【摘要】 脆性和准脆性材料在外部载荷作用下,通常会表现出复杂的应力应变关系。其中,受压剪作用的裂纹是否摩擦滑动,对材料的剪切本构关系会产生很大的影响。之前在一些文献中提出过这种考虑裂纹摩擦效应的损伤本构模型,但只是理论假设,并没有进行过严格的证明。可以考虑一个受压剪作用的单元体,其中心含一条微裂纹,利用弹性力学理论中的复变函数方法可以给出单元体边界及裂纹所在平面处的位移场,通过某种平均化的方法,可得到单元体基体平均剪应变的一种形式,而这种形式与单元体边界及裂纹的几何尺寸有关,进一步可定义与这些几何尺寸相关的剪切损伤变量,将基体平均剪应变代入到弹性剪切本构关系中,可得到考虑摩擦效应的脆性和准脆性材料弹性剪切损伤本构关系。这种方法利用了现有的弹性力学理论,所以得到的结论是可靠的。更多还原

【Abstract】 The stress-strain relation of brittle and quasi-brittle materials is usually very complex under the external load.In compression shearing,the crack surface of materials may slide relatively,which can make a great influence to shear constitutive relation.In some of the existing literature,the friction effect has been considered,but the related constitutive equations have not been rigorously proved,only as a hypothesis.Considering a volume element with one micro crack,and using the method of function of the complex variable based on the theory of the elasticity,the displacement field of the boundary and the crack surface is analyzed.It can be got a form of the matrix average shear strain which related to the geometry of the element and the crack by some averaging method,further can define the shear damage variable associated with the geometry.By putting the matrix average shear strain into the elastic shear constitutive relation,the elastic shear damage constitutive relation with friction for brittle and quasi-brittle materials can be obtained.This method has applied the theory of the elasticity,so the result would be reliable.更多还原