Two-dimensional Contact Mechanics Of Functionally Graded Magneto-electro-elastic Composite Materials

Magneto-electro-elastic composite materials (MEEMs) which are comprised of piezoelectric phase and piezomagnetic phase have been received considerable attentions in lots of high technology applications due to their coupling effects among the mechanical deformations and the electromagnetic fields. In practical engineering applications, smart devices and structures made of MEEMs may suffer from surface indentation damage because of the external contact forces and friction loads. Besides, the frictional heating always plays an important role in the sliding frictional contact problems, and the temperature rise induced by the frictional heating may significantly influence the performance of the contact system. In the past several years, theoretical and experimental studies in contact mechanics of functionally graded materials (FGMs) have discovered that the resistance to contact deformation and damage can be significantly improved by adjusting the gradient index of FGMs. In this thesis, the frictionless contact problem and the sliding frictional thermal contact problems of the functionally graded magneto-electro-elastic materials (FGMEEM) are derived to provide the information in improving the resistance to contact damage and electromagnetic failures. The main contents and conclusions include:1. The frictionless contact problem between FGMEEM layered half-plane and the rigid flat and cylindrical punches is investigated. It is assumed that the punches are electro-magnetic conductors, and the electro-magnetic parameters of FGMEEM layer varies exponentially along the thickness direction. It is seen that the gradient index and the electro-magneto-mechanical loads have significant effects on surface MEE fields. The contact behavior can be influenced and the resistance to contact deformation can be improved by adjusting the gradient index of FGMEEM.2. The sliding frictional contact problem of the FGMEEM layered half-plane under a rigid flat conducting punch is studied. The Coulomb type friction law is adopted in the contact region. By using the Fourier integral transform, the problem is converted to Cauchy singular integral equations of the first and the second kind. By developing an iterative algorithm, these equations are then solved numerically. The results show that the gradient index and the friction coefficient have effects on surface MEE fields. With the increasing of the friction coefficient, a greater concentration of surface normal contact stress takes place near the trailing end of the flat punch, which means the contact damage can be induced in this region. The interior MEE fields are sensitive to the variation of the gradient index. However, the friction coefficient has no effect on the interior MEE fields except the longitudinal distribution of the normal stress.3. The contact problem of the homogenous MEE half-plane subjected by a rigid flat punch is considered. The punch is assumed to slide over the surface of the MEE half-plane at a slow constant velocity, and the heat flux generated by friction is totally absorbed by MEE half-plane. It can be seen that the surface normal contact stress and the normal magnetic induction are sensitive to the variations of the friction coefficient and the punch sliding speed. However, the friction coefficient and the punch sliding speed have no effect on normal electric displacement. With the increasing of the friction coefficient and the punch sliding speed, the surface temperature field and the in-plane contact stress within the contact region increase.4. The sliding frictional contact problem between the FGMEEM layer resting on a perfectly insulated rigid half-plane and a rigid flat punch is researched. It is assumed that the electro-magnetic parameters of the FGMEEM layer vary as an exponential function through the thickness direction. With the help of Fourier transform, we convert the problem to the coupled Cauchy singular integral equations of the first and the second kind. The iterative algorithm is adopted to solve the equations numerically and the surface temperature field and MEE fields are obtained. The results show that the gradients index, the friction coefficient and the punch sliding speed have significant effect on the surface temperature field and the MEE field. With the increasing of the friction coefficient and the punch sliding speed, a greater concentration of the contact stress takes place near the trailing end of the punch. The surface temperature field increases with the increasing of the friction coefficient and the punch sliding speed, and decreases with the increasing of the gradient index.