构元组集模型对结构弹性损伤至断裂过程的描述及与内聚区模型的比较

结构的响应实质上是材料的响应，宏观结构损伤至断裂的发展过程也是材料性质不断演化的结果。构元组集模型从材料的微观物理变形机制出发，基于对泛函势理论和Cauchy-Born准则，抽象出两种构元——弹簧束构元和体积构元。在微观层次上，结构损伤和断裂的实质都是原子间键合力减弱和丧失的结果，而弹簧束构元是同一方向上的原子键的抽象，因此损伤可以通过弹簧束构元的响应曲线来反映。组集两种构元的响应，建立了材料的弹性损伤本构关系，从而能一致描述材料从弹性到损伤、破坏的发展过程。将构元组集模型的本构关系嵌入ABAQUS的用户材料单元子程序UMAT，实现对结构响应的数值模拟。本文模拟了包含中心预制裂纹三点弯曲梁的裂纹扩展过程，并与内聚区模型比较，给出了内聚区模型所假设的应力——位移关系曲线，并从材料损伤演化的角度对材料裂纹扩展过程做出了物理解释。

The description of elasto-damage to fracture process of structures using component assembling model and comparison with cohesive zone model

The responses of structures originate from those of materials. The damage and failure process of structure corresponds to the deterioration of materials essentially. Considering the microscopic deformation mechanism of materials, based on pair functional potentials and Cauchy-Born rule, component assembling model is developed with two kinds of components, spring-buddle and cubage components. Since the essence of damage and fracture is the decrease and loss of atomic bonding force in microscopic and that the spring-buddle component is abstracted from the atomic bonds in the same direction, damage can be reflected by the force response function of spring-buddle components. Assembling the responses of two kinds of components, the elasto-damage constitutive equations are derived. This model can describe the whole deformation process of elastic, damage and failure of materials consistently. It is coded using the user subroutine UMAT and then implemented in ABAQUS to simulate the response of structures. In this paper, a numerical simulation of three point bending beam with precrack is performed to describe the crack propagation process. Comparing the response of structure using the present model with that obtained by the cohesive zone model, the stress-displacement curve are given by the present model and compared with that assumed in cohesive zone model, and a physical explanation is given to the crack propagation process in terms of damage evolution of materials.