A new analytical solution of pure bending beam in couple stress elasto-plasticity: Theory and applications

An analytical solution in couple stress elasto-plastic theory is presented for the pure bending beam under small deformation. This solution considers the effects of both elastic deformation and plastic deformation, and gives the relationship between the moment M and the curvature κ implicitly. This solution can eliminate the shortcomings in the rigid-plastic solutions by Stolken and Evans (1998), Chen and Wang (2000, 2001) et al., and is proved to be more effective in materials with high plastic hardening or small plastic deformation. Moreover, numerical results show that the solution can be used to predict the size effects in the microbend tests and to measure their material length parameter.