A micromechanical strain gradient theory for instability problems in granular materials
Material instabilities play an important role in many engineering problems because they trigger zones of highly localized straining, which often act as a precursor to failure. Classical continuum mechanics approach has been proven insufficient to study material instability problems which involve highly localized straining. Instead, an enhanced approach is required to describe strongly nonlinear behavior and local weakness of the material.
In this research, high-gradient constitutive models have been developed to study the instability problems of materials, in particular of granular materials. In a high-gradient model, strain gradient and higher-order stress are incorporated in the constitutive equation as additional variables. Therefore, the high-gradient model is useful in describing highly localized straining.
A strain gradient model is developed using the microstructural approach in elastic range as the basis and starting point of the research. The developed strain gradient model is implemented in the finite element formulation based on a modified variational principle. Several numerical examples are presented and compared with the results of the classical continuum models.
To study material instability, the strain gradient model is extended to inelastic range. The von-Mises, Drucker-Prager and Cam-Clay strain gradient plasticity models have been developed. A simple shear test and a biaxial test are analyzed using the developed strain gradient plasticity model. The results demonstrate that the strain gradient model effectively removes the spurious mesh sensitivity of finite element simulations. The finite element solutions also show that the shear bandwidth is not only a function of material internal length but also of the distribution of weak spots.
Two soil instability problems are analyzed using the strain gradient plasticity model. The results show that the traditional limit equilibrium methods could possibly overestimate the ultimate bearing capacity of the foundation. It is necessary to use the more realistic soil models to evaluate the performance of the foundation.
Finally, a micromechanical strain gradient plasticity model is derived from the mobilization behavior of micro-scale local planes. The model is calibrated based on the experimental data. The model is capable to simulate stress strain curves including: pre-peak strain hardening, post-peak strain softening, dilatancy, critical state. Instability of boundary value problems is analyzed and the results are compared with other strain gradient models.