近场动力学框架下的键基对应模型

传统键基近场动力学模型存在泊松比限制的问题,为了解决这一问题发展了态基近场动力学模型。其中非常规态的近场动力学模型通过定义非局部的变形梯度将近场力和传统应力关联起来,方便使用传统本构,但是态基近场动力学计算效率低于键基近场动力学。结合态基模型和键基模型的优势,提出键基对应模型,定义了基于键的变形梯度,参考连续介质力学中变形梯度的极分解过程,将键的变形分为转动部分和伸长部分。从而进一步定义了应变,通过物理方程求应力,进而计算键传递的近场力。键基对应模型解决了键基近场动力学的泊松比限制问题,也不需要进行近场动力学微观材料常数的计算。数值算例和理论推导证明了键变形梯度定义以及近场力计算方式的正确性。

A bond-based corresponding model for peridynamics

Traditional bond-based peridynamics has defects in its fixed Poisson''s ratio.To solve this problem,a state-based peridynamics is developed.In non-ordinary state-based peridynamics,the nonlocal deformation tensor is defined,and the pairwise force can be obtained from the traditional stress tensor.However,the computational cost of state-based peridynamics is higher than the bond-based peridynamics.Combining the advantages of state-based peridynamics and bond-based peridynamics,this study proposed a new bond-based corresponding peridynamics.Different from the non-local deformation tensor in non-ordinary state-based peridynamics,bond-based corresponding peridynamics focuses on the bond deformation tensor.Similar to the polar decomposition of deformation tensor,bond deformation is decomposed into length changes and rotation changes.As the deformation tensor is defined,strain and stress of bonds are obtained.Further,the pairwise force through the bond is obtained by strain and stress.Bond-based corresponding peridynamics has no restriction in choices of physical constants,and auxiliary parameters are not needed in calculating the pairwise forces.Numerical examples and theoretical analysis prove the validation of bond-based corresponding peridynamics.