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

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=μ0/E10 and n=E20/E10, where μ0 is the shear modulus parallel to the foliation plane and E10 and E20 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.