Microstretch Elasticity Research Articles

Nonlocal elasticity theory for microstretch circular plate with mechanical source

ABSTRACTIn the present manuscript, the eigenvalue approach is used for the two-dimensional problem of nonlocal microstretch circular plate subjected to mechanical source. The Laplace and Hankel transforms are applied to solve the problem. The inversion of the Laplace and Hankel transforms are carried out using the inversion formula of the transforms together with Fourier expansion techniques. Numerical inversion methods are applied to obtain the results in the physical domain. The results for microstretch and nonlocal elasticity are deduced as special cases from the present formulation. Numerical results are represented graphically and discussed to show the effect of nonlocal and microstretch.

Asymptotic piezoelectric plate models in microstretch elasticity

AbstractThis paper is concerned with the formal deduction of piezoelectric plate models in microstretch elasticity, by means of an asymptotic analysis with respect to a small parameter ε, being the thickness of the plate. Two different boundary conditions pertaining to electric quantities are considered, leading to two different models: the sensor model and the actuator model, respectively. Each of the two plate problems turns out to be decoupled into a bending problem and a certain microstretch membrane problem, partially coupled with the electric behavior.

In-plane wave propagation through a microstretch slab sandwiched by two half-spaces

Abstract The problem of in-plane wave propagation through a sandwiched slab which is governed by the micro-stretch elasticity is discussed in this paper. Different from the classical elastic solid, the mass particles in a micro-stretch solid can undergo the micro-rotation and the micro-stretch in addition to the displacement. As a result, there are five kinds of dispersive waves in a micro-stretch medium. The interface conditions between two microstretch solids are also different from that between two classic elastic solids. By incorporating the non-traditional interface conditions at two interfaces, a set of algebraic equations is obtained from which the amplitude ratios of reflection and transmission waves can be obtained. A numerical example is provided and the energy conservation law is used to check the numerical results. Based on the numerical results, the influences of the microstretch constants and the non-dimensional thickness (relative to the wavelength) of the slab, and the four kinds of possible interface conditions between the micro-stretch slab and the classic elastic half-spaces are discussed. Some special cases as the degeneration of present model are discussed.

Physical meaning of elastic constants in Cosserat, void, and microstretch elasticity

Physical meaning of elastic constants in Cosserat, void, and microstretch elasticity

On the bending of plates in the electromagnetic theory of microstretch elasticity

AbstractThis paper deals with the electromagnetic theory of microstretch elasticity. The full dynamic theory, which describes the interaction of electromagnetic fields with piezoelectric bodies, called piezoelectromagnetism, is considered. First, we derive the equations governing the bending theory of thin piezoelectromagnetic microstretch plates. Then, the boundary‐initial value problem is formulated and a uniqueness result is presented. Finally, the effects of a concentrated charge density in an infinite plate are studied.

Spatial behavior in the electromagnetic theory of microstretch elasticity

This paper is concerned with the electromagnetic theory of microstretch elasticity. First, the initial boundary value problem is formulated in the framework of the linear dynamic theory of microstretch magnetoelectroelastic solids. Then, the spatial behavior of solutions is studied in both bounded and unbounded regions. The obtained result gives an exact idea of the domain of influence, in the sense that for each fixed time in a given interval, the entire activity vanishes at distanced from the support of the given data greater than a time-dependent threshold value. The study of spatial behavior is completed by an exponential decay estimate inside the domain of influence. As a by product a uniqueness result holding for both bounded and unbounded bodies is derived. Finally, the effect of a concentrated microstretch body force is studied.

Elastic waves in an electro-microelastic solid

The present study is concerned with the wave propagation in an electro-microelastic solid. The reflection phenomenon of plane elastic waves from a stress free plane boundary of an electro-microelastic solid half-space is studied. The condition and the range of frequency for the existence of elastic waves in an infinite electro-microelastic body are investigated. The constitutive relations and the field equations for an electro-microelastic solid are stemmed from the Eringen’s theory of microstretch elasticity with electromagnetic interactions. Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the stress free plane boundary of an electro-microelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical computations are performed for a specific model to calculate the phase speeds, amplitude ratios and energy ratios, and the results obtained are depicted graphically. The effect of elastic parameter corresponding to micro-stretch is noticed on reflection coefficients, in particular. Results of Parfitt and Eringen [Parfitt, V.R., Eringen, A.C., 1969. Reflection of plane waves from a flat boundary of a micropolar elastic half-space. J. Acoust. Soc. Am. 45, 1258–1272] have also been reduced as a special case from the present formulation.

On microcontinuum field theories: the Eshelby stress tensor and incompatibility conditions

We investigate linear theories of incompatible micromorphic elasticity, incompatible microstretch elasticity, incompatible micropolar elasticity and the incompatible dilatation theory of elasticity (elasticity with voids). The incompatibility conditions and Bianchi identities are derived and discussed. The Eshelby stress tensor (static energy momentum) is calculated for such inhomogeneous media with microstructure. Its divergence gives the driving forces for dislocations, disclinations, point defects and inhomogeneities which are called configurational forces.

A spatial decay in the linear theory of microstretch piezoelectricity

The electromagnetic theory of microstretch elasticity is an adequate tool to describe the behavior of porous bodies, animal bones and solids with deformable microstructures. In this paper we study the linear theory of microstretch piezoelectricity. First, we establish a spatial decay estimate. Then, we obtain an upper bound for the amplitude term.

Lie point symmetries and conservation laws in microstretch and micromorphic elasticity

In this paper, following Noether’s theorem we investigate Lie point symmetries of linear theories of microstretch elasticity and micromorphic elasticity. We restrict our consideration to isotropic, compatible and homogeneous materials. Conservation and balance laws are derived, thereby extending results from micropolar elasticity.

Method of complex potentials in linear microstretch elasticity

The paper is concerned with the plane strain of homogeneous and isotropic microstretch elastic bodies. We give a new representation of the solution in terms of complex potentials. The method is useful for the treatment of the constitutive equations established by Eringen in [A.C. Eringen, Microcontinuum Field Theories. I. Foundations and Solids, Springer-Verlag, New York, 1999], where the introduction of stress functions leads to difficulties. The complex variable technique is used to study Kirsch problem in the context of the theory presented in [A.C. Eringen, Microcontinuum Field Theories. I. Foundations and Solids, Springer-Verlag, New York, 1999].

Electromagnetic theory of microstretch elasticity and bone modeling

A continuum theory of microstretch elasticity subject to electromagnetic fields is introduced as a microstructural model to determine deformations and stress fields in elastic solids having interconnected voids, microcracks or stretchable microelements. Such materials include animal bones and solids with deformable microstructures, e.g., nanocomposites in solids.