A vector form conjugated-shear bond-based peridynamic model is proposed to overcome the limitation of the fixed Poisson’s ratio based on the assumption of central force between material points in bond-based peridynamic theory. In the virtue of this proposed approach, the angle variation of a pair of conjugated-shear bonds is derived as a vector in terms of the displacements at three points located at the conjugated-shear bonds instead of the direct use of the angle, which improves the computational efficiency in both two and three dimensional conditions. Emphasis is placed on deriving the relationship between micro moduli in the proposed model and macro constants by equating peridynamic strain energy to the macroscopic strain energy. It is found that the micro moduli in this proposed approach can reduce to classical bond-based peridynamic parameters when the rotation effect of conjugated-shear bonds is not considered. A comparative study of the proposed approach and the FEM or analytical solutions on a square isotropic plate and a three-dimensional rectangular block under uniaxial tension shows that this proposed approach can well investigate the behavior of elastic solids under both two and three dimensional conditions. We test the numerical convergence behavior of the proposed model to classical solutions in the varying horizon/grid spacing ratios or horizon sizes. Moreover, the improvement of computational efficiency of the proposed model is verified by comparison of the CPU time computed from the scalar form conjugated bond-based peridynamic model. The capability of the proposed model in simulating dynamic brittle fracture problems is demonstrated by comparing the results obtained by the proposed model with the previous numerical results in the case of Kalthoff-Winkler experiment.

为了克服基于键的近场动力学理论中物质点间中心力的假设，固定泊松比的局限性，提出了一种基于矢量形式的共轭剪切键近场动力学模型。凭借这种提出的方​​法，一对共轭剪切键的角度变化是根据位于共轭剪切键的三个点处的位移导出的矢量，而不是直接使用角度，这改进了二维和三维条件下的计算效率。重点是通过将近场动力学应变能等同于宏观应变能来推导所提出模型中的微模量与宏观常数之间的关系。发现当不考虑共轭剪切键的旋转效应时，该方法中的微模量可以减少到经典的基于键的近场动力学参数。对所提出的方法与单轴拉伸下方形各向同性板和三维矩形块上的有限元法或解析解的比较研究表明，该方法可以很好地研究弹性固体在二维和三维条件下的行为。我们在不同的地平线/网格间距比或地平线尺寸下测试了所提出模型对经典解的数值收敛行为。此外，通过比较基于标量形式共轭键的近场动力学模型计算的 CPU 时间，验证了所提出模型的计算效率的提高。