有强化材料圆形压力孔道体的弹塑性解析分析

采用弹性-幂律塑性本构模型来考虑材料的应变硬化特性,基于Hencky全量理论和Von Mises屈服准则,用应力解法统一导出了有强化材料圆形压力孔道体孔道附近的弹塑性应力、应变和位移分量的封闭表达式,为圆形压力孔道问题的力学分析建立了一种新的解析格式。分析表明,已知的含圆形压力孔道体的线弹性Lame解和弹性-理想塑性P.Hill解只是本文解的两个特例。本文解作为一般解,既能反映材料的弹性变形,也能计入材料的塑性应变强化。

An Elasto-plastic Analytical Solution for an Internally Pressurized Circular Tunnel Constructed of a Strain-hardening Material

In this paper,the closed-form expressions for the clasto-plastic stress,strain,and displacement components of an internally pressurized circular tunnel made of a strain-hardening material are derived using the elastic power-law plastic material model to represent the strain-hardening effect of material .taking the stress components as the basic unknowns.and employing the deformation theory of hencky and the yield criterion of Von Mises to develop the expressions. As a result,a new analytical model for the elasto-plastic analysis of an internally pressurized circular tunnel made of strain-hardening material is formulated. It is shown that the well-known Lame solution to a linear-elastic material and solution of R. Hill to an e-lastic-perfectly plastic material for internally pressurized circular tunnel are only two specific cases of the solution presented in this paper. As a general one,the presented solution can represent not only the Linear-elastic response but also the plastic strain hardening of an actual material.