Investigation of instabilities arising in internal element connectivity parameterization

In this paper, we address a newly discovered local instability observed in geometrically nonlinear analysis using the Internal Element Connectivity Parameterization (I-ECP) approach. I-ECP offers advantages in topology optimization of nonlinear elastic structures compared to conventional material scaling approaches (e.g. SIMP), including more robustness against excessive deformations. However, under certain conditions, we observe local instabilities in low-density areas using I-ECP as well. These instabilities can result in analysis failure and premature termination of the topology optimization process. We report on this finding and present a small numerical example exhibiting the undesired behavior. Furthermore, we provide insight into its origin on a fundamental level based on an I-ECP truss as well as using the general I-ECP governing equations. In conclusion, when sufficient support of surrounding elements is lacking, highly compressed I-ECP patches can trigger a buckling mode on system level. Our analysis reveals that the element-link arrangement employed in I-ECP results in a magnification of negative eigenvalues, which promotes the instability. In addition to an investigation of this phenomena, we provide various directions for stabilization. Keywords: Topology optimization, Internal Element Connectivity Parameterization, geometrical nonlinearity, material nonlinearity, instability.