Identification of contact forces and Thermomechanical Couplings in 2D granular systems using simulations and full-field measurement techniques: VFM, LSA and IRT

Abstract

Granular materials are collections of solid particles of various shapes, materials and sizes, making their behavior complex. In the past, effective understanding was mainly derived from experiments, which were limited by the equipment available at the time. Numerical approaches based on the Discrete Element Method were then developed. These are powerful, reliable and widely used as efficient tools for studying granular media. In comparison, experimentation was not as widespread due to difficulties of preparation and instrumentation. In recent decades, non-contact full-field measurement techniques based on cameras have become increasingly familiar and attractive in the experimental mechanics community. This is due to rapid advances in equipment. Some of these were used to study two-dimensional (2D) granular media under mechanical loading: particle image velocimetry (PIV) to measure strain patterns; digital image correlation (DIC) to measure strains within deformable particles; photoelasticimetry to measure shear stresses in particles made of birefringent material; and thermoelastic stress analysis (TSA) based on infrared thermography (IRT) to measure hydrostatic stresses in particles. Some of these techniques enabled identifying the interparticle forces using appropriate image processing. However, there are certain limitations due to the specifications of each technique. Besides, soft granular materials have rarely been studied with these techniques. In this context, the aim of the thesis is to develop other full-field techniques for two purposes: 1) to identify contact forces using the virtual fields method (VFM) from knowledge of the strain distribution obtained by localized spectrum analysis (LSA); 2) to identify thermomechanical couplings in soft particles using IRT. Synthetic strain data provided by a finite element model were first used for the first objective. It was 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 an integral of the measured strains weighted by their virtual counterparts. Various strategies were tested to propose kinematically admissible fields for the virtual displacements. Identification robustness was studied with respect to various sources of error. Measurements by LSA, providing a relevant compromise between strain resolution and spatial resolution, were then performed on a three-particle system and bigger systems made of PA66 cylindrical particles. In addition to the VFM equations, particle equilibrium and Newton’s third law of motion were considered to propose a relevant strategy for processing the experimental data. The statistical analysis for bidisperse and tridisperse systems allowed to characterize the exponential and power laws for the strong and weak force networks, respectively, that are usually found in polydisperse dry systems. For the second objective, granular media made of thermoplastic polyurethane (TPU) cylinders with ellipsoidal cross-section were subjected to cyclic confined compression while being observed by an IRT camera. TPU was chosen because it features entropic elasticity, which gives a higher thermal signature than the materials used for TSA. This material also lends a soft character to the granular systems produced. Based on considerations of adiabaticity and thermodynamic cycle completion, strong thermoelastic coupling (TEC) was revealed in the contact areas between all particles due to stress concentrations. Strong mechanical dissipation (MD) was found at specific contacts and within some particles due to damage, viscosity and friction. TEC data was processed for a granular system comprised of about 600 interparticle contacts, providing statistical information. It is demonstrated that IRT provides valuable information to open prospects for building thermodynamically relevant models suitable for soft granular materials.