Finite Element Model And Software Development Based On Plane Cosserat Elastoplastic Theory

Classical continuum theory has been widely used in engineering fields,but people gradually realize that certain materials,such as concrete,rock,ceramics,etc.,will have obvious size effect at the macro level.Other materials,such as metallic materials,exhibit strong dimensional effects when the structural dimensions are on the order of microns and below,while classical continuum theory does not adequately explain the dimensional effects exhibited by materials at different sizes.The Cosserat continuum theory differs from the classical continuum theory in that it is a more general continuum theory.It considers an object to be composed of continuously distributed micro-polar particles of a certain size,which is introduced into the constitutive equation.The internal size establishes the link between the macro scale and the micro scale.Therefore,the Cosserat theory can show higher precision and better simulation results when analyzing the microscopic scale or analyzing the mechanical properties at the macroscopic scale.The research content of this paper is as follows:(1)The constitutive equation and yield criterion based on Cosserat elastoplastic theory are systematically derived.Based on the Cosserat elastic theory,the Cosserat elastoplastic theory is further studied,and the expressions of the constitutive equations,the yield function expressions of the four plasticity criteria of Tresca,Mises,Mohr-Coulomb and Drucker-Prager are derived.The yield criterion for the quasi-brittle material is obtained,and the expression of the plastic flow vector based on the plane Cosserat elastoplastic theory and the value of the calculated constant are obtained.(2)A planar Cosserat elastoplastic finite element model is established.Based on the Cosserat theory,a plane elastoplastic finite element model is established,and the finite element program PCE is compiled by Fortran language.The numerical solution obtained is in good agreement with the general software ABAQUS based on classical theory,which proves the limited preparation.The correctness of the metamodel.In addition,considering the internal crucible size,the numerical simulation analysis of the flexural members of the brittle material alumina ceramics is carried out.The numerical solution of the bending strength calculated by PCE agrees well with the experimental results,further verifying that the established finite element model is Solve the feasibility of the size effect problem.(3)The application software PCES was developed using VB language to realize the visualization of finite element numerical simulation analysis.The finite element software system is divided into three parts:visual pre-processing,core numerical analysis program(PCE)and visual post-processing.It forms a user-friendly and practical finite element analysis software.