Optimization of a lattice spring model with elastoplastic conducting springs: a case study

The article considers a simple lattice spring model in which every spring is elastoplastic and is capable of conducting current. The elasticity bounds of spring i are taken as [−ci,ci] and the resistance of spring i is taken as 1/ci, which allows computation of the resistance of the system. The model is further subjected to a gradual stretching and, due to plasticity, the response force increases until a certain terminal value. It is demonstrated that the recently developed sweeping process theory can be used to optimize the interplay between the terminal response force and the resistance on a physical domain of parameters ci. The proposed methodology can be used by practitioners for the design of multi-functional materials as an alternative to topological optimization.