Microelastic Solids Research Articles

On time-dependent nonlinear dynamic response of micro-elastic solids

A new approach to the mechanical response of micro-mechanic problems is presented using the modified couple stress theory. This model captured micro-turns due to micro-particles' rotations which could be essential for microstructural materials and/or at small scales. In a micro media based on the small rotations, sub-particles can also turn except the whole domain rotation. However, this framework is competent for a static medium. In terms of dynamic investigations of micro materials, it is required to involve micro-rotations' mass inertias. This fact persuades us to pay particular attention to the micro mechanics' samples and directed us to re-derive the modified couple stress model to propose and represent a new micro-mechanic approach which is well-deserved, especially for dynamic studies of microstructures. In carrying out this job, the classical beam has provided the basic form of formulation procedure. The continuum medium has been limited to a square flat non-porous beam deducing a homogeneous isotropic micromaterial. As long as the time-dependent results are concerned due to studying micro-mass inertia in time history, there would be two solution steps. The Galerkin decomposition technique is imposed in accord with an analytical postulate to issue the algebraic problem distributing time-dependent equations. The latter, the Homotopy perturbation method delivers time-dependent outcomes. The solution methods have been validated by building numerical models in Abaqus software. On the new achievements of this study, one can declare that both static and dynamic length scale parameters are very effective in order to study vibrations of microstructures. If the values of these characteristic lengths are considerable, the nonlinear frequency analysis will be essential. Furthermore, the stiffness of the structure will be higher if the values of both length scale parameters increase.

Microelastic wave field signatures and their implications for microstructure identification

This work combines closed-form and computational analyses to elucidate the dynamic properties, termed signatures, of waves propagating through solids defined by the theory of elasticity with microstructure and the potential of such properties to identify microstructure evolution over a material’s lifetime. First, the study presents analytical dispersion relations and frequency-dependent velocities of waves propagating in microelastic solids. A detailed parametric analysis of the results show that elastic solids with microstructure recover traditional gradient elasticity under certain conditions but demonstrate a higher degree of flexibility in adapting to observed wave forms across a wide frequency spectrum. In addition, a set of simulations demonstrates the ability of the model to quantify the presence of damage, just another type of microstructure, through fitting of the model parameters, especially the one associated with the characteristic length scale of the underlying microstructure, to an explicit geometric representation of voids in different damage states.

Three-dimensional finite element formulation for microelastic solids

Materials with microstructure have long been known to display a different mechanical behavior than those materials considered classically elastic. To account for these differences, a microelastic model can be used to describe the behavior of these latticed materials. This model has six material constants, as opposed to only two constants found in classical elasticity, and extra degrees of freedom. A three-dimensional microelastic brick element is formulated with six degrees of freedom at each node, representing three translational and three microrotational. Several case studies which have analytical solutions are investigated to determine the validity of numerical solutions generated by this model.

Holographic screening method for microelastic solids

An experimental method is presented for the rapid evaluation of structured solids with microelastic degrees of freedom associated with the microstructure. By contrast with earlier methods based on size effect studies, the present method makes use of a single specimen subjected to holographic interferometry. Results are presented for polymethyl methacrylate and for a dense polyurethane foam, which in previous studies were demonstrated to behave, respectively, as classically elastic and Cosserat solids.

Couple stresses in a normally loaded micropolar elastic cylinder

Using Mindlin's theory of couple stresses, Nowinski and Ismail exhibited that the effect of the couple stresses in the deformation of a circular cylinder under normal load is quite significant. Our analysis based on Eringen's theory of microelastic solids, however shows that the couple stresses in this problem do not play an important role. The latter is to be expected physically except in special circumstances.

Wave propagation in a micro-isotropic, micro-elastic solid

Abstract This is an extension of Koh's work[1] on micro-elastic solids. Restrictions on the elastic moduli have been obtained from the positive definiteness of the strain energy function. These restrictions are applied to the dispersion relations of plane harmonic waves propagating in the medium. It is found that all the velocities of propagation have real values above certain cut-off frequencies. The medium theoretically allows the propagation of twelve waves, eleven dispersive and one non-dispersive, with six distinct velocities of propagation and three cut-off frequencies.

Theory of micromorphic materials with memory

A constitutive theory of memory-dependent microelastic solids and microviscous fluids is developed. Nonlinear constitutive functionals are considered to depend on the continuous past history of macro and micro-deformation gradients, temperature and the temperature gradients. By use of the second law of thermodynamics and the principle of fading memory a set of exact functional constitutive equations are derived. The linear theory is presented in full for memory-dependent anisotropic and isotropic microelastic solids and microfluids.

A special theory of microelasticity

The Eringen-Suhubi[1] linear theory of microelastic solids is re-examined. With the application of internal constraints derived from a postulate of principal coincidence more stringent than that used by Koh [2], further simplification of the general theory is achieved. The special theory so obtained reduces from eighteen to ten the number of elastic moduli required to characterize the microelastic continua. The basic equations of the special theory are subsequently derived.

Inequalities between the constants of a linear micro-elastic solid

A set of inequalities between the eighteen constants of a linear micro-elastic solid have been obtained, which are both necessary and sufficient to ensure that the internal energy density should be positive definite. The classical results of Kelvin and Kirchhoff have been extended to micro-elastic solids.

Nonlinear theory of micro-elastic solids—II

The present paper is a continuation of our previous work on the same topic. After the introduction of material and strain measures of micro-elasticity we give the specific form of constitutive equations for isotropic micro-elastic materials, various approximate theories, the linear and the determinate theory of couple stress. Field equations of the linear theory for the latter case are obtained and applied to the study of the Rayleigh surface waves in micro-elasticity.

Nonlinear theory of simple micro-elastic solids—I

The present work is concerned with the formulation of the basic field equations, boundary conditions and constitutive equations of what we call ‘simple micro-elastic’ solids. Such solids are affected by the ‘micro’ deformations and rotations not encountered in the theory of finite elasticity. The theory, in a natural fashion, gives rise to the concept of stress moments, inertial spin and other types of second order effects and their laws of motion. The mechanism of the surface tension is contained in the theory. In a forthcoming paper (Part II) explicit expressions of constitutive equations of several simple micro-elastic solids will be given and applied to some special problems.