Deformation of ductile inclusions in a multiple inclusion system in pure shear

Abstract

This paper analyzes the deformational behavior of mutually interacting spherical inclusions in a multiple inclusion system, considering two physical factors: viscosity ratio between inclusion and matrix ( m) and the ratio of inclusion diameter to mean inter-inclusion distance ( a/ b). For a given value of m, the strain partitioning between a stiff inclusion and the bulk system (i.e. ratio of their natural extension rates) increases non-linearly with increasing a/ b ratios and the gradient of increase becomes steeper when the inter-inclusion distance is less than about twice their diameter (i.e. a/ b>about 0.5). The strain distribution within a deformed inclusion is homogeneous when the a/ b ratio is less than about 0.6. For larger values of a/ b, the internal deformation becomes heterogeneous, with the strain increasing or decreasing towards the core in the case of stiff ( m>1) and soft ( m<1) inclusions, respectively. The deformed shape of inclusions in section also shows departure from an ideal ellipse with an increase in the a/ b ratio. Stiff inclusions develop shapes similar to that of a super-ellipse in contrast to soft inclusions that resemble a sub-ellipse. The heterogeneity of internal deformation is also reflected in the distortion of passive foliations initially at right angles to the bulk extension direction, which become curved with convexity outward and inward, respectively, within stiff and soft inclusions.