Linear grade-consistent micropolar theory

A linearization is performed of a previously presented, so-called grade-consistent micropolar theory, where the free energy is assumed to contain also second order derivatives of the displacement, an order which is argued to match the conventional first order derivatives of the micropolar angle. Dimensionless constitutive constants are introduced, which facilitates the discussion of orders of magnitude. The theory is applied to harmonic plane waves. By means of the dispersion relations the possible magnitudes of the different, conventional and new micropolar effects are preliminarily discussed.     

Acceleration waves in simple and linear viscoelastic micropolar materials

In this work the conditions of propagation of acceleration waves are studied in different types of micropolar media: (a) in simple media whose constitutive equations are given in functional form, (b) in linear viscoelastic media of which the constitutive equations are obtained in the limit of small deformations from a simple micropolar medium obeying the axiom of fading memory. In contrast to the first case, two kinds of acceleration waves can propagate independently in the second case.     

Reflection and transmission of plane harmonic waves at an interface between liquid and micropolar viscoelastic solid with stretch

A solution of the field equations governing small motions of a micropolar viscoelastic solid half-space with stretch is employed to study the reflection and transmission at the interface between a liquid and a micropolar viscoelastic solid with stretch. The amplitude ratios for various reflected and refracted waves are computed and depicted graphically. Effects of axial stretch and viscosity on the amplitude ratios are discussed     

On dual-phase-lag thermoelasticity theory with memory-dependent derivative

A new mathematical model of generalized thermoelasticity with memory-dependent derivatives for the dual-phase-lag heat conduction law is constructed. The governing equations of the new model are applied to a half-space subjected to ramp-type heating. Laplace transforms technique is used. The solution is obtained for different types of functions representing the thermal shock and for different values of the parameter of the time fraction derivative of the model. The effects of time-delay and arbitrary kernel function on elastic material are studied and represented graphically. The predictions of the theory are discussed and compared with dynamic classical coupled theory.     

Axi-symmetric problem in micropolar elastic half-space with stretch

The present investigation is concerned with axisymmetric problem in micropolar elastic half-space with stretch. The displacement, force stress, couple stress and vector first moment are obtained for a half-space subjected to an arbitrary normal load and a particular case of impulsive force is studied in detail. The graphs for various quantities have been drawn to illustrate the effect of stretch in each particular case.     

A theory of crack growth in viscoelastic materials

The principle of the conservation of energy is used to derive a solution for the velocity of crack growth in viscoelastic materials. This work generalizes earlier work by the same method that yielded only asymptotic solutions for crack velocity.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer with stretch

This paper deals with the propagation of 2-dimensional waves in a thermo-elastic micropolar solid layer which can stretch and contract. Thermo-elastic Rayleigh wave velocity equation in the micropolar medium with stretch has been deduced from the above theory. The wave velocity equation obtained is in agreement with the classical result of Rayleigh when the layer is unstretched and thermal and micropolar effects are negligibly small.     

On the bending of micropolar viscoelastic plates

The theory of micropolar elastic plates has been established by [A.C. Eringen, Linear theory of micropolar viscoelasticity, Int. J. Engng. Sci. 5 (1967) 191–204]. The present paper is concerned with the bending of micropolar viscoelastic plates within the dynamic theory. First, the basic equations of the bending theory of viscoelastic thin plates are presented. Then, a variational characterization of solutions and a minimum principle of Reiss type are established.     

Variational algorithm for the stability of the flow of micropolar fluids with stretch

The flow of incompressible microstretch fluids is governed by a coupled system of differential equations involving the velocity vector −q, microrotation vector −v and the scalar v representing the microstretch of the fluid element. The paper employs the energy method for obtaining criteria for the universal stability of microstretch fluid flows and provides an algorithm for the determination of the critical Reynolds number. It is seen that the Reynolds number can be defined in terms of the maximum speed of the primary flow.     

Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.     

On the linear theory of micropolar elasticity

The present paper is concerned with some theorems in the linear dynamic theory of homogeneous and anisotropic micropolar elastic solids. The reciprocity theorem is derived without using the Laplace transform. Two variational theorems which fully characterize the solution of the mixed problem are given.     

The coupled theory of micropolar thermoelastic diffusion

The general equations of motion and constitutive equations are derived for a general homogeneous anisotropic medium with a microstructure, taking into account the effects of heat and diffusion. We establish a reciprocal relation, which involves two thermoelastic diffusion processes at different instants. We show that this relation can be used to obtain reciprocity, uniqueness and continuous dependence theorems. The reciprocity theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. The uniqueness theorem is derived without the positive definiteness assumption on the elastic, conductivity and diffusion tensors. We prove also that the reciprocal relation leads to a continuous dependence theorem studied on external body loads. Finally we prove the existence of a generalized solution by means of the semigroup of linear operators theory.     

Linear viscoelastic behavior of porous media with non-uniform saturation

Heterogeneous moisture distribution is usually observed in partially saturated porous media in the form of saturation patches. Such local heterogeneity can significantly influence the macroscopic hydro-mechanical and acoustic behavior of porous media. In this paper, a linear viscoporoelastic model is presented that can be used to address the effects of local fluid flow in the heterogeneously saturated porous media subjected to a small perturbation. The effects of local flow are characterized using the notion of capillary relaxation. The complex, frequency-dependent material properties characterizing the viscoporoelastic behavior are derived. A rigorous procedure is presented to evaluate the material parameters. The proposed model describes well the effects of patchy saturation on the dispersion and attenuation of the compressional wave in partially saturated rocks. It is found that at high saturation the effects of local gas-pressure redistribution are not negligible. A procedure is proposed to determine the capillary relaxation times using acoustic data. The proposed model provides an alternative methodology to characterize the effects of patchy saturation on the acoustic behavior of partially saturated porous media.     

Reflection of plane micropolar viscoelastic waves at a loosely bonded solid-solid interface

A solution of the field equations governing small motions of a micropolar viscoelastic solid half-space is employed to study the reflection and transmission of plane waves at a loosely bonded interface between two dissimilar micropolar viscoelastic solid half-spaces. The amplitude ratios for various reflected and refracted waves are computed for a particular model for different values of bonding parameter. The variations of these amplitude ratios with the angle of incidence are shown graphically. Effects of bonding parameter and viscosity on the amplitude ratios are shown.     

Generalized thermoelasticity with memory-dependent derivatives involving two temperatures

A new generalized model of two-temperature thermoelasticity theory with time-delay and Kernel function is constructed. Taylor theorem in terms of memory-dependent derivatives is proved. The governing coupled equations of the new generalized thermoelasticity with time-delay and Kernel function, which can be chosen freely according to the necessity of applications, are applied to a one-dimensional problem of a half-space. The bounding surface is taken to be traction free and subjected to a time-dependent thermal shock. Laplace transforms technique will be used to obtain the general solution in a closed form. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory have been constructed. Some comparisons are shown in the figures to estimate the effects of the temperature discrepancy and time-delay parameter on all of the studied fields.     

Shell elements with drilling degree of freedoms based on micropolar elasticity theory

Based on the theory of micropolar elasticity, new degenerated shell elements with drilling degree of freedoms are presented. The proper stiffness on the drilling degree of freedom is derived and no spurious modes are encountered in these elements. The implementation of these new shell elements on general structural finite element programs has many advantages, especially for the analysis of a folded shell or the treatment of the twist moment normal to the shell. Several numerical examples are carried out to demonstrate the accuracy and applicability of the present elements. The effects of the coupling factor and the body moment induced in magneto-solid mechanics are also studied.