THE INVERSE PROBLEM OF PLANE STRAIN IN POWER-HARDENING ELASTICOPLASTICITY MATERIALS

Power-hardening elastoplastic materials have a wide range of engineering applications, such as metal pipe manufacturing and geotechnical analysis. The constitutive parameters of power-hardening elastoplastic materials (such as Young's modulus) and the boundary conditions of a structure (such as displacements) are often difficult to be determined. Under this circumstance, the inverse problem provides a new approach for determining these parameters. In the present work, ABAQUS UEL (user element subroutines) and the CVDM (complex variable-differentiation method) are combined to solve the inverse problem of plane strain mechanics based on power-hardening elastoplastic materials. Firstly, the traditional user element subroutine is used as the framework to convert a real variable in the subroutine into a complex variable, and the complex user element is established. Then the complex variable-differentiation method is used to determine the sensitivity matrix of the displacements at measurement point with respect to the inverse parameters. Finally, the inverse problem is solved iteratively by the Least-squares method and Gaussian elimination method. Numerical examples are given to discuss the influence of the CVDM on the accuracy of the direct problem calculation, and the accuracy of the present algorithm. The influence of initial value and measurement errors on inversion results are also investigated.