An energy-based method for interface connectivity of incompatible microstructures through parametric modeling

Abstract

With recent developments in topology optimization and additive manufacturing technology, it is now possible to fabricate architected materials with spatially varying microstructures. However, in designing these microstructures, the absence of proper interface connectivity can cause reduced effectiveness or even failure. We present a method for ensuring smooth interface connectivity for orthotropic microstructures through supershape-based parametric modeling. A microstructure can be reproduced by deleting the non-material regions, or voids, from a fully solid material domain. The proposed algorithm utilizes this void based representation to fuse two incompatible microstructures. Each of the voids of the input designs is detected and expressed using a superformula based implicit equation. To connect the two incompatible microstructures, a transition zone of intermediate microstructures are generated by morphing the voids of one structure to another. The morphing operation is posed as an optimization problem, which tries to minimize the difference between the two microstructures by altering their supershape parameters. An exact match at the interface of the intermediate microstructures is attained by putting restrictions on the shape of the voids that are neighboring each other. To prevent sharp changes in structural properties during morphing, homogenized total strain energy of the generated microstructure is constrained so that the properties are within a specified range from its previous microstructure in the sequence. Ancillary constraints on attainable volume fraction as well as on overlap of voids are also prescribed for controlling the optimization process. Several examples are provided to demonstrate the applicability of the void morphing method to find intermediate microstructures in the design space under these constraints. The proposed algorithm is a post-processing approach, therefore it is versatile and applicable to a wide variety of results since it requires the optimization problem to be formulated only at the interface region.