Bending of elastic plates with a physically nonlinear inclusion

An infinite elastic isotropic plate with an elliptical, physically nonlinear inclusion loaded at infinity by uniformly distributed moments is considered. Surface loads are absent. The problem of the stress-strain state of the plate is solved in a closed form. It is shown that, for reasonably general stress-strain relations for the inclusion, the bending-moment field (and the corresponding curvatures) in the inclusion is homogeneous. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 152–157, November–December, 2006.     

Effective characteristics of elastic physically nonlinear composites

Moscow Chemical Machine Construction Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 1, pp. 12–16, January, 1990.     

A crack on the interface between a linear elastic medium and a stress-state dependent physically nonlinear medium

A crack on the interface between a linear elastic medium and a stress-state dependent physically nonlinear medium is studied. A numerical method to solve such problems is proposed. Some asymptotic distributions of stresses, strains, and displacements near the crack tip are obtained under the assumption that the forces and displacements are continuous on the interface.     

Inverse problem of deformation of a physically nonlinear inhomogeneous medium

An isotropic linearelastic (viscoelastic) plane containing various physically nonlinear elliptic inclusions is considered. It is assumed that the distances between the centers of the inclusions are much greater than their dimensions. The problem is to determine the orientation of the inclusions and the loads applied at infinity which ensure a specified value of the principal shear stress in each inclusion. Necessary and sufficient conditions of existence of the solution of the problem are formulated for a plane strain of an incompressible inhomogeneous medium.     

Determination of elastic moduli of composite medium containing bimaterial matrix and non-uniform inclusion concentrations

Reservoir porous rocks usually consist of more than two types of matrix materials,forming a randomly heterogeneous material.The determination of the bulk modulus of such a medium is critical to the elastic wave dispersion and attenuation.The elastic moduli for a simple matrix-inclusion model are theoretically analyzed.Most of the efforts assume a uniform inclusion concentration throughout the whole single-material matrix.However,the assumption is too strict in real-world rocks.A model is developed to estimate the moduli of a heterogeneous bimaterial skeleton,i.e.,the host matrix and the patchy matrix.The elastic moduli,density,and permeability of the patchy matrix differ from those of the surrounding host matrix material.Both the matrices contain dispersed particle inclusions with different concentrations.By setting the elastic constant and density of the particles to be zero,a double-porosity medium is obtained.The bulk moduli for the whole system are derived with a multi-level effective modulus method based on Hashin's work.The proposed model improves the elastic modulus calculation of reservoir rocks,and is used to predict the kerogen content based on the wave velocity measured in laboratory.The results show pretty good consistency between the inversed total organic carbon and the measured total organic carbon for two sets of rock samples.     

Formation fronts of a nonlinear elastic medium from a medium without shear stresses

The fronts of phase transition of a medium without shear stresses to a nonlinear incompressible anisotropic elastic medium are considered. The mass flux through unit area of a front is assumed to be known. The variation of the tangential components of the medium’s velocity and the variation of the arising shear stresses are studied. An explicit form of boundary conditions is found using the existence condition of a discontinuity front structure. The Kelvin–Voight viscoelastic model is adopted for this structure.     

Anti-plane pull-out of a rigid line inclusion from an elastic medium

The transient and static anti-plane problem of a rigid line inclusion pulled out from an elastic medium is studied. The singular integral equation method is used to solve the stress field. Under the static load, the stress intensity factor(SIF) at the inclusion tips increases with the medium length. The problem becomes equivalent to an inclusion in a medium with an infinite length when the length of the medium is 3.5times longer than that of the inclusion. However, under the transient load, the ...     

Spheroidal rigid inclusion in an elastic medium under torsion

The displacement field is determined when a rigid spheroidal inclusion is present in an infinite, isotropic and homogeneous elastic medium under torsion. The values of the force and moment are derived. The solutions for the limiting cases of a sphere and a circular disk are also presented. The analysis is based on suitable distributions of singularities on the axis of symmetry of the inclusion.     

Tensor-linear determinative equations for a nonlinear elastic anisotropic medium

International Applied Mechanics -     

Bonding a linearly piezoelectric patch on a linearly elastic body

A rigorous study of the asymptotic behavior of the system constituted by a very thin linearly piezoelectric plate bonded on a linearly elastic body supplies various models for an elastic body monitored by a piezoelectric patch.     

Stress state of infinite medium with elastic paraboloidal inclusion

S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 12, pp. 15–21, December, 1993.     

Heterogeneous linearly piezoelectric patches bonded on a linearly elastic body

In [1], we studied the response of a thin homogeneous piezoelectric patch perfectly bonded to an elastic body. Here we extend this study to the case of a very thin heterogeneous patch made of a periodic distribution of piezoelectric inclusions embedded in a linearly elastic matrix and perfectly bonded to an elastic body. Through a rigorous mathematical analysis, we show that various asymptotic models arise, depending on the electromechanical loading together with the relative behavior between the thickness of the patch and the size of the piezoelectric inclusions.