Improvement of size effect simulation based on an energy-balanced exponential softening bond model and fracture energy regularization

Although the Mode I fracture of rock demonstrates a noticeable size effect, current contact models in the discrete element method cannot simulate the size effect very well. An exponential softening bond model is proposed to address this issue based on an exponential damage law and an elliptic yield criterion. Its basic formulas are established on energy balance to ensure that the total fracture energy of the normal and shear springs always equals the fracture energy dissipated by the resultant contact force. The simu-lations of uniaxial tensile and three-point bending tests were conducted to demonstrate the perfor-mances of the proposed model on the fracture simulations. The particle size dependency is successfully eliminated by fracture energy regularization, in which the force-displacement relationship is adjusted based on fracture energy and particle size. The simulation results show that the exponential softening bond model effectively simulates the whole load-displacement curves of experimental tests. It also demonstrates a perfect energy balance among external work, internal energy, and fracture energy. Besides, compared with the other two bond models, the exponential softening bond model is more pre-cise in representing the fracture toughness, the fracture process zone, and the size effect of the Mode I fracture of limestone. (c) 2023 Elsevier Ltd. All rights reserved.