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This study aims to develop a viscoelastic database for muscles (VM: vastus medialis and Sr: sartorius) and subcutaneous adipose tissue with multifrequency magnetic resonance elastography (MMRE) coupled with rheological models. MMRE was performed on 13 subjects, at 70-90-110 Hz, to experimentally assess the elastic properties (μ) of passive and active (20% MVC) muscles. Then, numerical shear modulus (μ) and viscosity (η) were calculated using three rheological models (Voigt, Zener, Springpot). The elastic properties, obtained with the Springpot model, were closer to the experimental data for the different physiological tissues (μ_{Springpot_VM_Passive} = 3.67 ± 0.71 kPa, μ_{Springpot_Sr} = 6.89 ± 1.27 kPa, μ_{Springpot_Adipose Tissue} = 1.61 ± 0.37 kPa) and at different muscle states (μ_{Springpot_VM_20%MVC} = 11.29 ± 1.04 kPa). The viscosity parameter increased with the level of contraction (η_{_VM_Passive_Springpot} = 4.5 ± 1.64 Pa.s versus η_{_VM_20%MVC_Springpot} = 12.14 ± 1.47 Pa.s) and varied with the type of muscle. (η_{_VM_Passive_Springpot} = 4.5 ± 1.64 Pa.s versus η_{_Sr_Springpot} = 6.63 ± 1.27 Pa.s). Similar viscosities were calculated for all tissues and rheological models. These first physiologically realistic viscoelastic parameters could be used by the physicians to better identify and monitor the effects of muscle disorder, and as a database for musculoskeletal model.

This paper considers the nonlinear in-plane behaviour of a circular arch subjected to thermal loading only. The arch is pinned at its ends, with the pins being on roller supports attached to longitudinal elastic springs that model an elastic foundation, or the restraint provided by adjacent members in a structural assemblage. By using a nonlinear formulation of the strain-displacement relationship, the principle of virtual work is used to produce the differential equations of in-plane equilibrium, as well as the statical boundary conditions that govern the structural behaviour under thermal loading. These equations are solved to produce the equilibrium equations in closed form. The possibility of thermal buckling of the arch is addressed by considering an adjacent buckled equilibrium configuration, and the differential equilibrium equations for this buckled state are also derived from the principle of virtual work. It is shown that unless the arch is flat, in which case it replicates a straight column, thermal buckling of the arch in the plane of its curvature cannot occur, and the arch deflects transversely without bound in the elastic range as the temperature increases. The nonlinear behaviour of a flat arch (with a small included angle) is similar to that of a column with a small initial geometric imperfection under axial loading, while the nonlinearity and magnitude of the deflections decrease with an increase of the included angle at a given temperature. By using the closed form solutions for the problem, the influence of the stiffness of the elastic spring supports is considered, as is the attainment of temperature-dependent first yielding of a steel arch.

A semi-analytical solution method, called the Finite Difference–Distributed Transfer Function Method, is developed for static and dynamic problems of two-dimensional elastic bodies composed of multiple rectangular subregions. In the development, the original two-dimensional elasticity problem is first reduced into a one-dimensional boundary-value problem by finite difference; the exact solution of the reduced problem is then obtained by using the distributed transfer functions of the elastic continuum. The proposed technique, which combines the simplicity of finite difference and the closed form of analytical solutions, is capable of handling arbitrary boundary conditions, delivers highly accurate solutions for static and dynamic problems, and is computationally efficient. The proposed method is illustrated on a square region and an L-shaped region.

The effectiveness of the measures provided in the 2005 American Institute of Steel Construction (AISC) Specification for elastic distortional buckling of doubly symmetric I-shaped flexural members with slender webs was evaluated in a previous study. It was demonstrated that the code equations generally provide conservative strength estimates for the slender-web I-beams, and the amount of the conservatism was found to be rather dramatic for some cases. As a continuation of this effort, the effectiveness and accuracy of the 2005 AISC code provisions as well as predictions for elastic distortional buckling of slender-web singly symmetric I-shaped members is investigated in this paper. Comparisons are made with the finite strip analysis results for distortional buckling and the two design equations for elastic distortional buckling proposed by other researchers. It is demonstrated that the code predictions are by and large conservative, and even overly conservative in some cases, which does not seem to be justifiable economically.

Beams and columns subjected to the axial pressure are studied. Critical buckling loads are established for stepped beams clamped at one end and elastically fixed at the other end. The beams under consideration are of piecewise constant thickness and are weakened by cracks emanating from re-entrant corners of steps. The cracks are assumed to be stable part-through surface cracks. The influence of a crack on the stability of the beam is modeled by the method of distributed line spring known in the elastic fracture mechanics. Numerical results are presented for beams with a single step making use of different stress correction functions.

Acute coronary syndromes originate from atherosclerotic plaque rupture and subsequent developement of coronary thrombosis. Available screening and diagnostic methods are insufficient to identify the atherosclerotic plaques that will rupture and precipitate the coronary event. We developed a new intracoronary diagnostic method based on intravascular ultrasound (IVUS) examination to evaluate the local mechanical properties of atherosclerotic plaques namely IVUS-elastography/palpography. The relationships between local strain, histological features of vulnerability, clinical presentation, and clinical markers of instability were assessed.

The goal of this paper is to examine the trapezius muscle tone by measuring simultaneously using Myoton-2 myometer i.e., the natural oscillation frequency, stiffness and the elasticity of the trapezius muscle. With this method, the mechanical response of the muscle, to a short applied mechanical impulse, is registered by an acceleration probe. From the acquired damped natural oscillation waveform, the frequency (Hz), the stiffness (N/m) and the logarithmic decrement of damping (characterizing tissue's elasticity) are calculated, quantifying the functional state of the muscle. The trapezius muscle on both sides of the body was tested in twenty adult women by two investigators using the Myoton-2 myometer. During the measurements, the subjects were in a relaxed sitting position. The Bland and Altman graphical test, comparing the differences of the measurements of two investigators, was used for assessing the inter-observer repeatability. The registered values for the trapezius muscle tension, stiffness and elasticity are varying between the tested subjects, but the intra-class correlation coefficient (ICC) was near 1 for three muscular properties, showing that the variation within the subject (due to the investigator) is negligible, compared with the variation between the subjects.

The primary renal arteries transport up to one fourth of cardiac output to the kidneys for blood plasma ultrafiltration, with a functional dependence on the vessel geometry, composition and mechanical properties. Despite the critical physiological function of the renal artery, the few biomechanical studies that have focused on this vessel are either uniaxial or only partially describe its bi-axial mechanical behavior. In this study, we quantify the passive mechanical response of the primary porcine renal artery through bi-axial mechanical testing that probes the pressure-deformed diameter and pressure-axial force relationships at various longitudinal extensions, including the in-vivo axial stretch ratio. Mechanical data are used to parameterize and validate a structure-motivated constitutive model of the arterial wall. Together, experimental data and theoretical predictions of the stress distribution within the arterial wall provide a comprehensive description of the passive mechanical response of the porcine renal artery.

Human neuroblastoma (SH-SY5Y) cells, with its ability to differentiate into neurons, have been widely used as the in vitro cell culture model for neuroscience research, especially in studying the pathogenesis of Parkinson's disease (PD) and developing therapeutic strategies. Cellular elasticity could potentially serve as a biomarker to quantitatively distinguish undifferentiated and differentiated SH-SY5Y cells. The goal of this work is to characterize the retinoic acid (RA) induced alternations of elastic properties of SH-SY5Y cells using atomic force microscopy (AFM). The elasticity was measured at multiple points of a single cell. Results have shown that the differentiation of SH-SY5Y cell led to a larger elastic modulus, which is three times more than that of undifferentiated cells. A higher indentation rate applied during AFM measurements led to a larger elastic modulus of the cell. This work provides new insights into the differentiation process identified by the elasticity marker, which could be extended to investigate the function, health and ageing of cells.

Biocompatible polyacrylamide gels are widely required for the development of mechanically “soft” magnetic material for the purposes of different biomedical applications. In this work, ferrogels were synthesized by radical polymerization of acrylamide in a stable aqueous suspension of magnetic maghemite $\gamma$-Fe${}_{2.04}$O${}_{2.96}$ nanoparticles (MNPs) with the median value in diameter of 11.4nm fabricated by laser target evaporation. Gel network density was set to 1:100, the concentrations of embedded MNPs were fixed at 0.00%, 0.25%, 0.50%, 0.75% or 1.0% by weight. Ferrogels’ Young’s modulus and affinity to the human dermal fibroblasts adhesiveness were tested. To estimate the cells adhesive activity to gels, the adhesion index was calculated as the number of adhered cells divided by the number of cells sown and multiplied by 100%. The gradual increase of MNPs concentration in the gel network resulted in the significant increase of ferrogel’s Young’s modulus and cells adhesion activity. In particular, at the MNPs concentration of 0.25%, the modulus and the adhesion index were equal to $\sim$30kPa and $\sim$90%, correspondingly. The adhesion index at highest MNPs concentration of 1.0% was close to 100% and modulus to $\sim$40kPa. The increase of cells adhesiveness rise with MNPs concentration closely correlated with the direct impact of MNPs on the gel stiffness.

We propose a new human inspired structure of the lower extremity mechanism by which a humanoid robot will be able to efficiently perform fast movements such as running and jumping. We build a dynamic model of the humanoid robot which includes an elastic model of the biarticular muscle gastrocnemius and determine the role of the biarticular muscles and the elastic tendons in performing the vertical jump. We demonstrate that biarticular links contribute a great deal to the performance of the vertical jump. We also show that timing of the biarticular link activation and stiffness of the biarticular link influence the height of the jump considerably.

Tissue elasticity and viscosity are always associated with pathological changes. As a new imaging method, ultrasound vibro-acoustic imaging is developed for quantitatively measuring tissue elasticity and viscosity which have important significance in early diagnosis of cancer. This paper developed an ultrasound vibro-acoustic imaging research platform mainly consisting of excitation part and detection part. The excitation transducer was focused at one location within the medium to generate harmonic vibration and shear wave propagation, and the detection transducer was applied to detect shear wave at other locations along shear wave propagation path using pulse-echo method. The received echoes were amplified, filtered, digitized and then processed by Kalman filter to estimate the vibration phase. According to the phase changes between different propagation locations, we estimated the shear wave speed, and then used it to calculate the tissue elasticity and viscosity. Preliminary phantom experiments based on this platform show results of phantom elasticity and viscosity close to literature values. Upcoming experiments are now in progress to obtain quantitative elasticity and viscosity in vitro tissue.

In this paper, by constructing a new functional, an improved complex variable moving least-squares (ICVMLS) approximation is presented. Based on element-free Galerkin (EFG) method and the ICVMLS approximation, a new complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented. Galerkin weak form is used to obtain the discretized equations and the essential boundary conditions are applied with Lagrange multiplier. Then the formulae of the new CVEFG method for two-dimensional elasticity problems are obtained. Compared with the conventional EFG method, the new CVEFG method has greater computational precision and efficiency. For the purposes of demonstration, some selected numerical examples are solved using the ICVEFG method.

Hill's lemma for the Cauchy continuum has been playing an important role in micromechanics. An extended version of Hill's lemma for non-Cauchy continua is formulated using the simplified strain gradient elasticity theory (SSGET), which contains only one material length scale parameter and can account for the microstructure-dependent strain gradient effect. As a corollary of the extended Hill's lemma, the Hill–Mandel macro-homogeneity condition for non-Cauchy continua is obtained along with the general forms of kinematically and statically admissible boundary conditions that are required for constructing an energetically equivalent homogeneous comparison material. Based on these general forms, four sets of uniform boundary conditions are identified, which are implementable in material tests and can be directly used in homogenization analyses of heterogeneous materials. It is shown that when the strain gradient effect is suppressed, the extended Hill's lemma recovers the classical Hill's lemma for the Cauchy continuum and the extended Hill–Mandel condition reduces to its classical counterpart.

Effective material properties of a composite with spheroidal and ellipsoidal inhomogeneities in an isotropic matrix are investigated analytically using the dilute approximation and the Mori–Tanaka approximation together with the Eshelby's equivalent inclusion method. Both uniaxially aligned and uniformly randomly oriented spheroidal and ellipsoidal inhomogeneities are treated. For a spheroid, both oblate and prolate spheroidal inhomogeneities are considered. It is analytically shown that a composite with uniaxially aligned anisotropic ellipsoidal inhomogeneities in an isotropic matrix is anisotropic in general in thermal conductivity. It is also analytically shown that a composite with uniformly randomly oriented anisotropic ellipsoidal inhomogeneities in an isotropic matrix is exactly isotropic in thermal conductivity. Various special cases are also treated for the effective thermal conductivity of a composite with ellipsoidal and spheroidal inhomogeneities. Similar results are also obtained for the effective elastic moduli. Newly obtained expressions for the effective elastic moduli of a composite with isotropic spheroidal inhomogeneities are rather involved. Conversely, an effective thermal conductivity of a composite with anisotropic ellipsoidal inhomogeneities is relatively simple. An effective thermal conductivity of a composite with isotropic spheroidal inhomogeneities reduces to a known result (Kerner, E. H. [1956] “The electrical conductivity of composite media,” Proceedings of the Physical Society London Section B69, 802–807; Hashin, Z. and Shtrikman, S. [1962] “A variational approach to the theory of the effective magnetic permeability of multiphase materials,” Journal of Applied Physics33, 3125–3131.) as the spheroid aspect ratio approaches 1 (i.e., a sphere). The effective thermal conductivity of a composite with uniformly randomly oriented isotropic spheroidal inhomogeneities in an isotropic matrix obtained in this paper as a special case is similar to the one obtained by Hatta and Taya (Hatta, H. and Taya, M. [1985] “Effective thermal conductivity of a misoriented short fiber composite,” Journal Applied Physics58, 2478–2486.) in some respects, but is different. Numerical results are shown for a composite with oblate spheroidal voids in an isotropic matrix.

Torsional loading of elastoplastic materials leads to size effects which are not captured by classical continuum mechanics and require the use of enriched models. In this work, an analytical solution for the torsion of isotropic perfectly plastic Cosserat cylindrical bars with circular cross-section is derived in the case of generalized von Mises plasticity accounting solely for the symmetric part of the deviatoric stress tensor. The influence of the characteristic length on the microrotation, stress and strain profiles as well as torsional size effects are then investigated. In particular, a size effect proportional to the inverse of the radius of the cylinder is found for the normalized torque. A similar analysis for an extended plasticity criterion accounting for both the couple-stress tensor and the skew-symmetric part of the stress tensor is performed by means of systematic finite element simulations. These numerical experiments predict size effects which are similar to those predicted by the analytical solution. Saturation effects and limit loads are found when the couple-stress tensor enters the yield function.

Boundary element methods (BEM) have obtained a mature state in the last years so that industrial applications are possible. However, to treat real-world problems, the so-called fast methods are necessary to reduce the original quadratic complexity to an almost linear order. Essentially, two methods are popular, the so-called fast multipole method, which uses a kernel expansion, and the algebraic approach based on ${\mathscr{H}}$-matrices with the adaptive cross approximation (ACA) to compress the matrix blocks. The latter is frequently used for scalar-valued problems, but for vector-valued problems, a modification of the pivot strategy is required. It has been suggested to search for the largest singular value out of all minimal singular values of the fundamental solution blocks. This strategy has been proposed by Rjasanow and Weggler and is studied here for elastostatics and elastodynamics. It is shown with numerical experiments that this strategy is mostly robust and results in an almost linear complexity.

Ultrasound can be used for mechanical property measurements of the arterial wall in addition to imaging of its morphology. This paper describes (1) accurate imaging of the carotid sinus which cannot be assumed to be a straight cylindrical shell, (2) measurement of elasticity and tissue characterization of the arterial wall based on the axial motion estimation, and (3) lateral motion estimation in the carotid artery.

Singular electro-elastic fields near the corners of wedges/junctions in piezoelectric-piezoelectric or elastic materials under antiplane loadings are analyzed. At first, a new weak form for solving eigenpair problems in piezoelectric materials is derived with stress equilibrium equations, Maxwell equation and boundary conditions; Then, with the asymptotic exponential assumption along the radial distribution and the bubble mode assumption along the circumferential distribution of the displacement and electric potential in an element around the tip of wedge/junction, a simple one-dimensional finite element formulation that only discretize the displacement and electric potential circumferentially is established. The polarization orientation of piezoelectric materials may be arbitrary. In numerical examples, the influences of wedge angles, poling orientation and boundary conditions are discussed. Through comparing the existing solutions, the validity and high precision of present method is proved.

The elastodynamic response of the transformation-toughened ceramics under an instantaneous phase transformation is investigated. Some composite materials, such as Zirconia toughened ceramics, are the remarkable material, which has a high strength, a high elastic modulus, and an improved toughness, etc. Most of the good qualities are common in many ceramic composite materials. These good qualities are made possible through the phase transformation of composite particles. The transformation toughening utilizes the stress-induced phase transformation of particles, which is accompanied by a volumetric expansion. In this paper a phenomenological model is proposed to describe the situation, which involves a dynamic martensitic transformation in a spherical particle of Zirconia embedded in an infinite elastic matrix. Following the ray methods, we clarify the stress-focusing effect caused by the instantaneous phase transformation in a spherical inclusion of Zirconia. It should be noted that the mechanism in the toughening of ceramics in the steady state does not hold in the dynamic state.