanced Composites Letters 5, no. 4 (July 1996): 096369359600500. http://dx.doi.org/10.1177/096369359600500402.
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A simple approximate solution has been derived for the stress distribution near a circular hole applicable to any orthotropic composite laminate subjected to biaxial loading. The degree of accuracy of this solution was found to be overall acceptable, but strongly dependent upon the laminate lay-up and biaxiality ratio.
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Cansiz, Baris, Hüsnü Dal, and Michael Kaliske. "Computational modeling of cardiac tissue with strongly coupled electromechanics and orthotropic viscoelastic effects." PAMM 14, no. 1 (December 2014): 119–20. http://dx.doi.org/10.1002/pamm.201410047.
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Turner, C. H., and S. C. Cowin. "Errors Induced by Off-Axis Measurement of the Elastic Properties of Bone." Journal of Biomechanical Engineering 110, no. 3 (August 1, 1988): 213–15. http://dx.doi.org/10.1115/1.3108433.
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Misalignment between the axes of measurement and the material symmetry axes of bone causes error in anisotropic elastic property measurements. Measurements of Poisson’s ratio were strongly affected by misalignment errors. The mean errors in the measured Young’s moduli were 9.5 and 1.3 percent for cancellous and cortical bone, respectively, at a misalignment angle of 10 degrees. Mean errors of 1.1 and 5.0 percent in the measured shear moduli for cancellous and cortical bone, respectively, were found at a misalignment angle of 10 degrees. Although, cancellous bone tissue was assumed to have orthotropic elastic symmetry, the possibility of the greater symmetry of transverse isotropy was investigated. When the nine orthotropic elastic constants were forced to approximate the five transverse isotropic elastic constants, errors of over 60 percent were introduced. Therefore, it was concluded that cancellous bone is truly orthotropic and not transversely isotropic. A similar but less strong result for cortical bone tissue was obtained.
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Colli Franzone, Piero, Luca F. Pavarino, and Simone Scacchi. "Bioelectrical effects of mechanical feedbacks in a strongly coupled cardiac electro-mechanical model." Mathematical Models and Methods in Applied Sciences 26, no. 01 (November 2, 2015): 27–57. http://dx.doi.org/10.1142/s0218202516500020.
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The aim of this work is to investigate by means of numerical simulations the effects of myocardial deformation due to muscle contraction on the bioelectrical activity of the cardiac tissue. The three-dimensional electro-mechanical model considered consists of the following four components: the quasi-static orthotropic finite elasticity equations for the deformation of the cardiac tissue; the active tension model for the intracellular calcium dynamics and cross-bridge binding; the orthotropic Bidomain model for the electrical current flow through the tissue; the membrane model of the cardiac myocyte, including stretch-activated currents (I SAC ). In order to properly take into account cardiac mechanical feedbacks, the electrical current flow is described in a strongly coupled framework by the Bidomain model on the deformed tissue. We then derive a novel formulation of the Bidomain model in the reference configuration, with complete mechanical feedbacks affecting not only the conductivity tensors but also a convective term depending on the velocity of the deformation. The numerical simulations are based on our finite element parallel solver, which employs both Multilevel Additive Schwarz preconditioners for the solution of linear systems arising from the discretization of the Bidomain equations and Newton–Krylov-Algebraic Multigrid methods for the solution of nonlinear systems arising from the discretization of the finite elasticity equations. The results have shown that: (i) the I SAC current prolongs action potential duration (APD) of about 10–15 ms; (ii) the inclusion into the model of both I SAC current and the convective term reduces the dispersion of repolarization of about 7% (from 139 to 129 ms) and increases the dispersion of APD about three times (from 13 to 45 ms). These effects indicate that mechanical feedbacks might influence arrhythmogenic mechanisms when combined with pathological substrates.
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Rossovskii, L. E., and A. L. Tasevich. "The first boundary-value problem for strongly elliptic functional-differential equations with orthotropic contractions." Mathematical Notes 97, no. 5-6 (May 2015): 745–58. http://dx.doi.org/10.1134/s0001434615050090.
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Kergaßner, Andreas, Johannes A. Koepf, Matthias Markl, Carolin Körner, Julia Mergheim, and Paul Steinmann. "A Novel Approach to Predict the Process-Induced Mechanical Behavior of Additively Manufactured Materials." Journal of Materials Engineering and Performance 30, no. 7 (April 12, 2021): 5235–46. http://dx.doi.org/10.1007/s11665-021-05725-0.
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AbstractThe grain structure and texture of additively manufactured materials depend strongly on the local temperature gradients during the solidification of the material. These grain structures and textures influence the mechanical behavior, ranging from isotropy to transversal and orthotropic symmetry. In the present contribution, a cellular automaton is used to model the grain growth during selective electron beam melting. The resulting grain structures and textures serve as input for a mesoscopic mechanical model. The mechanical behavior on the mesoscale is modeled by means of gradient-enhanced crystal plasticity, applying the finite element method. Computational homogenization is applied to determine the resulting macroscopic elastic and plastic properties of the additively manufactured metals. A general orthotropic yield criterion is identified by means of the initial yield loci computed with mesoscopic simulations of representative volume elements. The numerical results are partly validated with experimental data.
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Pozorski, Zbigniew, Jolanta Pozorska, Ireneusz Kreja, and Łukasz Smakosz. "On Wrinkling in Sandwich Panels with an Orthotropic Core." Materials 14, no. 17 (September 3, 2021): 5043. http://dx.doi.org/10.3390/ma14175043.
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This paper deals with the local loss of stability (wrinkling) problem of a thin facing of a sandwich panel. Classical solutions to the problem of a facing instability resting on a homogeneous and isotropic substructure (a core) are compared. The relations between strain energy components associated with different forms of core deformations are discussed. Next, a new solution for the orthotropic core is presented in detail, which is consistent with the classic solution for the isotropic core. Selected numerical examples confirm the correctness of the analytical formulas. In the last part, parametric analyses are carried out to illustrate the sensitivity of wrinkling stress to a change in the material parameters of the core. These analyses illustrate the possibility of using the equations derived in the article for the variability of Poisson’s ratio from −1 to 1 and for material parameters strongly deviating from isotropy.
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Walker, C. A., and Jamasri. "The Characterization of Mixed-Mode Energy Release Rates in Orthotropic Materials." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 210, no. 1 (January 1996): 33–42. http://dx.doi.org/10.1243/pime_proc_1996_210_167_02.
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The aim of this work was to predict, from the material constants, mixed-mode energy release rates in orthotropic materials, in particular the general cases in which the crack is aligned at a random angle to the principal material direction, normal to the plane of orthotropy. Two-dimensional finite element models with various fibre orientations were generated. The finite element models were validated by comparing two sets of contour plots of deformation, one resulting from the finite element analysis and the other from moiré interferograms of the experimental work. On comparison there was shown to be a strict similarity between experimentally determined and computational deformation fields. Variations of the energy release rates were investigated for both rapid and stable crack growth. This was accomplished by generating two-dimensional stable crack growth finite element models. In general, energy release rates were found to be strongly affected by the fibre orientation. An increase of the angle of the crack growth direction caused a decrease of the mode I energy release rate and, by contrast, an increase of the mode II energy release rate, but the mode II energy release rate was always a small fraction of the mode I value. Crack extension caused a gradual increase of the mode I energy release rate both for coplanar and non-coplanar crack growth. However, there was no significant effect found on the mode II energy release rate.
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Hidayat, Syarif, Bambang K. Hadi, Hendri Syamsudin, and Sandro Mihradi. "Stress-Distribution around Pin-Loaded Hole for Orthotropic Laminates." Applied Mechanics and Materials 842 (June 2016): 53–60. http://dx.doi.org/10.4028/www.scientific.net/amm.842.53.
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Stresses were calculated for orthotropic laminate plate loaded by a frictionless pin in a circular hole of the same diameter. These calculations were based on finite-element analysis for five laminates; 00, [±450]s, [00/900]s,[00/±450]s, and quasi-isotropic [00/±450/900]s. stress distribution, based on nominal bearing stress, were determined for wide ranges of the ratios of width to diameter and edge distance to diameter. Orthotropic had a significant influence on both the magnitude and location of the maximum tensile stress concentration on the boundary of the hole. The laminates with 00 plies developed the peak tensile stress near the ends of the pin-hole contact arc. But the ±450 laminates had peaks where ply fiber were tangent to the hole. The finite width and edge distances strongly influenced the tensile stress concentration. In contrast, the finite widths and edge distances had little effect on bearing stress concentration. For the practical range w/d = 2, the peak tensile stresses were as much as 50 percent larger than the infinite-laminate value. For e/d=1, these stresses were greater 60 percent than infinite-laminate value. In contrast, the finite width and edge distance had little effect on bearing stress concentrations.
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Yang, Qian, Yan Ping Kong, and Jin Xi Liu. "Love Waves in a Piezoelectric Half-Space with an Anisotropic Elastic Layer." Applied Mechanics and Materials 117-119 (October 2011): 1160–63. http://dx.doi.org/10.4028/www.scientific.net/amm.117-119.1160.
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This work is concerned with the dispersion characteristics of Love waves propagating in a layered structure consisting of an anisotropic elastic layer and a piezoelectric half-space. The layer processes one symmetric plane, while the half-space is transversely isotropic. The explicit dispersion equation is derived. As an example, an inclined orthotropic material is chosen as an elastic layer to reveal the effect of material anisotropy on the dispersion behaviors. The numerical results show that the phase velocity is strongly influenced by the anisotropic degree.
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Tasevich, A. L. "Smoothness of Generalized Solutions of the Dirichlet Problem for Strongly Elliptic Functional Differential Equations with Orthotropic Contractions." Journal of Mathematical Sciences 233, no. 4 (July 23, 2018): 541–54. http://dx.doi.org/10.1007/s10958-018-3942-6.
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Arani, A. Ghorbanpour, E. Haghparast, and Z. Khoddami Maraghi. "Vibrational response of coupled orthotropic protein microtubules immersed in cytosol considering small-scale and surface effects." Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems 231, no. 3 (June 16, 2017): 131–39. http://dx.doi.org/10.1177/2397791417712851.
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In this research, orthotropic Euler–Bernoulli beam and Timoshenko beam models are developed to investigate vibrational behavior of coupled protein microtubules. Microtubules are hollow cylindrical filaments in the living cells which are surrounded by filament network, which is simulated by Winkler–Riley Model. Temperature-dependent material properties for microtubules are used to study the thermal effect on vibration frequency. To apply the size effect, nonlocal theory is utilized, and the motion equations are derived based on Hamilton’s principle. In order to examine reliability of presented study, effects of various parameters such as environmental conditions, temperature change, boundary conditions and small-scale parameters on vibration characteristics of isotropic and orthotropic microtubules for both Euler–Bernoulli beam and Timoshenko beam models are discussed in detail. Results revealed that dynamic behavior of coupled microtubules is strongly dependent on the surface elasticity modulus of cytosol, so that, increasing surface elasticity modulus leads to increase in frequency of coupled microtubules. Results of this investigation can be provided as a useful reference in bio-medical clinical application.
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Luo, Ying, and Zi Ping Wang. "Fabrication and Performance Evaluation of OPCM Array Transducer." Applied Mechanics and Materials 83 (July 2011): 109–15. http://dx.doi.org/10.4028/www.scientific.net/amm.83.109.
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Orthotropic piezoelectric compose material (OPCM) is used as functional material for a new OPCM array transducer which can be applied in a wide range of fields such as natural gas, power industry, aero-space, and other non-destructive evaluation fields. The development of ultrasonic array transducer is still in the initial stages and it can be strongly enhanced by using design tools. The transducer is designed by flat construction and composed of backing layer, OPCM array element and protective layer. A procedure and a specific constitutive model are presented in this work together with simulation of OPCM element transducer of general array parameters and matching layer thickness. Models are required for the design and fabrication of OPCM array transducer. Also the properties of frequency, impedance, directivity and relative sensitivity distribution are measured from calibration experiment. The OPCM array transducer is excited by voltage and the corresponding sensitivity analysis is presented. To frequency and impedance, the experimental results show that the bandwidth is increased and the effects of side and grating lobe are reduced by using the matching layer. The OPCM array transducer has orthotropic performance. This special performance can be used to actuate and sense the stress wave in special direction.
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Djokovic, Jelena M., and Ružica R. Nikolić. "Characteristic Parameters of Dynamic Crack Growth along the Interface between the Two Orthotropic Materials." Advanced Materials Research 452-453 (January 2012): 1184–89. http://dx.doi.org/10.4028/www.scientific.net/amr.452-453.1184.
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In this paper is analyzed the behavior of parameters that characterize the process of a dynamic crack growth along the interface between the two orthotropic materials. The emphasis is placed on the application of the fracture mechanics concept for the interfacial crack that propagates dynamically, at high speed. In this work is considered the behavior of the oscillation index, the traction resolution factor and the energy factor depending on the crack tip speed and the stifnesses ratio. The oscillatory index increases with the crack tip speed and tends to infinity when the crack speed approaches the Rayleigh wave speed of the less stiff of the two materials. The traction resolution factor depends strongly on the crack speed but weakly on the stiffness ratio. The behavior of the energy factor is completely different from the behavior of the traction resolution factor. Results provided in this paper can be used as a guide for micromechanical modeling of materials.
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Lo, K. Y., and Y. N. Lee. "Time-dependent deformation behaviour of Queenston shale." Canadian Geotechnical Journal 27, no. 4 (August 1, 1990): 461–71. http://dx.doi.org/10.1139/t90-061.
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New methods for simultaneous measurement of three orthogonal strains in time-dependent deformation under several stress systems are described. Results of an extensive series of tests on oriented specimens of Queenston shale, with known magnitude and direction of in situ stress, are reported, together with tests on other shales from southern Ontario. It is found that over the stress range expected in field problems, the swelling behaviour is orthotropic and highly stress dependent. The application of stress in one principal direction not only suppresses the swelling in that direction but also reduces the swelling in the orthogonal directions. A method for representing this strongly nonlinear behaviour is described. Key words: shales, Queenston shale, time-dependent deformation, stress dependency, three-dimensional swelling.
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YONEDA, KEISHI, AKIO YONEZU, HIROYUKI HIRAKATA, and KOHJI MINOSHIMA. "ESTIMATION OF ANISOTROPIC PLASTIC PROPERTIES OF ENGINEERING STEELS FROM SPHERICAL IMPRESSIONS." International Journal of Applied Mechanics 02, no. 02 (June 2010): 355–79. http://dx.doi.org/10.1142/s1758825110000536.
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This study proposes a method of reverse analysis to estimate the anisotropic plastic properties of engineering steels by spherical indentation. The method takes into consideration materials that obey the work-hardening law and show in-plane anisotropic yield stress. Finite element analysis was first carried out to compute the indentation behavior of such materials, showing that a permanent impression exhibited an anisotropic shape which was strongly dependent on the orthotropic axis. Based on the anisotropy of the impression geometry, we developed a simple approach to determine the yield stress, work-hardening exponent and yield stress ratio. The approach consists of several functions related to the parameters of two impression geometries, produced by dual spherical indentations with different indentation forces. Since the present method uses only two impression geometries and does not necessitate indentation force — displacement curves (indentation curves), it is a particularly useful technique to evaluate "indistinguishable materials" which are special sets of materials with distinct plastic properties, yet yield almost identical indentation curves.
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Grechka, Vladimir. "Multiple cracks in VTI rocks: Effective properties and fracture characterization." GEOPHYSICS 72, no. 5 (September 2007): D81—D91. http://dx.doi.org/10.1190/1.2751500.
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The existing fracture-characterization techniques are based on assuming the unfractured host rock either to be isotropic or the magnitudes of both the background and crack-induced anisotropies to be small. I relax both assumptions and examine the effective media caused by fractures with realistic (not small) crack densities in a strongly anisotropic, primarily transversely isotropic (TI) host rock. The analysis of penny-shaped cracks in the noninteraction approximation (NIA) reveals the dependence of their excess fracture compliance tensors on the orientation of the background symmetry axis. As a result of this dependence, the excess fracture compliance tensor generally becomes rotationally noninvariant even when the cracks are circular. One of the consequences of this complication (compared to the background isotropy) is a reduction of symmetry from TI to monoclinic resulting from the presence of a single oriented fracture set. Verti–cal dry cracks in a vertically transversely isotropic (VTI) host constitute an important exception to this general rule.The effective symmetry for this arrangement is approximately orthorhombic (or orthotropic) even in the presence of multiple fracture sets that have arbitrary azimuths. I perform finite-element simulations on the so-called digital rocks to verify both the proximity of effective symmetry to orthotropy and the accuracy of the NIA up to the crack density of 0.15. Multiple sets of dry vertical cracks in a VTI host not only result in nearly orthorhombic effective symmetry but also their cumulative influence is equivalent to that of just two orthogonal (or principal) fracture sets. The possibility of replacing multiple fracture sets with two orthogonal ones paves the way for their characterization. The inverse problem of estimating the parameters of two orthogonal crack systems in a VTI background from the effective elasticity, however, is known to be nonunique. I suggest overcoming its ambiguity by combining 3D, wide-azimuth, multicomponent seismic data with sonic logs.
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Taber, Larry A., and Jay D. Humphrey. "Stress-Modulated Growth, Residual Stress, and Vascular Heterogeneity." Journal of Biomechanical Engineering 123, no. 6 (July 25, 2001): 528–35. http://dx.doi.org/10.1115/1.1412451.
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A simple phenomenological model is used to study interrelations between material properties, growth-induced residual stresses, and opening angles in arteries. The artery is assumed to be a thick-walled tube composed of an orthotropic pseudoelastic material. In addition, the normal mature vessel is assumed to have uniform circumferential wall stress, which is achieved here via a mechanical growth law. Residual stresses are computed for three configurations: the unloaded intact artery, the artery after a single transmural cut, and the inner and outer rings of the artery created by combined radial and circumferential cuts. The results show that the magnitudes of the opening angles depend strongly on the heterogeneity of the material properties of the vessel wall and that multiple radial and circumferential cuts may be needed to relieve all residual stress. In addition, comparing computed opening angles with published experimental data for the bovine carotid artery suggests that the material properties change continuously across the vessel wall and that stress, not strain, correlates well with growth in arteries.
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Florisson, Sara, Johan Vessby, Winston Mmari, and Sigurdur Ormarsson. "Three-dimensional orthotropic nonlinear transient moisture simulation for wood: analysis on the effect of scanning curves and nonlinearity." Wood Science and Technology 54, no. 5 (August 14, 2020): 1197–222. http://dx.doi.org/10.1007/s00226-020-01210-4.
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Abstract This paper introduces, with the development of user-subroutines in the finite-element software Abaqus FEA®, a new practical analysis tool to simulate transient nonlinear moisture transport in wood. The tool is used to revisit the calibration of moisture simulations prior to the simulation of mechanical behaviour in bending subjected to climate change. Often, this calibration does not receive sufficient attention, since the properties and mechanical behaviour are strongly moisture dependent. The calibration of the moisture transport simulation is made with the average volumetric mass data experimentally obtained on a paired specimen of Norway spruce (Picea abies) with the dimensions $$30\times 15\times 640\, {\mathrm{mm}}^{3}$$ 30 × 15 × 640 mm 3 . The data, from a 90-day period, were measured under a constant temperature of 60 °C and systematic relative humidity cycles between 40 and 80%. A practical method based on analytical expressions was used to incorporate hysteresis and scanning behaviour at the boundary surface. The simulation tool makes the single-Fickian model and Neumann boundary condition readily available and the simulations more flexible to different uses. It also allows for a smoother description of inhomogeneity of material. The analysis from the calibration showed that scanning curves associated with hysteresis cannot be neglected in the simulation. The nonlinearity of the analysis indicated that a coherent set of moisture dependent diffusion and surface emission coefficient is necessary for the correct description of moisture gradients and mass transport.
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Clauß, Sebastian, Corina Pescatore, and Peter Niemz. "Anisotropic elastic properties of common ash (Fraxinus excelsior L.)." Holzforschung 68, no. 8 (December 1, 2014): 941–49. http://dx.doi.org/10.1515/hf-2013-0189.
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Abstract Hardwoods in principle show a similar orthotropic behavior as softwoods; however, the ratios of the mechanical parameters between the three anatomical directions and their magnitudes are different and depend strongly on the individual microstructure of the species. The aim of the current study was to characterize the 3-D elastic behavior of common ash (Fraxinus excelsior L.) by tensile, compression, and shear tests in the three anatomical directions and stepwise in between, by means of a universal testing machine in combination with a digital image correlation technique. Young’s moduli, shear moduli, and Poisson’s ratios have been determined for the different load directions. From studies on the radial-tangential plane of other wood species, it is known that the elastic moduli in the principal directions and the off-axis elastic moduli vary in a nonlinear correlation, depending on density gradients between earlywood and latewood. This angular dependency has been experimentally and theoretically proven for ash. Furthermore, the dependency of mechanical parameters on the fiber-load angle has been experimentally determined. The measurements for principal and off-axis load directions provide a sound basis for modeling of hardwood structures.
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Venuti, Fiammetta. "Influence of pattern anisotropy on the structural behaviour of free-edge single-layer gridshells." Curved and Layered Structures 8, no. 1 (January 1, 2021): 119–29. http://dx.doi.org/10.1515/cls-2021-0011.
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Abstract Free-edge gridshells represent the majority of built gridshells. Indeed, the gridshell reference geometry usually needs to be trimmed in order to provide building access or to insert the gridshell within an existing building, giving rise to one or more elastic boundaries. Despite the current design practice, so far a very limited number of scientific studies has been devoted to investigate the influence of elastic boundaries on the overall structural behaviour of gridshells. This paper focuses on the effects of the orientation of the boundary structure with respect to the grid direction. This is done by studying the buckling behaviour of an ideal single-layer steel gridshell, for different grid layout (quadrangular, hybrid, triangular) and orientation. The results of the parametric study demonstrate that the sensitivity of free-edge single-layer gridshells to the free-edge orientation strongly depends on the grid pattern. In particular, isotropic gridshells have shown an almost negligible influence of the free-edge orientation in terms of buckling load, in opposition to orthotropic gridshells. Moreover, the change in free-edge orientation induces significant variations of the global structural stiffness for all the layouts, resulting in possibly unacceptable displacements in service conditions.
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Junhao, Xu, Zhang Yingying, and Xue Jigang. "Off-axial failure analysis of polytetrafluoroethylene-coated woven glass fibers under different loading rates." Journal of Industrial Textiles 47, no. 3 (April 27, 2016): 310–30. http://dx.doi.org/10.1177/1528083716647198.
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This paper presents the research on off-axial tensile behaviors of polytetrafluoroethylene-coated woven glass fibers under different loading rates. First, groups of off-axial tensile tests were carried out, and the corresponding failure mechanisms were analyzed. Then, the effect of loading rate on the tensile behaviors of off-axial specimens was studied. Finally, several current strength criteria were compared to predict the material failure strength under different loading rates. Results show the tensile behaviors of polytetrafluoroethylene-coated woven glass fibers are typical orthotropic. The material failure strength is strongly related with failure modes and yarn orientations. Three typical failure modes are observed in the tests, including interface failure, yarn breakage, and composite failure. The loading rate has significant effects on the material tensile strength and the elongation at break. With loading rate increasing, the tensile strength increases and the elongation at break decreases. The tensile strength shows a good linear correlation with the loading rate’s logarithm. Most of current quadratic strength criteria can be used to predict the material failure strength, except for the specimens of small bias angles. This is because traditional quadratic criteria are always based on the strain energy theory of homogeneous materials, which may not reflect the failure mechanisms of coated fabrics and other important details.
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Kardomateas, G. A. "Koiter-Based Solution for the Initial Post-buckling Behavior of Moderately Thick Orthotropic and Shear Deformable Cylindrical Shells Under External Pressure." Journal of Applied Mechanics 64, no. 4 (December 1, 1997): 885–96. http://dx.doi.org/10.1115/1.2788996.
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The initial post-buckling behavior of moderately thick orthotropic shear deformable cylindrical shells under external pressure is studied by means of Koiter’s general post-buckling theory. To this extent, the objective is the calculation of imperfection sensitivity by relating to the initial post-buckling behavior of the perfect structure, since it is generally recognized that the presence of small geometrical imperfections in some structures can lead to significant reductions in their buckling strengths. A shear deformation theory, which accounts for transverse shear strains and rotations about the normal to the shell midsurface, is employed to formulate the shell equations. The initial post-buckling analysis indicates that for several combinations and geometric dimensions, the shell under external pressure will be sensitive to small geometrical imperfections and may buckle at loads well below the bifurcation predictions for the perfect shell. On the other hand, there are extensive ranges of geometrical dimensions for which the shell is insensitive to imperfections, and, therefore it would exhibit stable post-critical behavior and have a load-carrying capacity beyond the bifurcation point. The range of imperfection sensitivity depends strongly on the material anisotropy, and also on the shell thickness and whether the end pressure loading is included or not. For example, for the circumferentially reinforced graphite/epoxy example case studied, it was found that the structure is not sensitive to imperfections for values of the Batdorf length parameter z˜ above ≃270, whereas for the axially reinforced case the structure is imperfection-sensitive even at the high range of length values; for the isotropic case, the structure is not sensitive to imperfections above z˜ ≃ 1000.
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Yang, Ping, and Ying Tong. "Constitutive Modelling for Anisotropic Damage in Woven E-Glass Reinforcements." Open Materials Science Journal 11, no. 1 (April 28, 2017): 9–21. http://dx.doi.org/10.2174/1874088x01711010009.
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It is easy for composite laminates to be damaged by relative lower velocity impact which could give rise to internal delamination that will strongly weaken the compressive strength of laminates. In order to predict the occurrence of matrix failure, the elastic-brittle behaviors of fiber-reinforced composites were modeled constitutively by an anisotropic damage model. The dynamic tensile testing was performed at a constant velocity of 2 mm/min until the sample broke to achieve the mechanical parameters of E-glass reinforcements. The elastic constitutive equation and the constitutive damage model were obtained on basis of the fundamental theory of mechanics about the orthotropic constitutive of reinforcements. The methodology for this constitutive model which is developed by Hashin considered both the effect of fiber and matrix failure. Then, the developed constitutive equations were incorporated into the FE (finite element) codes, ABAQUS, through the user subroutine module to simulate the process of projectile impacting GFRP composite laminates. The results show that the material deformation reaches a maximum at 24 μs, then occurs rebound with the increase of the time. The stress of reinforcements traverse section linearly increases outward from 0 MPa to 509.8 MPa. Material damage area increases with the prolonging of time, and for a fixed time, material damage gradually increases from the edges to the center and reaches a constant value of 1, which means the rupture of the damage process.
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Landkammer, Philipp, Andreas Loderer, Eugen Krebs, Benjamin Söhngen, Paul Steinmann, Tino Hausotte, Petra Kersting, Dirk Biermann, and Kai Willner. "Experimental Verification of a Benchmark Forming Simulation." Key Engineering Materials 639 (March 2015): 251–58. http://dx.doi.org/10.4028/www.scientific.net/kem.639.251.
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Forming of near-net-shaped and load-adapted functional components, as it is developed in theTransregionalCollaborative Research Centreon Sheet-Bulk Metal FormingSFB/TR73, causes different problems, which lead to non-optimal manufacturing results. For these high complex processes the prediction of forming effects can only be realized by simulations. A stamping process of pressing eight punches into a circular blank is chosen for the considered investigations. This reference process is designed to reflect the main aspects, which strongly affect the final outcome of forming processes. These are the orthotropic material behaviour, the optimal design of the initial blank and the influences of different contact and friction laws. The aim of this work is to verify the results of finite element computations for the proposed forming process by experiments. Evaluation methods are presented to detect the influence of the anisotropy and also to quantify the optimal blank design, which is determined by inverse form finding. The manufacturing accuracy of the die plate and the corresponding roughness data of the milled surface are analysed, whereas metrological investigations are required. This is accomplished by the help of advanced measurement techniques like a multi-sensor fringe projection system and a white light interferometer. Regarding the geometry of the punches, micromilling of the die plate is also a real challenge, especially due to the hardness of the high-speed steelASP2023(approx. 63 HRC). The surface roughness of the workpiece before and after the forming process is evaluated to gain auxiliary data for enhancing the friction modelling and to characterise the contact behaviour.
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Srivastava, P. K., P. Mahajan, P. K. Satyawali, and V. Kumar. "Observation of temperature gradient metamorphism in snow by X-ray computed microtomography: measurement of microstructure parameters and simulation of linear elastic properties." Annals of Glaciology 51, no. 54 (2010): 73–82. http://dx.doi.org/10.3189/172756410791386571.
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AbstractThe process of temperature gradient metamorphism in snow strongly affects the microstructure and associated mechanical properties of the snow. The purpose of this study was to: (1) examine the temporal variations in three-dimensional snow microstructure under the influence of a strong temperature gradient for 6 days using X-ray computed microtomography (μCT); and (2) numerically simulate the linear elastic properties of snow from microtomographic data using a voxel-based finite-element technique. The temporal changes in the snow structure were analyzed in terms of density, specific surface area (SSA), thickness distribution of ice matrix and pores, structure model index and mean intercept length (MIL) fabric tensor. The structural indices and orthotropic elastic compliance matrix were computed over several sub-volumes within the reconstructed volume to account for statistical uncertainties. The mean density increased by about 14% on day 1 and no significant trend was observed thereafter. The SSA decreased by 22%, whereas both the ice and pore thickness distributions widened with time. The computed Young’s moduli were 1.5–4 times larger than previously published dynamic measurements and found to be significantly correlated with ice volume fraction and MIL fabric measures. The increasing trend in computed moduli during the experiment is consistent with the observed development of thicker vertical ice structures. Multiple linear regression models of elastic compliances using fabric tensor formulation and ice volume fraction could explain 89.9–93.0% of the variance. Our results suggest a strong dependence of elastic properties on both density and microstructural fabric.
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Martin, Isabel, Diego Saenz del Castillo, Antonio Fernandez, and Alfredo Güemes. "Advanced Thermoplastic Composite Manufacturing by In-Situ Consolidation: A Review." Journal of Composites Science 4, no. 4 (October 13, 2020): 149. http://dx.doi.org/10.3390/jcs4040149.
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This article provides an overview of the evolution of the in-situ consolidation (ISC) process over time. This evolution is intimately linked with the advancements in each of the steps of the ISC manufacturing process, is additive in nature, and is limited by the orthotropic nature of composite materials and the physicochemical behavior of the thermoplastic matrix. This review covers four key topics: (a) Thermal models—simulation tools are critical to understand a process with such large spatial gradients and fast changes. Heating systems once marked a turning point in the development of industrial ISC systems. Today, lasers are the most recent trend, and there are three key issues being studied: The absorption of energy of light by the material, the laser profile, and the laser focusing. Several approaches have been proposed for the distributed temperature measurements, given the strong temperature gradients. (b) Adhesion—this refers to two subsequent mechanisms. In the first place, the process of intimate contact is one by which two surfaces of thermoplastic pre-impregnated composite materials are brought into contact under pressure and temperature. This enables closure of the existing gaps between the two microscopic irregular surfaces. This process is then followed by the healing or diffusion of polymer molecules across the interface. (c) Crystallinity—mostly influenced by the cooling rate, and strongly affects the mechanical properties. (d) Degradation—this refers to the potential irreversible changes in the polymer structure caused by the high temperatures required for the process. Degradation can be avoided through adequate control of the process parameters. The end goal of the ISC manufacturing process is to achieve a high product quality with a high deposition rate through an industrial process competitive with the current manufacturing process for thermoset composites.
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Knopf, Kevin B., Samantha Siegel, and Charles L. Bennett. "Avoidance of fulminant liver failure from hepatitis B reactivation with chemotherapy and immunotherapy: A value-based approach." Journal of Clinical Oncology 32, no. 30_suppl (October 20, 2014): 134. http://dx.doi.org/10.1200/jco.2014.32.30_suppl.134.
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134 Background: Fulminant liver failure (FLF) is a potentially fatal complication of hepatitis B reactivation in patients who receive rituximab and cytotoxic chemotherapy. Often patients receiving these regimens are treated with curative intent (e.g. diffuse large cell Non Hodgkin’s lymphoma, adjuvant chemotherapy for breast cancer) and thus avoidance of this complication is desirable. The only known treatment for fulminant liver failure is orthotropic liver transplant. We have developed a cost-effective approach to avoiding FLF. Methods: NCCN recommends screening for hepatitis B serologies in any patient who is to receive Rituximab therapy. Review of the literature regarding fulminant liver failure and cytotoxic chemotherapy revealed that the regimens most strongly associated with reactivation of HepB and fulminant liver failure included doxorubicin and high dose of cyclophosphamide—we have targeted Hepatitis B screening to patients receiving these two chemotherapy drugs. We target patients either felt to have a high probability of occult hepatitis B are screened—these include patients who have had a blood transfusion in a foreign country, those with a transfusion more than 20 years ago, and those patients where Hepatitis B can be passed vertically—including first and second generation Asian American immigrants. Patients deemed at high risk are checked for Hepatitis B surface Antigen and Hepatitis B Core antibodies. No routine imaging is performed. Patients who are HepBSag or HepBCoreAb positive who are to receive high risk chemo/immunotherapy are then started on entecavir 0.5 mg/d two weeks before starting therapy and this is continued for 6 months after completion of therapy. Patients who are HepBAg- and HepBCab+ are monitored with HBV DNA levels monthly during therapy with initiation of entecavir if HBV DNA becomes detectable. Results: Patients receiving chemo/immunotherapy associated with Hep B reactivation can be safely identified and given prophylactgic entecavir treatment. Conclusions: We have created a value-driven cost effective approach to minimizing FLF in patients receiving chemo/immunotherapy. Cost estimates based on US pricing will be presented.
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Xie, Shi Hui, Mi Mi Li, Mei Juan Zhou, Min Sun, and Shi Feng Huang. "Study on Acoustic Emission of 1-3 Orthotropic Cement Based Piezoelectric Sensors." Advanced Materials Research 487 (March 2012): 471–75. http://dx.doi.org/10.4028/www.scientific.net/amr.487.471.
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1-3 orthotropic cement based piezoelectric composites were fabricated by cut-filling and arrange-filling technique, using PZT-51 ceramic as functional material and cement as passive matrix. 1-3 orthotropic cement based piezoelectric composites were prepared into Acoustic Emission (AE) sensors, the attenuation of AE signal on the concrete and the response of different sensors on the concrete with increasing distance were researched. The results showed that the signal strength received by sensing element increases with the increasing PZT volume fraction; signal peaks and amplitude decrease gradually when the testing distance increases; signal strength received on the ceramic title is stronger than on the concrete; the attenuation of signal wave shape received on the concrete is much slower when compared with ceramic title.
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Profant, Tomáš, and Michal Kotoul. "On the Inclined Surface Crack Terminating at the Orthotropic Bimaterial Interface." Key Engineering Materials 385-387 (July 2008): 541–44. http://dx.doi.org/10.4028/www.scientific.net/kem.385-387.541.
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The evaluation of the stress singularities and generalised stress intensity factor (GSIF) for the case of an inclined surface crack terminating perpendicular to the interface between two orthotropic materials is considered. The knowledge of the regular and auxiliary solution allows evaluating the GSIF using the reciprocal theorem (Ψ-integral). A co-operating effect of a stronger and a weaker singular stress field for a crack impinging a bimaterial interface is investigated.
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Garbowski, Tomasz, Tomasz Gajewski, and Jakub Krzysztof Grabski. "Torsional and Transversal Stiffness of Orthotropic Sandwich Panels." Materials 13, no. 21 (November 6, 2020): 5016. http://dx.doi.org/10.3390/ma13215016.
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In the present work, an analytical equation describing the plate torsion test taking into account the transverse shear stiffness in sandwich plates is derived and numerically validated. Transverse shear becomes an important component if the analyzed plate or shell is thick with respect to the in-plane dimensions and/or its core has significantly lower stiffness than the outer faces. The popular example of such a sandwich plate is a corrugated cardboard, widely used in the packaging industry. The flat layers of a corrugated board are usually made of thicker (stronger) material than that used for the corrugated layer, the role of which is rather to keep the outer layers at a certain distance, to ensure high bending stiffness of the plate. However, the soft core of such a plate usually has a low transverse shear stiffness, which is often not considered in the plate analysis. Such simplification may lead to significant calculation errors. The paper presents the generalization of the Reissner’s analytical formula, which describes the torsional stiffness of the plate sample including two transverse shear stiffnesses. The paper also presents the implementation of the numerical model of the plate torsion test including the transverse shear stiffnesses. Both approaches are compared with each other on a wide range of material parameters and different aspect ratios of the specimen. It has been proved that both analytical and numerical formulations lead to an identical result. Finally, the performance of presented formulations is compared with other numerical models using commercial implementation of various Reissner–Mindlin shell elements and other analytical formulas from the literature. The comparison shows good agreement of presented theory and numerical implementation with other existing approaches.
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Gourgiotis, Panos A., and Davide Bigoni. "The dynamics of folding instability in a constrained Cosserat medium." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2093 (April 3, 2017): 20160159. http://dx.doi.org/10.1098/rsta.2016.0159.
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Different from Cauchy elastic materials, generalized continua, and in particular constrained Cosserat materials, can be designed to possess extreme (near a failure of ellipticity) orthotropy properties and in this way to model folding in a three-dimensional solid. Following this approach, folding, which is a narrow zone of highly localized bending, spontaneously emerges as a deformation pattern occurring in a strongly anisotropic solid. How this peculiar pattern interacts with wave propagation in the time-harmonic domain is revealed through the derivation of an antiplane, infinite-body Green’s function, which opens the way to integral techniques for anisotropic constrained Cosserat continua. Viewed as a perturbing agent, the Green’s function shows that folding, emerging near a steadily pulsating source in the limit of failure of ellipticity, is transformed into a disturbance with wavefronts parallel to the folding itself. The results of the presented study introduce the possibility of exploiting constrained Cosserat solids for propagating waves in materials displaying origami patterns of deformation. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’
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Doyle, Lucía, Ingo Weidlich, and Marcus Illguth. "Anisotropy in Polyurethane Pre-Insulated Pipes." Polymers 11, no. 12 (December 12, 2019): 2074. http://dx.doi.org/10.3390/polym11122074.
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The polyurethane foam in district heating pre-insulated pipes has a critical role to play both as thermal insulation and as load bearing element, as it serves as bond between the medium pipe and the casing. Hence, knowledge on how the foam behaves under multiaxial stresses is of great importance for the design as well as for aging predictions of the network. It is known that cell shape anisotropy in polymeric foams leads to anisotropy in its mechanical properties. In this study, we evaluate and quantify the microstructural anisotropy of PU foam from pre-insulated pipes as well as its mechanical behaviour under compression in the three orthogonal directions. We cover rigid and flexible PU foam, batch and continuous manufacturing, and different pipe diameters. The results were compared with those predicted by available rectangular and Kelvin cell shape models. We have found that PU from pre-insulated pipes is orthotropic and present stronger anisotropy than that typically found in PU slabs. The traditional bonded pipes under consideration behaved in a similar way. However, when comparing the two flexible pipes in this study, despite no significant differences in cell shape anisotropy were found, a significantly different behaviour for the E modulus ratio was observed. This shows that while the manufacturing process exerts the main influence on cell shape anisotropy, to explain the difference in stiffness behaviour other factors need to be taken into consideration, such as cell size and cell size variability.
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Gennaro, V. De, J. Canou, J. C. Dupla, and N. Benahmed. "Influence of loading path on the undrained behaviour of a medium loose sand." Canadian Geotechnical Journal 41, no. 1 (February 1, 2004): 166–80. http://dx.doi.org/10.1139/t03-082.
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The results of an experimental programme aimed at studying the undrained behaviour of Hostun sand are presented in this paper. Specific conditions concerning the initial relative density (medium loose arrangements) and the loading paths (compression and extension under monotonic and cyclic loadings) were considered in the test programme. Monotonic tests carried out in both drained and undrained conditions show a significant difference in behaviour between compression and extension. It is observed that, in undrained conditions, Hostun sand is weaker in extension than in compression. In compression, the material is stable (dilatant) and the phase-transformation state controls the mechanical behaviour. In extension, the experimental results show an unstable behaviour (contractant), with monotonic, liquefaction-induced instability in undrained conditions. The results of cyclic tests, carried out with one- and two-way stress reversals, show a good correlation with the results of monotonic tests. The loading path strongly influences the undrained mechanical behaviour of the sand, mainly by inducing liquefaction in extension. This situation suggests that differences in soil fabric, caused by the sample preparation technique (air pluviation), can influence the sand behaviour by inducing a significant contraction in extension. By further analysing the cyclic results, it is shown that, during unloading, the stress paths reflect the transverse isotropy (orthotropy) of the sand, with stiffer elastic characteristics in the vertical direction than in the horizontal direction.Key words: liquefaction, cyclic mobility, sands, triaxial test, anisotropy, loading path.
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Song, Weiju, Lingling Du, Yafei Zhang, Huimin Yin, and Changjiang Liu. "Strongly Nonlinear Damped Vibration of Orthotropic Membrane under Initial Displacement: Theory and Experiment." Journal of Vibration Engineering & Technologies, April 23, 2021. http://dx.doi.org/10.1007/s42417-021-00302-0.
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Yamada, Seishi, James G. A. Croll, and Nobuhisa Yamamoto. "Nonlinear Buckling of Compressed FRP Cylindrical Shells and Their Imperfection Sensitivity." Journal of Applied Mechanics 75, no. 4 (May 13, 2008). http://dx.doi.org/10.1115/1.2839894.
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An elastic, nonlinear, Ritz analysis has been developed to allow investigation of the imperfect behavior of axially compressed orthotropic fiber reinforced polymer cylindrical shells. In a particular mode, buckling loads are shown to be strongly influenced by the constitutive material coefficients and are sensitive to initial geometric imperfections. Just as for the previously analyzed isotropic cylindrical shells, the reduced stiffness criteria are shown to provide close lower bounds to the imperfection sensitive elastic buckling loads. The potential benefits in the use of the reduced stiffness theoretical results to allow specification of the optimal designs are illustrated.
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Tomar, Vikas. "Modeling of Dynamic Fracture and Damage in Two-Dimensional Trabecular Bone Microstructures Using the Cohesive Finite Element Method." Journal of Biomechanical Engineering 130, no. 2 (April 1, 2008). http://dx.doi.org/10.1115/1.2903434.
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Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Micro-finite-element models have been used to investigate the elastic and yield properties of trabecular bone but have only seen limited application in modeling the microstructure dependent fracture of trabecular bone. In this research, dynamic fracture in two-dimensional (2D) micrographs of ovine (sheep) trabecular bone is modeled using the cohesive finite element method. For this purpose, the bone tissue is modeled as an orthotropic material with the cohesive parameters calculated from the experimental fracture properties of the human cortical bone. Crack propagation analyses are carried out in two different 2D orthogonal sections cut from a three-dimensional 8mm diameter cylindrical trabecular bone sample. The two sections differ in microstructural features such as area fraction (ratio of the 2D space occupied by bone tissue to the total 2D space), mean trabecula thickness, and connectivity. Analyses focus on understanding the effect of the rate of loading as well as on how the rate variation interacts with the microstructural features to cause anisotropy in microdamage accumulation and in the fracture resistance. Results are analyzed in terms of the dependence of fracture energy dissipation on the microstructural features as well as in terms of the changes in damage and stresses associated with the bone architecture variation. Besides the obvious dependence of the fracture behavior on the rate of loading, it is found that the microstructure strongly influences the fracture properties. The orthogonal section with lesser area fraction, low connectivity, and higher mean trabecula thickness is more resistant to fracture than the section with high area fraction, high connectivity, and lower mean trabecula thickness. In addition, it is found that the trabecular architecture leads to inhomogeneous distribution of damage, irrespective of the symmetry in the applied loading with the fracture of the entire bone section rapidly progressing to bone fragmentation once the accumulated damage in any trabeculae reaches a critical limit.
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Childs, Dara W., and Clint R. Carter. "Rotordynamic Characteristics of a Five Pad, Rocker-Pivot, Tilting Pad Bearing in a Load-on-Pad Configuration; Comparisons to Predictions and Load-Between-Pad Results." Journal of Engineering for Gas Turbines and Power 133, no. 8 (April 6, 2011). http://dx.doi.org/10.1115/1.4000893.
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Rotordynamic data are presented for a rocker-pivot tilting pad bearing in load-on-pad (LOP) configuration for (345–3101 kPa) unit loads and speeds from 4000 rpm to 13,000 rpm. The bearing was directly lubricated through a leading edge groove with five pads, 0.282 preload, 60% offset, 57.87 deg pad arc angle, 101.587 mm (3.9995 in.) rotor diameter, 0.1575 mm (0.0062 in.) diametral clearance, and 60.325 mm (2.375 in.) pad length. Measured results were reported for this bearing by Carter and Childs (2008, “Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration,” ASME Paper No. GT2008-50069) in the load-between-pad (LBP) configuration. Results for the LOP are compared with predictions from a bulk-flow Navier–Stokes model (as utilized by San Andres (1991, “Effect of Eccentricity on the Force Response of a Hybrid Bearing,” STLE Tribol. Trans., 34, pp. 537–544)) and to the prior LBP results. Frequency effects on the dynamic-stiffness coefficients were investigated by applying dynamic-force excitation over a range of excitation frequencies. Generally, the direct real parts of the dynamic-stiffness coefficients could be modeled as quadratic functions of the excitation frequency, and accounted for by adding a mass matrix to the conventional [K][C] model to produce a frequency-independent [K][C][M] model. Measured added-mass terms in the loaded direction approached 60 kg. The static load direction in the tests was y. The direct stiffness coefficients Kyy and Kxx depend strongly on the applied unit load, more so than speed. They generally increased linearly with load, shifting to a quadratic dependence at higher unit loads. At lower unit loads, Kyy and Kxx increase monotonically with running speed. The experimental results were compared with predictions from a bulk-flow computational fluid dynamics analysis. Stiffness orthotropy was apparent in test results, significantly more than predicted, and it became more pronounced at the heavier unit loads. Measured Kyy values were consistently higher than predicted, and measured Kxx values were lower. Comparing the LOP results to prior measured LBP results for the same bearing, at higher loads, Kyy is significantly larger for the LOP configuration than LBP. Measured values for Kxx are about the same for LOP and LBP. At low unit loads, stiffness orthotropy defined as Kyy/Kxx is the same for LOP and LBP, progressively increasing with increasing unit loads. At the highest unit load, Kyy/Kxx=2.1 for LOP and 1.7 for LBP. Measured direct damping coefficients Cxx and Cyy were insensitive to changes in either load or speed, in contrast to predictions of marked Cyy sensitivity for changes in the load. Only at the highest test speed of 13,000 rpm were the direct damping coefficients adequately predicted. No frequency dependency was observed for the direct damping coefficients.