Equilibrium analysis of 2D complex discrete assemblies modelled using cracking blocks with non-dilatant interfaces

In recent years, innovative computational methods for designing sustainable discrete element assemblies have gained attention, focusing on materials with low carbon footprints and environmentally friendly joinery methods. In particular, dry joints, used to assemble blocks without mortar, can perform minimal environmental impact as reduces material consumption as well as providing sustainable assembling and disassembly processes. This research introduces Joint Layout Design (JLD), a new 3D computational approach for modelling and assessing discrete element assemblies with complex-shaped, non-planar interfaces. Unlike standard methods that consider blocks as rigid, JLD accounts for potential internal failures by considering finite internal material strengths in tensile and shear modes. The JLD method models potential failure planes within blocks using inner interfaces with a finite tensile and shear strength, while the contact among rigid blocks occurs on dry unilateral interfaces governed by a non-associative Mohr-Coulomb friction law. The mechanical problem is framed as a limit analysis equilibrium problem and solved via interactive second-order cone programming. JLD analyses of 2D mechanical problems are proposed and validated to demonstrate its advantages and limitations, including an analysis of a flat arch inspired by Leonardo's arch, which is benchmarked against the distinct element method in 3DEC.