Stress-driven nonlocal homogenization method for cellular structures

Strong size-dependent mechanical behaviors can be observed in cellular structures violating the principle of scale separation and cannot be captured by classical homogenization methods. This paper proposes a stress-driven nonlocal homogenization method to capture the size-dependent mechanical behavior due to the nonlocal force of cellular structures. A nonlocal discrete element model is proposed first to describe the nonlocal deformation mechanism of cellular structures. Then, a continuum stress-driven nonlocal homogenization method is calibrated by deriving the continuum limit from the nonlocal discrete element model. The continuum homogenization method releases the assumption of scale separation by introducing an intrinsic length, which can be calibrated by high throughput numerical computation. Also, for efficient prediction of size-dependent mechanical behaviors, an offline dataset of the intrinsic length is constructed for different unit cells. With the help of the offline dataset, the proposed homogenization method improves the accuracy of the classic homogenization method and reduces the computational cost of the high-fidelity finite element method. Finally, a cellular rod under tension is used as an application to illustrate the efficiency and accuracy of the proposed homogenization method. Results indicate that compared with the classic homogenization method, the relative error of the proposed homogenization method is less than 1% which has a good consistency with the high-fidelity method. Moreover, the computational efficiency of the proposed homogenization method is more than five times that of the high-fidelity finite element method.