一种近场动力学非普通状态理论零能模式控制方法

近场动力学非普通状态理论在采用节点积分时将引起零能模式,造成位移场、应力应变场的数值不稳定性,影响计算精度甚至会导致完全错误的结果,因此必须对其进行控制.目前国际上还没有十分有效的零能模式控制方法.本文针对零能模式问题,提出了一种通用的、高效的控制方法.根据近场动力学线性键理论,确定非均匀变形对应弹性张量的具体形式,考虑了微模量随不同作用键的变化.通过最小位能原理推导出非均匀变形引起的力状态,结合近场动力学力状态,得到稳定力状态表达式.从而建立起基于线性键理论的稳定关联材料模型,并应用于含圆孔平板、三点弯试件线弹性变形和损伤破坏过程模拟.数值结果表明,本文模型能有效抑制近场动力学非普通状态理论中的零能模式现象.与已有零能模式控制方法相比,其物理意义明确,不包含控制参数,避免了复杂的零能模式参数调节过程,提高了计算效率. 

A ZERO-ENERGY MODE CONTROL METHOD OF NON-ORDINARY STATE-BASED PERIDYNAMICS

Non-ordinary state-based peridynamics suffers from zero-energy mode due to nodal integration. Instabilities of displacement, stress and strain fields are induced and they will affect the computational precision or even ruin the results. Thus, the zero-energy mode needs to be suppressed. However, so far there are no effective zero-energy mode control methods. To address this issue, this work proposes a general and high efficient control method. The specific form of the elastic coefficient tensor corresponding to the nonuniform part of deformation is proposed according to linearized bond-based peridynamic theory in which the difference of micromodulus of different bonds is considered. The force state incorporated by nonuniform deformation is derived through minimum potential principle. The stabilized force state is arrived at by adding the nonuniform force state to the peridynamic force state. The linearlized bond-based peridynamics based stabilized correspondence material model is established and applied to the simulation of the elastic properties and damage process of the plate with a circular hole and the three point bend specimen. The numerical results indicate that the proposed model is effective for controlling zero-energy mode in non-ordinary state-based peridynamics. In comparison with existing zero-energy mode control methods, it has definite physical meaning and the complicated process of adjusting parameters is avoided. Hence, the computational efficiency is evidently improved.