Controlling the maximum stress in bi-modulus material structure topology optimization based on a novel four-phase material model

Bi-modulus material structures have wide applications in practical engineering. However, existing research on bi-modulus material structure design has an inaccurate finite element analysis. Furthermore, these studies fail to consider stress constraints, leading to deviations in the calculated response of the resulting designs and the presence of stress concentration. This is the first study to propose a topology optimization design method for bi-modulus material structures under stress constraints, which is based on a four-phase material model. Firstly, a bi-modulus material substitution method is constructed, which incorporates tensile-dominant, compressive-dominant, orthotropic, and void materials. This method enables a rational and effective solution for the response of bi-modulus material structures. Secondly, a criterion for determining element state based on principal stress values and tensile/compressive tolerance limits is proposed, which can more accurately identify the tension/compression state of elements. Subsequently, a topology optimization model for bi-modulus material structures under stress constraints is established by integrating the Solid Isotropic Material with Penalization (SIMP) method, the Kreisselmeier-Steinhauser (K–S) aggregation function, and the Stability Transformation Method (STM), and the Method of Moving Asymptotes (MMA) is employed to update the design variables. Finally, the effectiveness and versatility of the proposed method are verified by several two-dimensional and three-dimensional numerical examples.