Research Of Multi-nonlinear Precise Algorithm Based On Bi-potential Theory And Metal Forming Software Development

The numerical simulation of metal forming plays an important role in the development of advanced industries,which will directly affect the realization of the blueprint of the “Made in China 2025” program.The multi-nonlinear precise algorithm is highly significant in the simulation of the metal forming.It is found that the bi-potential expression of elasto-plastic materials based on the bi-potential theory can not only satisfy the constitutive laws,but also describe the orthogonality clearly.In addition,the bi-potential contact algorithm can efficiently produce accurate contact forces.However,there are few researches about the bi-potential of elastic-plastic materials with large deformation in the study of multi-nonlinear precise algorithm.Moreover,it will be difficult and time-consuming to develop a customized CAE software for the metal forming.Although the software development platform OMTDesk provides powerful preprocessing and postprocessing functionalities,the lack of metal forming modules limits its application in industrial manufacturing.This thesis focuses on the numerical simulation of the metal forming and takes the multi-nonlinear precise algorithm as the breakthrough point.Based on the bi-potential theory,the geometric nonlinearity,material nonlinearity and contact nonlinearity related to the metal forming process are investigated.Combining with the OMTDesk software development platform,a customized CAE software FEM/Form for metal forming is developed independently.This thesis summarizes the research work from four aspects: theoretical derivation,numerical implementation,numerical verification and software development as follows:1.The theoretical derivation of the multi-nonlinear precise algorithm for the metal forming is provided.The Updated-Lagrange framework is adopted for tackling the geometric nonlinearity.In combination with the requirement of objectivity,the variables involved in the constitutive laws for models with large deformation are determined.Based on the bi-potential theory,an efficient method is designed for establishing the bi-potential function of elasto-plastic models with material nonlinearity.Thus,the bi-potential functions of the isotropic hardening Prager-Ziegler model,the kinematic hardening Armstrong-Frederick model and the non-associated Drucker-Prager model under large deformation are derived.For the contact nonlinearity,the complete contact friction laws are described by the bi-potential contact expressions.The elastic-plastic bi-potential factor is introduced to calculate the predicted contact force,whose projection on the friction cone can be used to correct the contact force.2.The numerical implementation of the multi-nonlinear precise algorithm is presented.The configuration transformation in the process of large deformation is established by using the hypothesis of the rotationally neutralized objectivity.Based on the idea of return mapping algorithm,the bi-potential constitutions of the three elastic-plastic models introduced in the theoretical derivation are numerically investigated.The contact pair of the system is defined by using the master-slave contact model.Meanwhile,the collision detected is performed by the brute force method.The Uzawa iterative solution is used in the bi-potential contact algorithm.Combining the three-part nonlinearity with the global equilibrium iterative solution,a multi-nonlinear precise algorithm for solving metal forming is obtained.3.The accuracy and stability of the multi-nonlinear precise algorithm are investigated.The stress-strain relations of the three elastic-plastic models introduced above are established by simulating the uniaxial tension and compression.The accuracy and stability of the bi-potential constitutive algorithm are numerically verified.Through the elastic and elasto-plastic contact examples,it is proved that the bi-potential contact algorithm can effectively control the penetration and make the calculation of contact force more accurate than other algorithms.The correctness of the geometric nonlinearity algorithm is proved by simulating the tensile necking of a circular rod.At the same time,the tensile simulation of the funnel specimen is successfully realized,and the relationship between stress and strain is modified by combining the experimental numerical coupling technique.In the case of considering dynamic effect,it is found that the multi-nonlinear precise algorithm satisfies the energy conservation of the system.The accuracy of the algorithm is further verified.4.Combined with the multi-nonlinear precise algorithm and based on the OMTDesk software development platform,the customized CAE software FEM/Form for metal forming is developed independently.The effects of the yield stress and the friction coefficient on the springback are investigated via simulating a block forging process.An extrusion forming process is simulated and the contact states between the extrusion piece and the die are studied.When the friction coefficient increases,the rolling phenomenon appears on the edge of the extrusion piece and agrees well with the practicality.FEM/Form can be customized targeted based on the character of the practical problem.The comparison between FEM/Form,ANSYS and ABAQUS verifies the reliability of the results of the FEM/Form.Numerical simulations of the straight pipe bending with small radius are carried out also.The deformation and changes of the cross section and the thickness during the bending process are discussed.Compared with the existing effective software,the FEM/Form can produce comparable and even better results.Therefore,the FEM/Form is practical and useful in the numerical simulation for the metal forming problems.The innovations of this doctoral dissertation are summarized as follows:1.Three kinds of elastic-plastic bi-potential constitutive models considering large deformation are proposed and implemented numerically;2.A set of multi-nonlinear precise algorithm is established,and numerical verification is carried out through three nonlinear problems: geometric nonlinearity,materials nonlinearity and contact nonlinearity.3.A large deformation elastoplastic solution module based on OMTDesk software development platform are developed,as well as a metal forming customized CAE software FEM/Form.