The multiple fields created by two perfectly‐conducting punches on piezoelectric/piezomagnetic materials with anisotropy

Abstract

This article proposes an analytical model of two perfectly conducting punches acting on piezoelectric/piezomagnetic materials with anisotropy. For six types of distinct or repeated roots, related auxiliary function are obtained. The closedform solutions of the reduced integral equations are derived for two electrically-conducting and magnetically-conducting flat punches. The stress, electric displacement and magnetic induction intensity factors at both edges of each punch are given explicitly in terms of the distance between the two punches and the width of each punch. Numerical test is done to demonstrate the contributions of the distances between the two flat punches and various material properties on the contact behaviors. The obtained results delineate that at the outer edges, there has stronger strength for the singularities of the surface contact stress, surface electric displacement and surface magnetic induction compared with that at the inner edges.Most materials exhibit anisotropic behavior [1], either due to crystalline structure or because the material possesses more complex structural composition at the nanoscale. Evolution of anisotropy has a significant impact on material properties [2]. Indentation technique is a powerful tool to study materials properties, which is widely used in the semiconductor, biomedical, and magnetic recording industries [3][4][5][6], and etc. Developing indentation technique needs the solution of contact problem of anisotropic materials, which is an important and interesting subject concerned by many researchers. Clements and Ang [7] solved generalized plane contact problems for an anisotropic half-space and layer in which the elastic moduli vary quadratically with the spatial variables. Kuchytsky-Zhyhailo and Rogowski [8] investigated the rigid spherical indenter contacting with an anisotropic linear elastic layer bonded to a rigid substrate. Boffy et al.[9] performed a contact analysis of deformable bodies loaded normally and tangentially against graded layers bonded to heterogeneous substrates. Recently, Barber and Ciavarella [10] proposed an approximate JKR solution for the adhesive contact of anisotropic materials, and found that the dimensionless degree of anisotropy can significantly increase the pull-off force.The growing application of new and especially anisotropic composite materials in modern engineering gives rise to new challenges in mechanics. For example, because of exhibiting a remarkable cross-coupling between the electric and magnetic ferroic orders [11][12][13], piezoelectric/piezomagnetic materials have great potentials to be widely used in smart materials/intelligent structures. The effect of anisotropy on the performances of piezoelectric/piezomagnetic materials is of interest. Zhao et al. [14] derived the analytical solutions in an anisotropic piezoelectric/piezomagnetic bi-material to reveal the effect of different non-uniform loadings (dislocations and tractions) on the induced fields. Problems of anisotropic piezoelectric/piezomagnetic materials...

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

“…The obtained right-hand side expression of Eq. (32), which is first given, reveals the noteworthy difference between the contact analysis of classical materials (e.g., piezoelectric materials [31] and piezomagnetic materials [32] ) and that of FGTEMs considered here. Specifically, from Eq.…”

“…As for homogeneous thermoelectric materials, there exists sQ 21 = Q ∞ 1 which can lead to K 22 (x, r) = 0. Then, the singular integral equation (32) for FGTEMs can degenerate into the case of isotropic thermoelectric materials. Furthermore, it should be noted that if without thermoelectric loads and gradient parameters, L 2 (s) associated with the particular solutions of the displacements will also vanish.…”