Research On Elastic-Plastic Behavior Of Hollow Cylinder Based On High-Order Continuum Theory

The macroscopic deformation behavior of many materials is closely related to their microstructure characteristics.It is necessary to consider the influence of microstructure characteristics on the macroscopic elastic-plastic mechanical behavior.High order continuum theory contains scale factors that can reflect the influence of material micro scale,but the solution process is complex and it is difficult to get an analytical solution.In this paper,the constitutive model is simplified within the framework of higher-order continuity theory,and an elastic analytical solution method which can be used to solve engineering problems is established.The elastic-plastic mechanical behavior of hollow cylinder is studied by introducing Tresca yield criterion.Taking the hollow cylinder expansive soil as the research object,the scale effect of expansive soil is studied by combining the high-order continuum theory with experiment to estimate the value of scale factor.The main research contents of this paper are as follows:(1)The micro scale influence of many materials mainly comes from volume expansion and contraction.We can only consider the influence of volume strain gradient in strain gradient theory,ignore the partial strain gradient term,and establish a simplified high-order constitutive model in cylindrical coordinate system.In the simplified high-order constitutive model,only the radial high-order stress of the main influencing factors is retained.Assuming that the radial high-order stress is related to the gradient of volume deformation,the simplified equilibrium equation is obtained,and then the analytical solution of elastic displacement of hollow cylinder material is derived.The analytical solution is compared with the exact numerical solution.(2)Based on the simplified higher-order strain gradient theory,the elastic-plastic behavior of materials is studied by using Tresca yield criterion.The elastic-plastic mechanical behavior of hollow cylinder entering the elastic-plastic and complete plastic stage under confining pressure is analyzed.The fourth-order ordinary differential equations with two-point boundary conditions are solved by numerical point injection method and Broyden iterative method,and solved by numerical program.The numerical results are compared with the traditional elasticplastic theoretical solutions.(3)The deformation test of hollow cylinder expansive soil is designed by GDS hollow torsional shear tester.Combined with the test data,the scale effect of expansive soil is studied by high-order theory.