Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements

This paper focuses on topology optimization utilizing incompressible materials under both small- and finite-deformation kinematics. To avoid the volumetric locking that accompanies incompressibility, linear and nonlinear mixed displacement/pressure (u/p) elements are utilized. A number of material interpolation schemes are compared, and a new scheme interpolating both Young's modulus and Poisson's ratio (E-nu interpolation) is proposed. The efficacy of this proposed scheme is demonstrated on a number of examples under both small- and finite-deformation kinematics. Excessive mesh distortions that may occur under finite deformations are dealt with by extending a linear energy interpolation approach to the nonlinear u/p formulation and utilizing an adaptive update strategy. The proposed optimization framework is demonstrated to be effective through a number of representative examples.