Abstract
A contact model for the normal interaction between elastoplastic spherical discrete elements has been investigated in the present paper. The Walton–Braun model with linear loading and unloading has been revisited. The main objectives of the research have been to validate the applicability of the linear loading and unloading models and estimate the loading and unloading stiffness parameters. The investigation has combined experimental tests and finite element simulations. Both experimental and numerical results have proved that the interaction between the spheres subjected to a contact pressure inducing a plastic deformation can be approximated by a linear relationship in quite a large range of elastoplastic deformation. Similarly, the linear model has been shown to be suitable for the unloading. It has been demonstrated that the Storåkers model provides a good evaluation of the loading stiffness for the elastoplastic contact and the unloading stiffness can be assumed as varying linearly with the deformation of the contacting spheres. The unloading stiffness can be expressed in a convenient way as a function of the Young’s modulus and certain scaling factor dependent on the dimensionless parameter defining the level of the sphere deformation.
Highlights
Nowadays, the discrete element method (DEM) is used for modelling various particulate and nonparticulate materials such as soils, rocks, ceramics
The plastic deformation is initiated at a low load and the contact force cannot be predicted using the elastic contact models, for instance the Hertz one
Both numerical and experimental results have shown that the force–displacement curve can be approximated by a linear relationship in quite a large range of elastoplastic deformation of the contacting spheres
Summary
The discrete element method (DEM) is used for modelling various particulate and nonparticulate materials such as soils, rocks, ceramics. The model proposed by Thornton [22] considers both the elastic and plastic ranges of the contact interactions. The elastoplastic loading and elastic unloading in the Walton–Braun model are governed by linear force-displacement relationships with different slopes, which ensures a residual overlap of the particles when the contact force drops to zero. The present work is aimed at numerical and experimental investigation of validity of the linear Walton– Braun-type elastoplastic model and suitability of analytical formulae for evaluation of model parameters defining the loading and unloading stiffness. 2, a brief formulation of the contact problem in the discrete element method is given, and the formulation of the considered elastoplastic model: the Walton–Braun model with the linear loading and unloading is presented.
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