To obtain the material true constitutive relation of tensile specimens after necking, we proposed an experimental-numerical combined method (ENM) based on the simple tension test results and finite element analysis (FEA). An iterative scheme was used to minimize the errors between the simulated and experimental load-displacement curves by modifying the imported stress-strain data step by step, and the true stress was determined when the error was less than a given infinitesimal value. In addition, we developed a special program to implement this algorithm automatically and save operating time. As a verification, the true stress-strain curves obtained by the traditional analytical method (TAM) and ENM were compared and employed to analyze the large deformation behavior of both cylindrical and rectangular specimens. The results showed that ENM was applicable for both specimens and could achieve an adequate description of the mechanical response of the materials after necking formation more effectively.

In this paper, we introduce a new notion named as Schrödinger soliton. Socalled Schrödinger solitons are defined as a class of special solutions to the Schrödinger flow equation from a Riemannian manifold or a Lorentzian manifold M into a Kähler manifold N . If the target manifold N admits a Killing potential, then the Schrödinger soliton is just a harmonic map with potential from M into N . Especially, if the domain manifold is a Lorentzian manifold, the Schrödinger soliton is a wave map with potential into N . Then we apply the geometric energy method to this wave map system, and obtain the local well-posedness of the corresponding Cauchy problem as well as global existence in 1 + 1 dimension. As an application, we obtain the existence of Schrödinger soliton of the hyperbolic Ishimori system. 2000 Mathematics Subject Classification. 58J60, 35L70, 37K25. Key words and phrases. Schrödinger soliton, Schrödinger flow, wave map with potential, Killing potential. Partially supported by 973 project of China, Grant No. 2006CB805902.(Proof. Directly computing by the definition of tension field, we getSince S t is an isomorphism, we have τ (S t ) = 0 and henceOn the other hand,The last equality holds because the single parameter group S t satisfies S t • S s = S t+s . Differentiating this at s = 0, we get dS t • V = V (S t ).2

We define a class of geometric flows on a complete Kähler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equations, derivative nonlinear Schrödinger equations etc. Furthermore, we consider the existence for these flows from S 1 into a complete Kähler manifold and prove some local and global existence results.