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Explore the Lattice Discrete Particle Model (LDPM) through this 10-minute conference talk that introduces JuLDPM, a Julia implementation for fracture simulations in engineering mechanics. Learn how lattice models simulate solid media behavior using dense networks of 1D elements connected on structured or unstructured node sets, tracing their origins from Navier and Cauchy's central force approach (1827) through Hrennikoff's framework method to modern LDPM applications. Discover how LDPM distinguishes itself by directly representing mesoscale material features through randomly placed poly-sized spheres that idealize inclusions like aggregate particles in concrete, with lattice elements constructed via Delaunay tessellation and inertial properties derived from dual tessellation designed for crack path representation. Follow three lightning talks covering significant LDPM advancements: stochastic approaches for porous cementitious composite fracture simulation, dual tessellation extensions for erosion simulation in flood protection infrastructure, and novel reduced-order modeling techniques using Proper Orthogonal Decomposition. Examine numerical implementation techniques in JuLDPM including automatic differentiation, graph coloring, multithreading via Threads.jl, and ongoing HPC cluster deployment research for solving elasticity and fracture problems in cementitious composites and granular assemblies.
