考虑粘结面厚度的局部粘结单元法

Local cohesive finite element method with finite interface thickness

传统无厚度粘结单元法CFEM(Cohesive finite element method)在模拟脆性材料断裂方面具有很强的优势,但也存在很大问题。一是单元尺寸增大,收敛性变差;二是单元尺寸变小,模型刚度发生折减。为了克服这两个问题,发展了考虑厚度的局部粘结单元法,即在裂纹可能扩展区插入具有一定厚度的粘结面单元。粘结面单元采用拓展虚内键本构(Augmented virtual internal bond)描述。由于考虑了厚度,粘结面交叉处会形成多边形空缺。为了弥补这一空缺,将其看作多边形键元胞,采用离散虚内键模型(Discretized virtual internal bond)对其建模,保证了模型的几何完整性。模拟结果表明,本文方法有效,克服了传统CFEM方法的刚度折减问题,提高了计算稳定性和收敛性。

The conventional cohesive finite element method is powerful in simulating fracture propagation in brittle materials.However,it has some limitations in fracture simulation.Firstly,the numerical convergence gets worse with increasing element size.Secondly,the model stiffness is seriously reduced with decreasing element size.To overcome the two limitations,the local cohesive finite element method with finite interface thickness(TCFEM)is developed.In TCFEM,the cohesive elements are set in the potential fracturing zone.Each cohesive interface element has finite thickness.The constitutive relation of the augmented virtual internal bond is adopted for the quadrilateral cohesive element,which intrinsically contains the cohesive law of material.Due to the finite thickness of a cohesive element,a polygonal void is formed at the nodal spot.The discretized virtual internal bond is adopted to model the polygonal void as a bond cell.This ensures the geometrical integrity of the numerical model.The numerical examples suggest that this method is feasible and effective.Compared with the conventional CFEM,the new approach is able to overcome the stiffness reduction and improve the stability of numerical computation.