A methodology for topology optimization to the design of compliant cellular mechanisms with and without internal contact is presented. A two-step procedure is pursued. First, a baseline noncontact mechanism is developed and optimized via an inverse homogenization method using the “solid isotropic material with penalization” approach. This compliant mechanism is optimized to yield specified elasticity coefficients, with the capability to sustain large effective strains by minimizing local linear elastic strain. In the second step, a system of internal contacts is designed. The initial continuum model of a noncontact mechanism is converted into a frame model, and possible contact links are defined. A computationally efficient algorithm is employed to eliminate those mechanisms having overlapping contact links. The remaining nonoverlapping designs are exhaustively investigated for stress relief. A differential evolution optimizer is used to maximize the stress relief. The results generated for a range of specified elasticity coefficients include a honeycomb-like cell, an auxetic cell, and a diamond-shaped cell. These various cell topologies have different effective properties corresponding to different structural requirements. For each such topology, a contact mechanism is devised that demonstrates stress relief. In one such case, the contact mechanism increases the strain magnification ratio by about 30%.

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