Measuring forces in a 2D multi-contact system using the virtual fields method: Principle, simulations and experimental application to a three-particle system

This paper proposes an experimental approach to measure contact forces in a two-dimensional system composed of cylindrical particles using the Virtual Fields Method (VFM). This identification method relies on the knowledge of the strain distribution in the particles forming the discrete medium. Synthetic strain data provided by a finite element model (with added noise) were first used as input data for the identification procedure. It is shown that if the mechanical response of the constitutive material is known, the contact forces applied to a particle can be identified, since they are proportional to a weighted average of the strain components, the weights being the virtual strain components. Various strategies were tested to propose kinematically admissible fields for the virtual displacement. Identification technique robustness was studied with respect to various sources of error, such as noise in the strain field, missing data along the boundaries, and a possible spurious shift between real and virtual fields. An experimental application was then performed on a three-particle system subjected to confined compression by processing strain maps obtained using Localized Spectrum Analysis (LSA) for each particle. In addition to the VFM equations, particle equilibrium and Newton's third law of motion were taken into account to propose a relevant strategy for processing the experimental data. The results open up prospects for applications to granular materials composed of numerous particles.