Structural topology optimization involving bi-modulus materials with asymmetric properties in tension and compression

Many materials show asymmetric performance under tension and compression and their mechanical property can be well simulated by a so-called bi-modulus type constitutive relation. The underlying non-smoothness nature associated with this kind of constitutive behavior, however, makes it extremely difficult to investigate structural topology optimization problems involving bi-modulus materials. In the present paper, rigorous sensitivity results and efficient solution procedure for topology optimization problems involving a single-phase bi-modulus material are established and generalized to two-phase bi-modulus materials case. The validity and effectiveness of the proposed approach are verified by analytical solutions and numerical results. It is also found that the optimal structural topologies may be highly dependent on the tension to compression modulus ratios and quite different from the one obtained under the assumption of linear elasticity. Besides, the present results can be successfully used for engineering applications such as design of no-tension/no-compression structures and strut-and-tie models.

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