Development of a visco-elastoplastic contact force model and its parameter determination for apples

• A visco-elastoplastic contact force model has been developed and tested for apples.
• Stiffness of different apple cultivars (Jonagold, Joly Red and Kanzi) was determined experimentally.
• Contact parameters were determined by fitting the model to impact data.
• The visco-elastoplastic model gives better results than a viscoelastic model.

A contact force model was developed to model the visco-elastoplastic (VEP) behaviour of apples. The model is based on the elastoplastic Thornton model and has been written in a pressure-based formulation to extend the application of the model to Discrete Element Method (DEM) simulations with arbitrary rounded shapes. The parameters of the new developed VEP contact force model were determined by fitting the experimental data acquired from Jonagold, Joly Red and Kanzi apples impacted by a pendulum. With only one parameter set per cultivar and for a large impact range (impact velocity range: 0.3–1.5 m/s), the VEP-model (R2 = 0.90 ± 0.13) provides a better description of the force-deformation profiles than the viscoelastic Kono and Kuwabara (KK) model (R2 = 0.71 ± 0.20). The equivalent Young’s modulus (E*) was also determined under quasi-static conditions, which resulted in measured E*-values for Jonagold, Joly Red and Kanzi apples of respectively 4.24 ± 0.96 MPa, 5.09 ± 1.27 MPa and 7.82 ± 0.41 MPa. The novel VEP-model has the potential to help predict and understand bruise damage in apples as well as other horticultural products.