A strain energy-based elastic parameter calibration method for lattice/bonded particle modelling of solid materials

A generic strain energy-based parameter calibration method is proposed to calibrate the elastic parameters of lattice or bonded-particle modelling of solid materials. Unlike surrogate models or general optimisation-based calibration methods in the discrete element method, this approach does not require running any physical simulations to obtain tentative solutions and thus ensures high calibration efficiency. The novelty of this method is achieved in five aspects: (1) the calibrated parameters are physically decoupled as elastic and strength parameters; (2) the calibration of elastic parameters is converted as an optimisation problem to minimise the difference of strain energy between the discrete and continuum systems; (3) the strain energy is analytically determined in both systems; (4) explicit expressions of gradients of the loss function facilitate obtaining the optimal particle-scale parameters; and (5) when subjected to two independence strain fields, a closed-form solution is derived for a pair of uniform normal and tangential stiffnesses. The proposed calibration framework is validated with four different examples. All the results confirm the reliability of the proposed calibration method in lattice or bonded-particle modelling of solid continua.