Lattice Discrete Particle Model (LDPM): Comparison of Various Time Integration Solvers and Implementations
2026-03-13 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors compare different ways to use the Lattice Discrete Particle Model (LDPM) to simulate how concrete and similar materials behave under stress. They test these methods using various computer setups (CPU and GPU) and solver types to see how well they handle realistic scenarios like cracking and compression. They measure accuracy, speed, and stability of the simulations and provide detailed data and code so other researchers can try and improve upon their work. This study helps understand which LDPM implementations work best for modeling complex concrete behavior.
Lattice Discrete Particle Modelconcrete simulationquasibrittle materialsimplicit solverexplicit solverGPU computingstrain softeningcrack patternsnumerical stabilitybenchmark testing
Authors
Erol Lale, Jan Eliáš, Ke Yu, Matthew Troemner, Monika Středulová, Julien Khoury, Tianju Xue, Ioannis Koutromanos, Alessandro Fascetti, Bahar Ayhan, Baixi Chen, Giovanni Di Luzio, Yuhui Lyu, Madura Pathirage, Gilles Pijaudier-Cabot, Lei Shen, Alessandro Tasora, Lifu Yang, Jiawei Zhong, Gianluca Cusatis
Abstract
This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of transient implicit and explicit solvers and steady-state (static) solvers and implementations for Central Processing Unit (CPU) as well as Graphics Processing Unit (GPU). The various implementations are compared on the basis of a set of benchmarks tests describing behaviors of increasing computational complexity. They include elastic vibrations, confined strain-hardening compressive response, tensile fracture, and unconfined strain-softening compressive response. Metrics of interest extracted from the simulations include macroscopic stress versus strain responses, computational times, number of iterations, and energy balance error. Pairwise comparison of final crack patterns is provided through the correlation coefficient and normalized root mean square error of the crack opening vectors. Moreover, for the most numerically challenging case of unconfined compression with sliding boundary conditions, the stability of the strain-softening response is tested by perturbing the solutions as well as changing the convergence criteria and time step size. Attached to this paper is the complete input data of the benchmark tests; this will allow researchers to run the examples and compare them with their own implementations. In addition, most of the reported implementations are publicly available in open source packages.