Composite structures possess lightweight and multifunctional characteristics, and are extensively utilized in engineering applications. However, the associated design and manufacturing technologies remain under development, particularly concerning the topology design of multi-material structures exhibiting distinct tensile and compressive material properties. This paper develops a multi-material topology optimization framework for addressing the rational allocation of multiple materials involving distinct tensile and compressive moduli. To address the challenges posed by the discontinuity between tensile and compressive moduli, a smooth constitutive model for materials with distinct moduli is introduced. By introducing multi-material design variables for each element, a linear multi-material interpolation scheme is proposed. Subsequently, an updating scheme for these multi-material variables is constructed based on optimality criteria (OC). The multi-material topology layouts with clear and smooth interfaces are achieved through the application of multiple floating projection constraints that gradually push the design variables towards values of 0 or 1. Finally, 2D and 3D numerical examples are presented to demonstrate the capability and effectiveness and advantages of the proposed topology optimization algorithm in exploiting material potentials and enhancing structural performances.
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