Bifurcation phenomena of a biphasic compressible hyperelastic spherical continuum

A basic linear bifurcation problem is solved for a representative biphasic composite spherical cell. Setting is that of an internal inclusion that expends with an external shell made of a different material. Exact rate equations are derived in the framework of hyperelastic continuum mechanics. Sample examples are solved numerically revealing sensitivity of critical strain levels and bifurcated mode pattern to strength differential between both phases. Mathematical framework can be adapted to other types of constitutive responses.