Development and implementation of inelastic material models for use in FEMDEM numerical methods with applications

Abstract

The combined Finite–Discrete Element Method (FEMDEM) is one of the most versatile numerical frameworks for the mechanical analysis of multi-body industrial applications. Currently, the inclusion of only elastic and brittle material models limits the problems that can be realistically simulated. This new work focuses on expanding the capabilities of existing FEMDEM codes in order to include inelastic material models successfully. After describing and implementing the appropriate theoretical and numerical framework for elasto-plasticity, a thorough numerical verification analysis is presented. Test cases, varying from simple one-dimensional quasi-static problems through to fully three-dimensional impact analysis, are explored to illustrate the stability, accuracy and robustness of the inelastic behaviour implemented. The extension of this plasticity implementation to finite deformations is then discussed. The ability of the extended simulation tool to capture large strain non-linear phenomena is then numerically demonstrated with the successful analysis of two benchmark problems: (a) the high-speed impact of a copper rod against a wall; (b) the unconfined uniaxial compression of a cylinder with Mohr-Coulomb plasticity. To explore the potential range of the new model, a complete case study to simulate concrete crushing behaviour during an impact test is performed. A simple experimental setup is designed to investigate steel-to-concrete inelastic collisions focusing on the energy losses via the coefficient of restitution. The processed experimental results, combined with concrete-characterisation tests are used to calibrate a two-parameter Mohr-Coulomb material model via parametric numerical analysis. In order to overcome current limitations, a generalised piece-wise Drucker-Prager plasticity model to accommodate non-linear material plasticity behaviour is developed and corresponding return-mapping equations are discussed in detail. The foregoing extension to large strain plasticity of the in-house FEMDEM multi-body simulator, Solidity, is discussed in a more general context by reviewing recent FEMDEM development and application research being undertaken at Imperial College. Finally, this work is put into the overall context of the multi-physics research plans by providing preliminary analysis results for two industrial applications: (a) concrete armour units impacts, (b) powder compaction.