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This work aims at introducing stress responses within a topology optimization framework applied to the design of periodic microstructures. The emergence of novel additive manufacturing techniques fosters research towards new approaches to tailor materials properties. This paper derives a formulation to prevent the occurrence of high stress concentrations, often present in optimized microstructures. Applying macroscopic test strain fields to the material, microstructural layouts, reducing the stress level while exhibiting the best overall stiffness properties, are sought for. Equivalent stiffness properties of the designed material are predicted by numerical homogenization and considering a metallic base material for the microstructure, it is assumed that the classical Von Mises stress criterion remains valid to predict the material elastic allowable stress at the microscale. Stress constraints with arbitrary bounds are considered, assuming that a sizing optimization step could be applied to match the actual stress limits un

This work investigates a simplified approach to cope with the optimization of preliminary design of structures under local fatigue constraints along with a global enforcement on the overall compliance. The problem aims at the minimization of the weight of linear elastic structures under given loads and boundary conditions. The expected stiffness of the optimal structure is provided by the global constraint, whereas a set of local stress-based constraints ask for a structure to be fatigue resistant. A modified Goodman fatigue strength comparison is implemented through the same formalism to address pressure-dependent failure in materials as in Drucker-Prager strength criterion. As a simplification, the Sines approach is used to define the equivalent mean and alternating stresses to address the fatigue resistance for an infinite life time. Sines computation is based on the equivalent mean and alternate stress depending on the invariants of the stress tensor and its deviatoric

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This paper shows how the design of a structure can evolve when considering a stressbased\ud topology optimization along with fatigue failure constraints. More precisely,\ud fatigue failure is added in a stress-based topology optimization Matlab code by following\ud the approach of the design of machine elements, i.e. based on S-N curves or\ud fatigue criteria. The fatigue is introduced through weel-known criteria for high-cycle\ud fatigue such as the Sines and Crossland criteria. The paper presents how these criteria\ud can be formulated for a topology optimization problem. Numerical results for\ud both criteria are successively compared and discussed. The character of fatigue failure\ud in the optimization procedure is illustrated as well as some issues that have to be\ud improved in future work