International Journal of Applied Mechanics

Hydrogels and shape memory polymers (SMPs) possess excellent and interesting properties that may be harnessed for future applications. However, this is not achievable if their mechanical behaviors are not well understood. This paper aims to discuss recent advances of the constitutive models of hydrogels and SMPs, in particular the theories associated with their deformations. On the one hand, constitutive models of six main types of hydrogels are introduced, the categorization of which is defined by the type of stimulus. On the other hand, constitutive models of thermal-induced SMPs are discussed and classified into three main categories, namely, rheological models; phase transition models; and models combining viscoelasticity and phase transition, respectively. Another feature in this paper is a summary of the common hyperelastic models, which can be potentially developed into the constitutive models of hydrogels and SMPs. In addition, the main advantages and disadvantages of these constitutive modes are discussed. In order to provide a compass for researchers involved in the study of mechanics of soft materials, some research gaps and new research directions for hydrogels and SMPs constitutive modes are presented. We hope that this paper can serve as a reference for future hydrogel and SMP studies.

The paper considers normal contact problems formulated as follows: an indenter with negligible weight presses the surface half-space with a certain force, i.e., normal stress acts on the contact surface and tangential stress is zero. In particular, we consider two types of distributed load that correspond to the following cases: when half-space is subjected to frictionless flat rigid indenter, and when half-space is subject to frictionless cylindrical rigid indenter. The paper considers plane deformation. Problems are solved by boundary element methods (BEM), which are based on singular solutions of Flamant (BEMF) and Boussinesq (BEMB) problems. The stress–strain state of the half-plane, particularly the constructed contours (isolines) of stresses in half-plane, was studied. The results obtained by BEMF and BEMB are discussed and compared.

This paper studies the characteristics of a micro-beam interacting with an incompressible fluid in a fluid chamber with an opening in its bottom face for fluid flow. The Euler–Bernoulli equation for transverse deformation of an elastic beam is coupled with the fundamental hydrodynamic equation, which is solved by Galerkin and separation of variables method. The 2D fluid flow assumption in Cartesian coordinate has been used. Natural frequencies and mode shapes of wet beam are calculated and compared with the dry beam. The effects of geometrical parameter changes are also computed as a benchmark for the design of the micro-pump. It is observed that fluid coupling causes a decrease for beam’s natural frequencies, especially in higher modes. Furthermore, since the results of the dry and wet beam show a small discrepancy in lower modes, the mode related to the dry beam was employed as the trial function in the forced vibration analysis of the coupled system.

Based on a new shear deformation theory and the modified couple stress theory, in this paper, the hygro-thermal buckling of porous FGM sandwich microplates and microbeams is investigated. Unlike the classical elasticity theory, the present model involves a material length scale parameter, and, thereby, can capture the small size effect. The four-variable shear deformation theory with a new shape function is utilized to derive the governing stability equations for the microplates and microbeams from the principle of virtual work. The present microstructures are composed of three layers and subjected to hygro-thermal conditions. The core is assumed to be fully homogeneous and isotropic material. While, the face layers are made from porous functionally graded materials that vary only in the thickness direction. The governing equations are solved analytically to obtain the thermal buckling of FGM sandwich microplates and microbeams under humidity effects. The temperature rise and moisture concentration are graded uniformly, linearly or nonlinearly through the thickness. Comparison studies are made between the present results and those available in the literature to check the validity of the obtained formulations and results. Moreover, the effects played by the length scale parameter, power-law exponent, moisture concentration, core thickness and other parameters on the thermal buckling of microplates and microbeams are all investigated.

The influence of a multi-layer core on the blast response of composite sandwich cylinders under internal explosive loading was investigated. Experiments were conducted first to obtain the fundamental deformation and failure patterns of composite cylinders with uniform, double-layer, and triple-layer profile cores. They were compared with the finite element model for prediction with good agreement. The mechanisms of energy absorption and deformation of a composite sandwich were explored by parametric analysis. Experimental results indicated that compaction wave in a double-layer core was initiated from the inner face sheet and then propagated to the outer face sheet when the gradient was positive; however, the core densification started at the inner surfaces of both layers and propagated to the outer face sheet together. The maximum radial deflection decreased with increasing face sheet thickness or decreasing blast loading. The percentage of energy absorbed by the core increased with decreasing face sheet thickness or increasing blast loading. This study revealed a possibility to reduce the maximum deflection (same structural mass and same energy absorption) for the sandwich cylinders by using a proper core distribution.

This is the first research on the buckling and free vibration analysis of functionally graded graphene platelets reinforced composite annular plate resting on elastic substrate and subjected to nonlinear temperature gradient and mechanical load within the framework of higher order shear deformation theory (HSDT). Governing equations and boundary conditions are established by employing Hamilton’s principle. Generalized differential quadrature method is applied to obtain numerical solution. Considering nonlinear temperature gradient instead of the linear one and also the effects of elastic substrate besides describing the kinematics on the basis of HSDT makes the results closer to real condition. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of stiffness of the substrate, patterns of temperature rise, temperature gradient, axial load, weight fraction and distribution patterns of GPLs, outer radius to inner radius ratio, inner radius to thickness ratio of the plate and geometric dimensions of GPLs on the response of the structure. This study provides essential information to engineers seeking innovative ways to promote the composite structures in a practical way.

In the present study, anti-plane wave propagation has been considered in a piezoelectric viscoelastic composite medium where the surface has been coated with an infinitesimally thin and perfectly conducting electrode which is grounded. The frequency equation has been obtained analytically and the result has been found in well agreement with the classical B-G wave frequency equation which validates the result. Moreover, Semi-Analytical Finite Element using Perfectly Matched Layer (SAFE-PML) method has been adopted in order to deduce frequency equation. Numerical computation and graphical illustration have been done in order to study some influencing parameters. Both frequency equations obtained through analytical method and SAFE-PML method have been compared through graphs which also validate the obtained results.

This paper presents is a solution for static torsion in a microtube made of bi-directional functionally graded materials (BDFGMs). The material properties are assumed to vary according to the arbitrary function along radius and length of microtube. As for the torque effect of the axial magnetic field, the well-known Maxwell’s relation is used. Couple stress theory is employed to study the influence of small-scale on static torsion of microtube. The Navier equation and boundary conditions of the size-dependent BDFG microtube were derived by the minimum potential energy. These equations were solved by employing the generalized differential quadrature method (GDQM). Comparison between the results of this work with the analytical method for static torsion of microtube made of one direction FG material reveals the accuracy of this study. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants on the static torsion of the bi-directional functionally graded microtube.

In this study, a theoretical model is developed to characterize the quantitative effect of temperature on the hardness of pure FCC and HCP metals. The model is verified by comparison with the available experimental results of Cu, Al, Zn, Mg, Be, Zr, Ni, Ir, Rh, and Ti at different temperatures. Compared with the widely quoted Westbrook model and Ito–Shishokin model which need piecewise fitting to describe experimental values, the present model merely needs two hardness values at different temperatures to predict the experimental results, reducing reliance on conducting lots of experiments. This work provides a convenient method to predict temperature-dependent hardness of pure metals, and it is worth noting that it can be applied to a wide temperature range from absolute zero to melting point.

A hydrodynamic model, with the incorporation of elasticity, is considered to study oblique incident waves propagating over a small undulation on an elastic bed in a two-layer fluid, where the upper layer fluid is bounded above by a rigid lid, which is an approximation to the free surface. Following the Euler–Bernoulli beam equation, the elastic bed is approximated as a thin elastic plate. The surface tension at the interface of the layers is completely ignored since its contribution will be minimal. The behavior and properties of the roots of the dispersion relation are analyzed using counting argument and contour plot. In this case, time-harmonic waves propagate with only one wavenumber. Considering an irrotational motion in an incompressible and inviscid fluid, and applying perturbation technique, the first-order corrections to the velocity potentials are evaluated by an appropriate application of Fourier transform and, subsequently, the corresponding reflection and transmission coefficients are computed through integrals containing a shape function which depicts the bottom undulation. To validate the theory developed, two particular undulating bottom topography are taken up as examples in order to evaluate the hydrodynamic coefficients which are represented through graphs. It is noted that the reflection coefficient shows an oscillatory pattern, when the wavenumber of the undulating bed takes a value almost double the wavenumber of the incident wave. When the ratio of the wavenumber of the undulating bed and the wavenumber of the incident wave approaches 2, the theory predicts existence of resonance between the undulating elastic bed and the interface of the layers. It is worthwhile to note that reflected wave energy of the incident wave is higher if the number of ripples of the bottom undulation is large. It is further noted that the reflected energy increases in response to an increase in the values of the elastic parameters of the ocean bed. The results for a patch of sinusoidal ripples having different wavenumbers are found to be similar. Further, the reflected energy decreases for an increase in the angle of incidence. It is noted that reasonable changes in elasticity, ripple wavenumber and the number of the ripples of the bed have a remarkable effect when the propagating wave passing through a channel encounters a small bottom undulation. When results are compared with the available results, good agreement is observed.