复杂加载状态下的剪切本构关系

Shear constitutive relation under complex loading

脆性材料的内部通常含有大量随机分布的微细观缺陷,在受到外部载荷作用时,材料会表现出相当复杂的力学响应。当内部微裂纹受到压剪载荷作用时,裂纹面之间可能会发生相对滑动,它与材料的损伤过程相互影响,表现为非线性应力应变关系等行为。可以从研究一个简单的含一条裂纹的单元体开始,令其承受双轴压力和剪力,利用弹性力学理论中的复变函数解法,考虑到裂纹面间的摩擦力,计算出单元体边界及裂纹所在平面上各点的位移,通过某种平均化方法,可以得到单元体的基体剪应变和总体剪应变,再根据弹性剪切本构关系,进一步得到单元体在该加载条件下的弹性剪切损伤本构方程,同时得到剪切损伤变量的细观描述形式。计算结果表明,2个方向上的压力大小均对材料的剪切损伤和剪切模量产生一定程度的影响。

The interior of brittle materials usually contains a large number of micro-defects with random distribution.When subjected to external loads,the material will show quite complex mechanical response.When the internal micro-cracks are subjected to compression-shear loads,relative sliding may occur between the crack surfaces,which interact with the damage process of the material,showing the behavior of non-linear stress-strain relationship etc.First,a simple element with a crack under biaxial compression and shearing can be studied.The function of the complex variable in elasticity theory is used to calculate the the displacement of the points on the boundary of the element and the plane where the crack is located.By some averaging method,the matrix shear strain and the total shear strain of the element can be obtained.According to the elastic shear constitutive relation,the elastic shear damage constitutive equation of the element under the loading condition is further obtained,and the mesoscopic description of the shear damage variable is also obtained.The results show that the shear damage and shear modulus of the material are affected by the compression in both directions.