近场动力学与有限元混合模型研究

兼顾近场动力学(peridynamics,PD)模拟不连续问题的优势和有限单元法(finite element method,FEM)较高的计算效率,采用近场动力学与有限元混合建模方法,建立了新的混合模型.该模型在裂纹出现区域,采用近场动力学建模,其他区域采用八结点等参元建模.通过杆单元连接PD物质点与等参单元结点,将PD物质点对间相互作用视为杆单元,最后对单元刚度集成,实现了在有限元框架体系中两种方法的混合建模.该混合模型无需引入人工阻尼,提高了计算效率.此外,相较于四结点混合模型,采用高阶(八结点)等参元与近场动力学方法建立的混合模型具有更高的计算精度.通过数值算例验证了该方法的有效性,为断裂破坏问题的解决提供了一种新思路.

Study on hybrid model of peridynamics and finite element method

Considering the advantages of peridynamics in simulating discontinuities and low computational cost of finite element method (FEM), a new hybrid model was established by using the hybrid modeling method of peridynamics and finite element method. The region where cracks appear was modelled by peridynamics theory, while the other regions were modelled by eight node isoparametric elements. The truss element was used to connect the material points with the isoparametric nodes, and the interaction between material points could be regarded as the truss element. Finally, the stiffness of the element was integrated to realize the hybrid modeling of the two methods in the finite element frame system. No artificial damping was needed in the model, which improved the calculation efficiency. In addition, compared with the four-node hybrid model, the proposed hybrid model based on high-order (eight-node) isoparametric element and peridynamics had higher accuracy. The validity of the method was verified by the numerical example. The proposed model provides a new idea to solve fracture problems.