Rotation of single rigid inclusions embedded in an anisotropic matrix: a theoretical study

Abstract

This paper presents a theoretical analysis of instantaneous rotation of elliptical rigid inclusions hosted in a foliated matrix under bulk tensile stress. The foliated matrix is modelled with orthotropic elastic rheology, considering two factors as measures of anisotropy: m = μ 0 / E 1 0 and n = E 2 0 / E 1 0 , where μ 0 is the shear modulus parallel to the foliation plane and E 1 0 and E 2 0 are the Young moduli along and across the foliation, respectively. Normalized instantaneous inclusion rotation ( ω) is plotted as a function of the bulk tension direction ( α) with respect to the long axis of the inclusion, taking into account two parameters: (1) anisotropic factors m and n, and (2) the inclination of the foliation plane to the long axis of inclusion ( θ). In the case of θ=0°, ω versus α variations are sinuous, showing maximum instantaneous rotation in positive and negative sense at α=45 and 135°, respectively, irrespective of m and n values. The magnitude of maximum ω increases with decrease in m, i.e. increasing degree of anisotropy in the matrix. On the other hand, decreasing the value of the anisotropic factor n results in decreasing instantaneous rotation. ω increases with the aspect ratio R of inclusion, assuming an asymptotic value when R is large. This asymptotic value is larger for lower values of m. In case of θ≠0°, ω versus α variations are asymmetrical, showing maximum instantaneous rotation at varying inclusion orientation for different m. For given m and n, with increase in θ the sense of instantaneous rotation reverses at a critical value of θ.