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

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.

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

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.
Paper Structure (24 sections, 12 equations, 8 figures, 15 tables)

This paper contains 24 sections, 12 equations, 8 figures, 15 tables.

Table of Contents

  1. Introduction
  2. LDPM Governing Equations
  3. Numerical Implementations
  4. LDPM Mesh Generation
  5. Explicit and Implicit Solvers
  6. AE: ABAQUS Explicit
  7. CI: Project Chrono
  8. CA: Cast3M
  9. OA: Open Academic Solver
  10. MP: FEMultiPhys code
  11. JA: JAX-LDPM
  12. JU: Julia LDPM (JuLDPM) package
  13. Numerical examples
  14. Free vibrations in linear elastic regime
  15. Hardening behavior in uniaxial strain compressive test
  16. ...and 9 more sections

Figures (8)

  • Figure 1: (a) LDPM particles in a cubic geometry following placement procedure; (b) set of two LDPM polyhedral cells composed of a single particle and their surrounding facets; (c) set of four LDPM particles and associated facets; (d) original and projected LDPM facets; (e) typical traction versus strain curves at the LDPM facet level; (d) typical normal traction versus normal strain curves in compression.
  • Figure 2: (a) dimensions of the specimen; (b) FFT of the response; (c) translations $u_x$ of the corner node in time.
  • Figure 3: The uniaxial strain test: (a) dimensions of the specimen; (b) nominal stress-strain response in the vertical direction; (c) number of iterations of implicit solvers; (d) kinetic energy; (e) percentage error in energy balance; (f) distribution of the volumetric strain scalar in the final time step.
  • Figure 4: The dog bone test: (a) dimensions of the specimen; (b) stress-displacement response in the vertical direction; (c) number of iterations of implicit solvers; (d) kinetic energy; (e) percentage error in energy balance; (f) crack pattern in the final time step.
  • Figure 5: The three-point bending test: (a) dimensions of the specimen & crack pattern in the final time step; (b) load-displacement response; (c) number of iterations of implicit solvers; (d) kinetic energy; (e) percentage error in energy balance.
  • ...and 3 more figures