  We examine how disordering joint position influences the linear elastic
behavior of lattice materials via numerical simulations in two-dimensional beam
networks. Three distinct initial crystalline geometries are selected as
representative of mechanically isotropic materials low connectivity,
mechanically isotropic materials with high connectivity, and mechanically
anisotropic materials with intermediate connectivity. Introducing disorder
generates spatial fluctuations in the elasticity tensor at the local (joint)
scale. Proper coarse-graining reveals a well-defined continuum-level scale
elasticity tensor. Increasing disorder aids in making initially anisotropic
materials more isotropic. The disorder impact on the material stiffness depends
on the lattice connectivity: Increasing the disorder softens lattices with high
connectivity and stiffens those with low connectivity, without modifying the
scaling between elastic modulus and density (linear scaling for high
connectivity and cubic scaling for low connectivity). Introducing disorder in
lattices with intermediate fixed connectivity reveals both scaling: the linear
scaling occurs for low density, the cubic one at high density, and the
crossover density increases with disorder. Contrary to classical formulations,
this work demonstrates that connectivity is not the sole parameter governing
elastic modulus scaling. It offers a promising route to access novel mechanical
properties in lattice materials via disordering the architectures.
