The Application Of Variational Principle And Low Order Element In Cosserat Continuum Theory

For Cosserat continuum model widely used in geotechnical engineering problems, using the interface subroutine UEL (user-defined element) provided by large finite element analysis of ABAQUS platform, and compiling Cosserat unit subroutine with FORTRAN, inplant the Cosserat unit into ABAQUS, with the help of preprocessing and postprocessing fountion of ABAQUS, finished the following work:Under the framework of Cosserat, introduced the four node quadrilateral element based on the Hu-Washizu mixed variational principle, to overcome the shortage that conventional four node unit can’t simulate incompressible problems, and have the advantages of resistanting to distort and small computation cost. Stress concentration model is established to simulatie the stress concentration phenomenon around a small hole by using conventional four node quadrilateral element u4ω4, variational principles of four node quadrilateral element u4ω4p, eight node quadrilateral u8ω8element. It shows that the u4co4p and u8ω8element has good performance with simulation of incompressible problems, and the u4co4element also have the advantage of resistanting to distort and small computation cost, so the u4ω4p and u8co8element may have better promising applications.Implanted pressure-related Cosserat elastic-plastic constitutive integration algorithm in the subroutine UEL, a plane plate compression test model is established to confirm the element that based on Cosserat continuum theory of variational principles of Hu-washizu Q1P0, Q1PS0element and based on the classical continuum Hu-washizu Q1P0element of variational principle, in which element is more suitable for application in practical engineering. It shows that the Cosserat continuum element based on ABAQUS platform is accord with general the general rules in terms of the strain localization phenomenon. The Cosserat continuum element based on variational principle overcomes the conventional four node quadrilateral element volume locking, and optimizes the mesh dependence. And it shows a good adaptability in the numerical simulation of large deformation capacity.Strain softening mechanism of the non-associated flow rule and associated flow rule materialsis is analyzed from two aspects.①In the process of finite element, strain softening can be divided into structure softening under non associated flow rule and the associated flow rule of material softening,the curve of stress-strain relationship is softening due to the uniqueness of solutions is lost.②From the perspective of material plastic constitutive relationship, the associated flow rule and the non associated flow rule is conncted by plastic factor, and obtained the equivalent stiffness modulus under non associated flow rule, so the non associated flow rule of strain softening phenomenon became more clearly.Based on the methods of the scale connection between Cosserat continuum and the the discrete particle model, according to discrete element material parameters derived the Cosserat continuum material parameters, and the continuum model is established with the same size of discrete element model to perform numerical simulations. Process of the formation of shear band and shear band pattern is analyzed. In addition, the conclusion reached by4.2.3is verified. It shows that the shear zone firstly produced in the four corners, and then developed to the whole model area in the experiment of plane strain. When there is strain softening materials, forming a pair of "X" type shear zone, else forming the two pairs of "X" type shear zone.Carsington dam numerical model is established respectively by classical continuum QIPSO element and Cosserat continuum QIPSO element to carry on the numerical simulation, the starting position of the plastic zone, plastic zone extending process, resulting in the crucial factor for the formation of landslide zone are analyzed. And the well-posedness of gradual destruction of the Cosserat continuum element is verified. It shows that the break began in the underlying yellow clay layer, and the plastic zone developed along the yellow clay layer and led to core turn to plastic collapse, the last layer of the load eventually led to the formation of slide surface, eventually led to the destruction of the dam body.