Lattice Discrete Particle Model (LDPM): Comparison of Various Time Integration Solvers and Implementations

Lattice Discrete Particle Model (LDPM): Comparison of Various Time Integration Solvers and Implementations

WoS Article

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 as well as implementations for central processing unit (CPU) and 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.

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 as well as implementations for central processing unit (CPU) and 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.

explicit solver, fracture, heterogeneity, implicit solver, inelasticity, lattice discrete particle model, LDPM, softening

explicit solver, fracture, heterogeneity, implicit solver, inelasticity, lattice discrete particle model, LDPM, softening

LALE, E.; ELIÁŠ, J.; YU, K.; TROEMNER, M.; STŘEDULOVÁ, M.; KHOURY, J.; XUE, T.; KOUTROMANOS, I.; FASCETTI, A.; AYHAN, B.; CHEN, B.; LUZIO, G.; LYU, Y.; PATHIRAGE, M.; PIJAUDIER-CABOT, G.; SHEN, L.; TASORA, A.; YANG, L.; ZHONG, J.; CUSATIS, G.

13.05.2026

Wiley

International journal for numerical and analytical methods in geomechanics

50

8

United Kingdom of Great Britain and Northern Ireland

3468

3488

21

https://doi.org/10.1002/nag.70286