Prof.  Sergey  Alexandrov
Beihang University,  China

Title: Geometric properties of principal stress trajectories in plasticity

Abstract:

Rigid plastic plane-strain and axisymmetric problems satisfying the hypothesis of Harr and von Karman are statically determinate. In particular, the stress equations are the stress equilibrium equations and a yield criterion. The principal stress trajectories form orthogonal nets in a generic plane of flow in plane-strain problems and a generic meridian plane in axisymmetric flows. These nets can be regarded as orthogonal coordinate systems. The scale factors of these coordinate systems are considered as new unknowns. It is shown that these factors satisfy simple algebraic equations. Using these equations, one can determine the coordinate curves and the principal stresses. In particular, the principal stresses are represented by simple transcendental equations for many widely used yield criteria. It is shown that the mapping between the principal-line coordinate systems and Cartesian or cylindrical coordinate systems is covered by hyperbolic systems of equations. The characteristics and characteristic relations are found for many widely used yield criteria. Numerical examples based on the approach above are provided for solving boundary value problems.

Biography:

Sergei Alexandrov is a professor at Beihang University (Beijing, China) and a research professor at the Institute for Problems of Mechanics of the Russian Academy of Science. He received his PhD in Physics and Mathematics in 1990 and DSc in Physics and Mathematics in 1994. He worked for ALCOA Technical Center (USA), GKSS Research Center (Germany), University of Aveiro (Portugal), and Seoul National University (South Korea). His research areas are plasticity theory, fracture mechanics, and their applications to metal forming and structural mechanics. He published three monographs and about 300 papers in journals included in SCIE. He is a member of the editorial boards of several international journals.