# On the Measurement of Particle Contact Curvature and Young's Modulus Using X-ray \(\mu\)CT
## 1 Introduction  
Contact curvature is a critical parameter in particle mechanical response based on [PERSON]'s contact theory. In particular, contact curvature plays a pivotal role in the measurement of Young's modulus, which is an indispensable input parameter in the discrete element method (DEM) for modelling particle-particle and particle-equipment interactions [1]. The significance of particle shape in DEM has been studied by [PERSON] et al. [2] and [PERSON] et al. [3]. This is because non-spherical particles are more diverse than spherical particles in nature and industries, which results in additional intricate features such as complicated contact force and secondary motion [4]. Over the past decades particle morphology and its influence on the mechanical properties of particulate materials such as Young's modulus have been vastly studied. Using a lower Young's modulus is a common practice to speed up the simulation in DEM. The reduction of Young's modulus in DEM simulation has been studied in various applications. For example, a study of Young's modulus in the range 0.0001-0.01 of the real value was carried out in the mixing of particles in a rotary drum [5]. It showed that [PERSON]'s modulus has a significant effect on the motion of individual particles during collision. However, little effect was found in the mixing of a granular bed which is the cumulative effect of all individual particles' motion. The effect of Young's modulus in DEM simulation of particulate systems has been specifically investigated by several researchers. The DEM simulation of flow behaviour for the discharging particlesimplies that a reduction in [PERSON]'s modulus can speed up the DEM simulations without altering the bulk flow behaviour [6]. The three reference values of [PERSON]'s modulus are varied at 0.02, 2.0 and 200 GPa. The corresponding time step is 5 \(\times\) 10\({}^{-6}\) s, 5 \(\times\) 10\({}^{-7}\) s, and 5 \(\times\) 10\({}^{-8}\) s, leading to the computation time as \(\sim\)0.5, \(\sim\)3 and 240 h, accordingly. It was further reported that the input value of [PERSON]'s modulus ranging from 10\({}^{7}\) to 10\({}^{11}\) has negligible effect on the repose angle measurement. However, in the cases of compression and penetration, the reduction of [PERSON]'s modulus should be cautioned with regards to bulk stiffness and bulk restitution. Complex imaging-based methods were proposed to quantitatively describe particle morphology and texture [7; 8; 9]. [PERSON] and [PERSON] showed that particle shape can impose a significant impact on stiffness [10]. The influence of geometrical properties of constituent grains on the overall granular material response was experimentally examined [11]. It was found that the threshold force where Hertzian behaviour takes over is dependent on topographical feature of the particle including size, roundness and roughness. Moreover, the influence of particle shape was much more pronounced than the influence of surface roughness in the macro-scale compression tests. Young's modulus of particle is routinely determined using [PERSON]'s equation [12], in which the averaging method of principal curvature is adopted regardless of the true profile of the particle. Given a natural particle with imperfect roundness, it will be problematic to choose the averaging radius as the equivalent radius. Furthermore, the effect of particle roundness on elastic stiffness should not be negligible especially when sphericity of a particle exceeds a tolerance level. Interestingly, few literatures are available to demonstrate the effect of contact curvature on the determination of elastic modulus even though the importance of particle shape has been recognized by the aforementioned studies. Although numerous experimental devices have been developed to measure the Young's modulus of a particle [13; 14; 15; 16], the measurement of contact curvature is scarce for non-spherical particles. As a consequence, the influence of contact curvature on [PERSON]'s modulus determination remains elusive.