In this paper, a level-set-based method is presented to deal with the multi-material topology optimization of compliant mechanisms with stress constraints. A novel stress-based multi-material topology optimization model of compliant mechanisms is proposed. In this model, the multi-material level set topology description model and the separable stress interpolation scheme are adopted.The weighted sum method is used to deal with the multi-objective optimization of the output displacement and compliance of compliant mechanisms. The penalty of stresses is also considered in the objective function to control the local stress level in different materials. To solve the optimization problem, the parametric level set method is employed, and the sensitivity analysis is conducted. Application of the method is demonstrated by 2 numerical examples. Results show that the multi-material structures without undesirable de facto hinges can be obtained. The output displacement and compliance of the compliant mechanisms are optimized, and stress constraints in different materials are simultaneously satisfied. KEYWORDS compliant mechanisms, level set method, multi-material topology optimization, stress constraint 1 | INTRODUCTION Compliant mechanisms are defined as those which utilize the deformation of the flexible pieces to transfer motion, force, and energy. 1 In the last 20 years, topology optimization of compliant mechanisms is always attracting great attention. 2-4 There are 2 kinds of compliant mechanisms: lumped compliant mechanisms and distributed compliant mechanisms.The flexibility of the lumped compliant mechanisms is mainly derived from the localized areas (ie, hinge areas), 5 while the flexibility of the distributed compliant mechanisms is provided by the whole mechanism. 6 Whether lumped or distributed compliant mechanisms are optimal is a long standing and still open question in the field. 7 One issue is certain; however, there are 2 main difficulties in the topology design of the compliant mechanisms, namely the combination of the stiffness and flexibility, and the control of the stress level. 8 Compliant mechanisms should be stiff enough to support the applied loads and flexible enough to meet the kinematic requirements at the same time. The methods of dealing with the topology optimization of compliant mechanisms can be classified into 2 categories. The first one is to maximize some kinds of mechanical measurements, including mechanical advantage, 9 geometrical advantage, 10,11 mechanical efficiency, 12 and output displacement. 7,13 A comparative study of the above formulations for the topology optimization of compliant mechanisms is given in the work by Deepak et al. 14 The second handling method is considering a multi-objective topology optimization based on both the stiffness

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