Hyperelastic model of a material which microstructure is formed by “balls and springs”

We develop a model of an incompressible material which microscopic structure is formed by flexible but incompressible balls connected mutually by linear springs. The model is motivated by the structure of smooth muscle tissues that exhibit perfect elastic (or visco-elastic) behavior in a large extent of deformations. Moreover, their bulk (macroscopic) stiffness may be very effectively controlled and changed from very low values to essentially higher ones by simply defined structural changes inside individual muscle cells. In the continuum limit, the “balls and springs” model gives a nontrivial, highly nonlinear hyperelastic material. The stored strain energy function has generally no analytical expression. However, we find an approximate analytic formula, that is suitable for describing certain mechanical effects coming from the special arrangement of smooth muscle cells.     

A non-classical Kirchhoff plate model incorporating microstructure,surface energy and foundation effects

A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale parameter to account for the microstructure effect, three surface elastic constants to describe the surface energy effect, and two foundation moduli to represent the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the newly developed plate model includes the models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases and recovers the Bernoulli–Euler beam model incorporating the microstructure, surface energy and foundation effects. To illustrate the new model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate with or without the elastic foundation predicted by the current model is smaller than that predicted by the classical model. Also, it is observed that the difference in the deflection predicted by the new and classical plate models is very large when the plate thickness is sufficiently small, but it is diminishing with the increase of the plate thickness. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the elastic foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. These predicted trends of the size effect at the micron scale agree with those observed experimentally. In addition, it is shown both analytically and numerically that the presence of the elastic foundation reduces the plate deflection and increases the plate natural frequency, as expected.     

A consideration of curved interfaces in stress-assisted martensite formation

A purely mechanical, sharp interface model is developed to consider curved interfaces that have been observed between martensite phase variants. The approach is based on a theory of small strains as distinct from small displacement gradients. It admits a realistic characterization of each phase with standard elasticity tensors and allows for inhomogeneous states of strain within each phase including inhomogeneous, finite rotations. The model indicates that any signficant interface curvature must be due to material rotation because interfaces cannot be finitely curved with respect to the material lattice. It is also found that the interface driving traction is not influenced by local lattice rotations unless inertia affects the reaction.     

First mushroom-shaped adhesive microstructure: A review

This letter reviews the adhesive and frictional properties of the first mushroom-shaped adhesive microstructure (MSAMS), which has come a long way from inspiration by the attachment devices evolved in beetles to a large-scale industrial production. It was shown to have an that about twice higher pull-off force compared to a smooth control made from the same material measured on smooth substrates. Pull-off forces measured underwater are even higher than those in air. Moreover, it retained adhesive performance over thousands of attachment cycles and initial adhesive capability could be recovered by washing after being contaminated. In shearing, MSAMS exhibits reduced and stabilized friction in comparison with a smooth control, which demonstrated pronounced stick-slip motion, and shows zero pull-off force in a sheared state, allowing the adhesion to be switched on and off. The presence of a fluid in the contact zone showed adhesion enhancement on both smooth and rough substrates. All these features lead us to conclude that MSAMS may have practical potential in a variety of applications.     

Method of solving problems of a plane crack which is nearly circular

Kiev Institute of Civil Aeronautical Engineering. Translated from Prikladnaya Mekhanika, Vol. 25, No. 7, pp. 99–104, July, 1989.     

Super-spherical cumulation: shock collapse which is more intense than the spherical one

A shock wave implosion in an axisymmetric chamber with a convex bounding wall is studied experimentally, analytically and numerically. The converging shock front area in this geometry shrinks quickly as the shock wave approaches the center point. The analytical theory predicts that the corresponding rate of post-shock pressure and density increase in this case exceeds essentially that achieved in the classical cylindrical or spherical shock implosions, hence, the phenomenon is referred to as “super-spherical cumulation”. The experiments confirm higher intensity of the super-spherical implosion compared with the cylindrical one, both driven by identical high-current pulsed electric discharges. The converging shock stability is analyzed in the framework of the CCW theory. The numerical results obtained using a locally-adaptive unstructured grid technique agree well with the theoretical predictions of the converging shock wave intensity. Received 28 January 1998 / Accepted 6 November 1998     

Structure of a shock wave in which multiple ionization of the atoms is taking place

Ionization relaxation in a shock wave of very large amplitude is considered, the atoms behind the front of the shock wave being multiply ionized. In calculating the structure of the shock wave and the kinetics of ionization, allowance is made for the electron component of the thermal conductivity which plays an important role in this. A simplified method of calculating the kinetics of multiple ionization is proposed, and an application of this method is presented. The results of the structure calculation show that, as a result of heating by thermal conduction, the gas is considerably ionized even in front of the jump in compression, while the electron component of the thermal conductivity passes through a maximum.Translated from Zhurnal Prikladnoi Mekhnika i Tekhnicheskoi Fiziki, No. 5, pp. 11–21, September–October, 1970.     

Fractional vapour content of a liquid pool through which vapour is bubbled

Data from a large number of Russian, American and German sources are examined and found to be correlated in general by

$\text{α}\text{1?α)}\text{1}\text{2}\text{= K[F}{}_{\mathrm{D}}\text{P}{}^{\mathrm{m}}\text{]}{}^{\mathrm{n}}$

where α is voidage or fractional vapour content, K is a constant, F_D is a Froude number and P is a physical properties group. However, the exponent m is found to vary from 0 to 0.3 and the exponent n from $\text{2}\text{3}$ to 0.79, depending upon the sources of the data. The most probable value for n is $\text{2}\text{3}$ but a firm choice cannot be made for m, which is either 0.16 or 0.3. The different values of m depend chiefly upon the method of measurement of the voidage.     

A micromechanics analysis for the microstructure design of a two-phase pseudoelastic composite

A micromechanics analysis on the possibility of designing a two-phase pseudoelastic composite is made for the case where ductile transformable shape memory alloy plastic particles are imbedded coherently in an elastic matrix. It is demonstrated that a pseudoelastic stress-strain loop in a macroscopic loading-unloading cycle can be obtained by microscopically stress induced forward and reverse martensitic transformations in the SMA particles. The relation between the macroscopic stress-strain response and the material parameters of the constituents of this composite is quantified through the micromechanics calculations, which reveals that the best ductility and thus the greatest energy absorption capacity of this novel microstructure can be obtained by the optimum material design.     

Flow of a non-Newtonian fluid between intersecting planes of which one is moving

We study the flow of an Oldroyd-B fluid between two intersecting plates, one of which is fixed and the other moving along its plane. This problem was first considered by Strauss (1975) for the Maxwell fluid using a similarity transformation. We find that even in the case of a Maxwell fluid, which can be obtained by setting a specific parameter, say , in the Oldroyd-B model to zero, our results disagree with those of Strauss (1975). We find that circulating cells are present, adjacent to the stationary plate while Strauss (1975) finds them adjacent to the moving plate. We also delineate the effect of the coefficient , which is a measure of the elasticity of the flow, on the flow pattern. We find that an increase in the elastic parameter reduces the cellular structure.     

Mixing of two gases one of which is expelled from a cylindrical space by the other

The flow structure and impurity distribution in an axisymmetric cylindrical space is obtained from the system of equations of convective heat and mass transfer in the Boussinesq approximation for different variants of the gas inflow and outflow conditions. The variation of the average impurity concentration in the space investigated, obtained as a result of numerical calculations, is compared with two limiting cases of expulsion of the contaminated gas: the gas piston case and total mixing. The dependence of the velocity and impurity concentration fields on the regime parameters (Reynolds, Grashof, and Schmidt numbers, velocity profiles at the gas inlet and outlet) and the geometric and design parameters (elongation of cylinder, inflow and outflow geometry) is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 31–38, May–June, 1986.     

Hypersonic flow past a rectangular profile through which gas is blown strongly

In the present paper, we consider the hypersonic flow past a rectangular profile and the end of a cylinder when there is strong distributed blowing of gas through their flat front parts. The injected gas is assumed to be inviscid, and the pressure on the contact surface which separates the exterior flow and the blowing layer is determined in accordance with Newton's formula. The use of perturbation theory in the case of a thin blowing layer has made it possible to obtain limit problems for different flow regions, and the analytic solution and subsequent asymptotic matching of these problems yield the form of the contact surface and the distribution of the pressure on the body. It is shown that the drag of the body depends nonmonotonically on the flow rate of the blown gas. The optimal blowing parameters and the corresponding minimal drag are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–166, January–February, 1982.I thank V. A. Levin for interest in the work and valuable discussions.     

A high-efficient nonlinear energy sink with a one-way energy converter

Nonlinear Dynamics - The nonlinear energy sink (NES) has been presented in the past two decades. Although it has very broad applications, some inherent limitation of the traditional NES is...     

Application of a partially relaxed shape memory free energy function to estimate the phase diagram and predict global microstructure evolution

In this work recent results regarding bounds of the relaxed free energy functions of a broad class of shape memory materials of arbitrary symmetry are leveraged to develop a simple and efficient numerical method to analyze several aspects of the thermomechanical response of such materials. This approach is shown to be useful for construction of the austenitic phase diagram used in many early phenomenological models. It is also demonstrated that the resulting implementation is suitable for finite element analysis, has desirable numerical properties, and makes realistic quantitative predictions regarding the evolution of the lattice correspondence variants, transformation stress and strain levels, and orientation dependence.