Project

ICARUS: higher-order constitutive relations for granular materials

Goal: The mechanical behaviour of granular materials subjected to large deformations is important in many problems in science and engineering. Current numerical simulation methods using zeroth-order constitutive relations give results that are dependent on the employed mesh size. This problem can be circumvented by using higher-order constitutive relations. However, current higher-order constitutive relations are heuristic, thus in many cases the results are still mesh-size dependent. Using an innovative multi-scale approach, I will constructively challenge current higher-order continuum theories from a fundamental perspective, namely by consideration of the underlying microstructure, in order to obtain mesh independent solutions. In ICARUS, I will: 1) develop micromechanical expressions for three-dimensional higher-order strain and stress tensors for granular materials, 2) construct higher-order constitutive models within the thermodynamic framework, based on micromechanical analyses of DEM simulations, and 3) demonstrate their capabilities in solving “benchmark” geotechnical large-deformation problems. My investigation results in a computational simulation method that provides valuable insights in large-deformation engineering problems and thus will aid in assessing and reducing risks of natural hazards, with benefits for society.

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Chaofa Zhao
added a research item
For granular materials, the kinematic degrees of freedom at the microscale of particles are the particles' displacements and rotations. In classical continuum mechanics, the kinematic degree of freedom at the macroscale is the (local) displacement field. The rotation of a material element is not independent but is determined by the antisymmetric part of the displacement gradient. The objective of this study is to investigate, mainly by means of discrete-element method simulations, whether the average particle rotation is equal to the continuum rotation determined from the average displacement gradient. In the three-dimensional discrete-element method simulations of shear tests (with nonzero average continuum rotation), simulations with and without contact couples have been analyzed. The simulation results show that the average particle rotation is effectively equal to the continuum rotation, over the whole range of strains. Additionally, the results of an X-ray tomography test of a rounded granular soil under triaxial compression are analyzed. The average rotation of soil particles inside shear bands agrees well with the average continuum rotation determined from the particle displacements. Comparison of simulation results with contact couples to those where contact couples were not considered reveals that the presence of contact couples has a significant effect on the stress ratio and on the volumetric strain. The stress tensor is symmetric, even when contact couples are included.
Chaofa Zhao
added a project goal
The mechanical behaviour of granular materials subjected to large deformations is important in many problems in science and engineering. Current numerical simulation methods using zeroth-order constitutive relations give results that are dependent on the employed mesh size. This problem can be circumvented by using higher-order constitutive relations. However, current higher-order constitutive relations are heuristic, thus in many cases the results are still mesh-size dependent. Using an innovative multi-scale approach, I will constructively challenge current higher-order continuum theories from a fundamental perspective, namely by consideration of the underlying microstructure, in order to obtain mesh independent solutions. In ICARUS, I will: 1) develop micromechanical expressions for three-dimensional higher-order strain and stress tensors for granular materials, 2) construct higher-order constitutive models within the thermodynamic framework, based on micromechanical analyses of DEM simulations, and 3) demonstrate their capabilities in solving “benchmark” geotechnical large-deformation problems. My investigation results in a computational simulation method that provides valuable insights in large-deformation engineering problems and thus will aid in assessing and reducing risks of natural hazards, with benefits for society.