Fracture And Contact Problems In Transversely Isotropic Medium

The interaction between mechanism, electricity, magnetism and temperature, as the defin-ing characteristic of magneto-electro-thermo-elastic materials, has been extensively exploit-ed in many areas of science and engineering. In the meantime, the multi-field couple of magneto-electro-thermo-elasticity poses mathematically challenge, which motivates recent sci-entific community to study the behaviors of magneto-electro-thermo-elastic materials.Generally, there are two categories of mathematical appratuses in solving boundary value problems in linear elasticity. One is the method of integral tranform, another is called "Potential Theory Method" intiated by Fabrikant(1989). The The seminal work, application of potential theory method to analyze thermal effects in transversely isotropic medium was dedicated by Chen and Ding(2004). The potential theory method, as a geniue mathematical appratus in trans-versely isotropic elasticity, allows us to obtain analytical solutions to some particular problems, which traditional methods are hardly or impossible to obtain. This thesis, as a logical continu-ation of Chen(2004), deals with fracture and contact induced by thermal effects in transversely isotropic medium. The main works are as follows:1) The problem of a penny-shaped crack subj ected to symmetric uniform heat flux in an infinite transversely isotropic magneto-electro-thermo-elastic medium is investigated. The exact solution in the full space is in terms of line integrals and the solution in the crack plane shows a great agreement with the solution for a transversely isotropic medium obtained by Tsai(1983). It is shown that analytical expressions for such a crack problem is impossible.2) The problem of a penny-shaped crack subjected to anti-symmetric uniform heat flux in an infinite transversely isotropic magneto-electro-thermo-elastic medium is investigated. Pre-vious researchers(Tsai1983; Niraula2006) expressed full-space solution in multiple integra-tion or line integrals involving Bessel functions. However, in this thesis, we find that the full-space solution could be in terms of the explicit elementary functions via potential theory method.3) The indentation problem of a flat circular punch with uniform heat flux distributed at its base, pressed into a semi-infinite transversely isotropic magneto-electro-thermo-elastic s- pace is investigated. The closed-form solution in the full space is obtained by potential theory method. The factors of indentation stiffness that relates mechanical force, electric charge, magnetic induction with the heat flux are presented.Due to the mathematical analogy of constitutive and governing equations between ther-mopiezoelectric, thermopiezomagnetic, thermoelastic medium and magneto-electro-thermo-elastic medium, the closed form solutions presented in this thesis are applicable for the simi-lar problems in these materials. In addition, the transversely isotropic solutions presented in this thesis can degenerated for the corresponding isotropic solutions, which can be employed to analyze the similar fracture or contact problems in isotropic medium. What’s more, the present-ed closed-form solutions can serve as a benchmark for the numerical analysis of behaviors of multi-field coupled materials.