Green’s Function Lattice Dynamics: a semi-analytical boundary element method for architected materials
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We present closed-form lattice Green’s functions for shearable beam-based lattice structures and use them in a semi-analytical boundary element method in line contact. We showcase load–indentation responses for different lattice topologies in contacts with widths ranging from below the size of individual lattice elements to the lattice characteristic length. The Green’s Function Lattice Dynamics method is an alternative to asymptotic homogenisation, multi-scale modelling, and the quasi-continuum method, capturing the sub-element mechanical properties while remaining computationally tractable across length scales.
