A three-dimensional crackable Lagrangian element method for modelling tensile cracking processes of rock-like materials

Subjects: Mechanics >> Basic Mechanics submitted time 2023-11-09 Cooperative journals: 《应用力学学报》

WANG Xuebin1,2, TIAN Feng2, MA Bing2, QIAN Shuaishuai2

Abstract： A three-dimensional crackable continuous-discontinuous method mainly suitable for cube elements is proposed to simulate deformation and tensile cracking processes of rocks.Its essence is a hybrid method of the three-dimensional Lagrangian element method and the fictitious crack model in fracture mechanics.Introduction of the fictitious crack model into the three-dimensional Lagrangian element method consists of three key steps.First,the nodal stress is obtained by averaging stresses of elements around the node,and the nodal separation is assessed according to the maximum principal stress of the node and the uniaxial tensile strength.Then,the element boundary closest to the plane perpendicular to the maximum principal stress of the node is selected.Finally,the fictitious fracture model is introduced to simulate the processes of crack initiation and propagation.Deformation and tensile cracking processes of specimens in uniaxial tension and three-point bending are simulated by using the present method.The effects of I-type fracture energy,rock specimen height and elements size on the direct tension processes are analyzed.Meanwhile,through comparing the present results with the theoretical peak stress and critical displacement of the specimen in direct tension and the numerical load-displacement curve of the specimen in three-point bending,the correctness of the proposed method is verified,laying a good foundation for future work.

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