Optimizing inclusion shapes and patterns in periodic materials using Discrete Object Projection

Current topology optimization methodologies assume a monolithic, free form approach to design. Many engineered materials and structures, however, are composed of discrete, non-overlapping objects such as fiber or particle-based materials. Application of the topology optimization methodology to these types of materials therefore requires controlling the shape and interaction of designed features to ensure solutions are meaningful and physically realizable. Achieving such control on continuum domains is challenging as features form via the union of elements of like phase. A topology optimization approach is proposed herein for optimizing the size, shape, and layout of inclusion-like features in a continuum domain. The technique is based on the Heaviside Projection Method and uses multiple regularized Heaviside functions whose interaction is tailored so that the designer may restrict the minimum and maximum length scale of inclusions, and minimum spacing between inclusions. The technique is demonstrated on the design of material microstructures with enhanced elastic stiffness.