A pressure-loaded soft functionally gradient spherical capsule under finite deformation

Abstract

Functionally gradient materials (FGMs) possess continuously varying properties, which avoid the problem of stress concentrations arising from abrupt material discontinuity in composite materials. Recent interests in soft FGMs for robotics and medical applications have motivated the present work, which develops analytical solutions for soft functionally gradient (FG) spherical capsules subjected to internal and external pressures. The work considers large deformation and second-order elasticity. Assuming power laws for the varying elastic constants, analytical solutions for the radial displacement and the first Piola-Kirchhoff and Cauchy stresses can be obtained in close and non-dimensional form. Considering gradient indices α and β for the second- and third-order elastic constants, the key results are: (1) the nonlinear elasticity contributes significantly to the elastic deformation, (2) different α and β values may result in displacement and stresses which are vastly different in magnitude and opposite in sign, (3) combined α and β values may be used to minimize the stress throughout the spherical capsule, thus aiding the theoretical design of FGMs, and (4) the thickness of the capsule influences the displacement and stress distributions significantly and the optimum thickness is dependent on the gradient indices.