Response evolution of mechanical metamaterials under architectural transformations

Architectural transformations play a key role in the evolution of complex systems, from design algorithms for metamaterials to flow and plasticity of disordered media. Here, we develop a general framework for the evolution of the linear mechanical response of network structures under discrete architectural transformations via sequential bond swapping: the removal and addition of elastic elements. We focus on a class of spatially complex metamaterials, consisting of triangular building blocks. Rotations of these building blocks, corresponding to removing and adding elastic elements, introduce (topological) architectural defects. We show that the metamaterials' states of self stress play a crucial role in the mechanical response, and that the mutually exclusive self stress states between two different network architectures span the difference in their mechanical response. For our class of metamaterials, we identify a localized representation of these states of self stress, which allows us to capture the evolving response. We use our insights to understand the unusual stress-steering behaviour of topological defects.