<p>In the realm of concrete structure design, the stress-based optimization method faces a significant limitation. This is because concrete strength is predominantly governed by strains rather than stresses, and the distribution of element strains often varies considerably. To address this issue, this paper puts forward a strain-based topology optimization approach. The method aims to minimize the structural peak strains while taking material nonlinearity into account. It utilizes the <i>p</i>-norm to approximate nonlinear strains and the adjoint method to establish the sensitivity for optimization. The research findings indicate a remarkable reduction in peak strains. Under the premise of ensuring numerical stability, using a larger <i>p</i>-value can achieve superior optimal topology results. By gradually filtering the sensitivity and updating the design variables, the influence of highly nonlinear strain characteristics on the optimization process can be alleviated. Consequently, compared with the stress-based topology optimization, the strain-based method is more conducive to the design of concrete structures. The nonlinear simulation results of the reinforcement design example further demonstrate that components designed with a reinforcement layout guided by a strut-and-tie model derived from strain-based topology optimization exhibit enhanced crack resistance compared to traditional methods. These components also possess a higher load-bearing capacity and improved ductility, thus fulfilling the optimization objectives.</p>