Continuum-like nonlocal deformation gradients have been constructed based on discrete simulation results. In this paper, the accuracy of the nonlocal deformation gradient based on different influence functions is examined for both representing material point deformation and mapping bonds. A new class of parameterized influence functions that accounts for both bond relative length and angle (with respect to a target bond) is proposed. Numerical example shows great accuracy of the nonlocal deformation gradient using the proposed influence functions in both representing material point deformation and mapping bonds. It is concluded that the proposed influence functions can be used to accurately capture bond-level continuum-like measures.

基于离散模拟结果构建了类连续体非局部变形梯度。在本文中，检查了基于不同影响函数的非局部变形梯度的准确性，以表示材料点变形和映射键。提出了一类新的参数化影响函数，它考虑了键的相对长度和角度（相对于目标键）。数值例子表明，使用所提出的影响函数来表示材料点变形和映射键时，非局部变形梯度具有很高的准确性。结论是，所提出的影响函数可用于准确捕获债券级别的类似连续体的度量。