Some Basic Problems In Mesoscale Couple Stress/strain Gradient Elasto-plasticity

Classical continuum theory includes the homogenization assumption that the material properties remain the same from macroscale to mesoscale, which has been successfully applied in structural analysis on macroscale. However, when the size scales down to mesoscale or microscale, the effect of micro-defects in material (e.g., dislocation, micro-void, micro-inclusion) emerges, which results in inhomogeneous material properties and is represented as size effects in practice. In this case, classical continuum theory is not applicable. Moreover, the pathological mesh-dependency is exhibited when classical finite element method is applied in localization problems of softening materials. Therefore, other theories are needed to solve both size effects and mesh-dependency problems.Based on Cosserat theory, many kinds of mesoscale couple stress/strain gradient theories have been developed. All of these theories include the material length parameters which can be used to describe the size of micro-defects and the width of localized deformation in softening material, and therefore can successfully predict the size effects and eliminate the mesh-dependency. However, there are some basic problems in mesoscale couple stress/strain gradient theories, e.g.,(1) The inconsistent opinions on how to build continuum theory at the mesoscale or microscale lead to the fact that unlike in the elastic mechanics, there does not exist a standard framework for the current couple stress/strain gradient theories, which are built on different concepts. Consequently, lots of mesoscale couple stress/strain gradient theories are proposed, more than 10 of which are frequently cited. It increases the difficulties in choosing proper theory for engineering application.(2) Besides several strain gradient theory based on physical mechanism, most theories include the material length parameters without specific physical meaning. The characteristics of these parameters need further research. At present, the micro-tests are used to determine the material length parameters in general, while exact and stable analytical solutions in couple stress/strain gradient elasto-plasticity are lacked as theoretical basis.Focusing on the above problems, this paper compares the characteristics of various couple stress/strain gradient theories which can be taken as reference in engineering applications, analyzes the characteristics of material length parameters based on theoretical and numerical methods, and develops two kinds of micro-bend solutions in couple stress elasto-plasticity for the convenience of determining material length parameters. The thesis is arranged as follows:In chapter 1, recent advances in mesoscale couple stress/strain gradient theories are introduced in detail, which includes the engineering backgrounds and characteristics of these theories, the differences of material length parameters between various theories, the corresponding finite element methods and mesh-free methods, and their specific applications.In chapter 2, the author summarizes several couple stress/strain gradient theories and provides the corresponding elasto-plastic constitutive relations. By analyzing the relations and differences between these theories, some basic principles are proposed as references in choosing couple stress/strain gradient theory.In chapter 3, the elasto-plastic solutions of pure-bending beam and cantilever beam are brought forward based on the couple stress theory where rotations depend on displacements. By comparison with numerical results, it is proved that both the solutions are reliable. With the corresponding micro-bend tests, both the analytical solutions can be used to determine material length parameters in mesoscale couple stress/strain gradient theories.In chapter 4, the rigid-plastic solutions are summarized in various mesoscale couple stress/strain gradient theories. Combining the solutions with experimental results of micro-torsion and micro-bend, the material length parameters in various theories are determined. Finally, it is observed that these parameters are deeply dependent on the type of couple stress/strain gradient theory.In chapter 5, two kinds of couple stress/strain gradient elements, i.e.,8-node parametric element and 18-DOF refined triangular element, are given and applied in elasto-plastic problems. By analyzing pure-bending and stress concentration problems, it is proved that the penalty approach is not stable in finite element implementation of the couple stress theory where rotations depend on displacements. By analyzing localization problems, it is shown that couple stress/strain gradient theories can effectively eliminate the mesh-dependency in classical continuum theory.