Lattice discrete particle modeling of concrete under cyclic tension–compression with multi-axial confinement

Zhongfeng Zhu, Madura Pathirage, Wenwei Wang, Matthew Troemner*, Gianluca Cusatis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Accurate modeling of concrete mechanical behavior under cyclic loading with different levels of confinement is crucial in design and analysis of structures subjected to seismic events. One robust model for simulating concrete behavior is the Lattice Discrete Particle Model (LDPM), a discrete model formulated at the scale of aggregate and composed of polyhedral cells connected through a lattice of nonlinear fracturing struts. To improve the performance of LDPM for the prediction of mechanical behavior under different cyclic loading schemes and multi-axial confinement, a comprehensive cycling constitutive model, a modified volumetric–deviatoric compression law, and a modified frictional behavior under compression are established in this study. An effective strain and a corresponding effective stress at the mesoscale are formulated and used to determine the stress–strain relationship under monotonic loading. In addition, the constitutive relationships related to the tension and shear stresses are established separately to ensure a smooth stress transition from tension to compression state. Two material parameters are used to control the stiffness attenuation: the residual plastic strain, and the energy dissipation of concrete during loading and unloading, under both tension and compression. Further, a new constitutive equation for the frictional behavior under compression is proposed to simulate the post-peak behavior under confinement. The proposed constitutive model is used to simulate the mechanical behavior and failure mode of concrete under tension–compression cycling and hydrostatic pressure. Triaxial tests under different levels of confinement and unconfined compression tests are also simulated. Model validation is performed using multiple data sets available in the literature on concretes of various strengths. Simulation results show that the established cyclic constitutive model can effectively characterize the mechanical response of concrete under different cycling loadings and confining pressures.

Original languageEnglish (US)
Article number128985
JournalConstruction and Building Materials
StatePublished - Oct 17 2022


  • Constitutive modeling
  • Cycling behavior
  • Lattice Discrete Particle Model (LDPM)
  • Multi-axial behavior
  • Tension–compression

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • General Materials Science


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