Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

A review of recent works on inclusions

This article presents a general theory on indentation over a multiferroic composite half-space. The material is transversely isotropic and magneto-electro-elastic with its axis of symmetry normal to the surface of the half-space. Based on the corresponding half-space Green’s functions to point sources applied on the surface, explicit expressions for the generalized pressure vs. indentation depth are derived for the first time for the three common indenters (flat-ended, conical, and spherical punches). The important multiphase coupling issue is discussed in detail, with the weak and strong coupling being correctly revisited. The derived analytical solutions of indentation will not only serve as benchmarks for future numerical studies of multiphase composites, but also have important applications to experimental test and characterization of multiphase materials, in particular, of multiferroic properties.

https://blogs.uakron.edu/ernianpan/files/2014/09/188-2010JMPSChenPanWangZhang.pdf

Theory of indentation on multiferroic composite materials

Wave propagation in non-homogeneous magneto-electro-elastic plates

Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip

By virtue of the separation of variables and orthogonal expansion technique, the plane strain dynamic problem of a magneto-electro-elastic hollow cylinder is reduced to two integral equations of two time functions. Then, by means of the interpolation method, the integral equations are solved successfully. As a result, all the transient responses of displacements, stresses, electric potentials, electric displacements, magnetic potentials and magnetic inductions are completely obtained. The present method is suitable for the analysis of hollow cylinders with arbitrary thickness and subjected to arbitrary mechanical and electromagnetic loads. Numerical results are also presented.

Peng-Fei Hou

Papers

The transient responses of magneto-electro-elastic hollow cylinders

The transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems

Green’s functions for transversely isotropic magnetoelectroelastic media

Fundamental solution for transversely isotropic thermoelastic materials

The transient responses of a special non-homogeneous magneto-electro-elastic hollow cylinder for axisymmetric plane strain problem