Topologically Interlocked Material (TIM) systems are assemblies of individual building blocks shaped such that individual elements cannot be removed from the assembly with disassembly of the entire system. Here, TIM systems based on irregular quadrilateral square tessellations are considered. The mechanical properties of such TIM assemblies are investigated and compared to those of the periodic reference TIM system. Finite element computations are performed to obtain force - deflection curves and to extract stiffness, strength, and toughness. We discover that a significant fraction (about 30%) of all randomly generated architectures possess properties exceeding those of the TIM with an underlying regular tessellation. We validate this finding by experiments on 3D printed physical realizations. Design parameters to represent the mechanical properties are studied by the use of Pearson correlation coefficients. In this process, dominant variables are determined and regression models for the properties are defined from the underlying design variables. By considering the dominant variables, network patterns in the assembly are discovered, which are strongly associated with each of the mechanical properties. The findings of this study enable the design of architectured material systems with exceptional stiffness-strength-toughness combinations.


TS acknowledges support by the National Science Foundation (Award 1662177). DYK acknowledges support by Samsung.