Numerical and experimental investigation of an elastoplastic contact model for spherical discrete elements

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.

Unloading of elastoplastic spheres from large deformations

“…Both figures show the limitations of using a linear model for unloading stiffness, even when the gradients are independently calibrated for each material. The results shown in Fig..10 may be compared with the analytical and numerical findings of Rojek et al[23], which, conversely, show that the linear relation of Luding is appropriate. However, it should be noted that a hardening plasticity model was used in this study with only a single set of parameters.…”

“…Rathbone et al used finite element studies to establish the magnitude of an effective curvature for a Hertzian unloading response as a function of Poisson's ratio and displacement before unloading, for spheres subject to small deformations. Finite element studies were conducted by Rojek et al [23] to determine the unloading response of metal spheres, described by a powerlaw hardening plasticity model, for a wide range of displacements, concluding that the linear Walton-Braun relationship between dimensionless load and dimensionless displacement is sufficiently accurate, and that unloading stiffness (defined as maximum load before unloading divided by recovered displacement) has a linear dependence on dimensionless displacement. Recognising the importance of contact area development for particle load-displacement response, Vu-Quoc et al [24] developed an incremental algorithm for elastoplastic contact based on tracking the development of total and plastic contact area, which was calibrated using finite element simulations and shown to be accurate for small displacements.…”

Analysis and Calibration of Parameters of Wet-Viscous Paddy Mud Particles Based on the Slump Experiment

“…The paddy mud studied in this paper has a high water content due to long-term soaking, and the adhesion between particles leads to complex and diverse mechanical behaviors of paddy mud. The Hertz-Mindlin with JKR cohesion contact model can better characterize the obvious adhesion and agglomeration between particles due to electrostatic force and water content, which is suitable for moisture-containing materials with significant bonding and agglomeration caused by moisture Rojek et al, 2019), as shown in Fig. 6.…”

Particle-Based Approach for Simulation of Nonlinear Material Behavior in Contact Zones

“…In this case, element-element interaction is traditionally modelled using harmonic interaction potentials (such an interaction is schematically represented by connecting the centers of the elements with two springs oriented in the central and tangential directions) [22,28,29]. Some models also use nonlinear (elastic-plastic or viscoelastic Maxwell type) formulations of pair-wise interaction forces F cp ik and F tp ik [30,31] for simulation of granular media and porous structures with non-linear/ductile rheological properties of the material of the skeleton walls or granules. However, such potentials make possible adequate description of the mechanical behavior of porous systems only at a "low" scale (the scale of discontinuities or granules).…”