Appl. Math. Mech. -Engl. Ed. 31(5), 605–616 (2010) DOI 10.1007/s10483-010-0508-x c Shanghai University and Springer-Verlag Berlin Heidelberg 2010 Applied Mathematics and Mechanics (English Edition) Response of loose bonding on reflection and transmission of elastic waves at interface between elastic solid and micropolar porous cubic crystal * Rajneesh KUMAR, Meenakshi PANCHAL (Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India) (Communicated by Xing-ming GUO) Abstract The problem of reflection and transmission of plane periodic waves incident on the interface between the loosely bonded elastic solid and micropolar porous cubic crystal half spaces is investigated. This is done by assuming that the interface behaves like a dislocation, which preserves the continuity of traction while allowing a finite amount of slip. Amplitude ratios of various reflected and transmitted waves have been depicted graphically. Some special cases of interest have been deduced from the present investiga- tion. Key words micropolar, porous, cubic crystal, reflection coefficients, transmission coefficients, bonding parameter Chinese Library Classification O345, O11 2000 Mathematics Subject Classification 74A10, 74A35, 74A60, 74B05, 74J05, 74J10, 74J15 1 Introduction A non-linear theory concerning solid elastic materials consisting of vacuous pores (voids) distributed throughout the body has been formulated by Nunziato and Cowin [1] . Later, Cowin and Nunziato [2] developed a theory of linear elastic materials with voids for the mathematical study of the mechanical behavior of porous solids. They introduced the presence of pores in the classical continuum model by assigning an additional degree of freedom to each material particle, namely, a fraction of the elementary volume which results in the void of matter. Consequently, the bulk mass density of such materials was given by the product of two fields, i.e., the void volume fraction and the mass density of the matrix material. The micromorphic theory [3–4] treats a material body as a continuous collection of a large number of deformable particles with each particle possessing a finite size and an inner structure. With the assumptions such as infinitesimal deformation and slow motion, the micromorphic theory can be reduced to Mindlin’s microstructure theory [5] . When the microstructure of the material is considered rigid, it becomes the micropolar theory [6] . Different researchers (Scarpetta [7] , Passarella [8] , and Marin [9] ) discussed different types of problems in micropolar materials with voids. Minagawa et al. [10] discussed the propagation of ∗ Received May 1, 2009 / Revised Jan. 14, 2010 Corresponding author Rajneesh KUMAR, Professor, E-mail: rajneesh kuk@rediffmail.com