基于弹性应变能的MohrCoulomb强度准则讨论

MohrCoulomb Strength Criterion Based on Elastic Strain Energy

摘要:

从弹性应变能释放是材料屈服的基本原理来看，MohrCoulomb (MC)强度准则认为屈服时材料的泊松比恒为0.5，这可能违反能量守恒定律.研究了弹性应变能、应力偏量第二不变量、应力张量第二不变量及泊松比之间的关系，提出广义应力偏量第二不变量概念；从弹性应变能角度对MC强度准则的物理意义进行分析，提出广义MC强度准则；利用强度准则对岩石的破坏强度进行了计算.结果表明，由于考虑了中间主应力与泊松比的影响，广义MC强度准则的计算精度更高，并分析了产生这种结果的内在机理.广义MC强度准则突破了材料破坏时的泊松比恒为0.5的假设，这对于定量描述材料的屈服与破坏特性具有重要的意义.

Abstract:

Based on elastic strain energy, it is assumed that Poisson’s ratio is 0.5 in yield of the material, which may be one of the important reasons for the poor calculation precision of the MC strength criteria. Therefore, based on the fact that releasing of elastic strain energy is the essential attribute of material yield, the internal relations between elastic strain energy, the second invariant of stress deviator, and the second invariant of stress tensor and Poisson’s ratio are explored. Consequently, the generalized second invariant of stress deviator is proposed. Secondly, MC strength criteria are set as the basis, and the generalized MC strength criterion is established based on energy release and material yield. Lastly, the failure strength is calculated using strength criterion. The results show the generalized MC strength criterion is more accurate and the error is more stable because of the consideration of Poisson’s ratio and the intermediate principal stress. The generalized strength criterion breaks the hypotheses that Poisson’s ratio is always 0.5, which is of great significance for accurate quantitative analysis of failure characteristics of the material.