近场动力学系统中波传播特性的探究

STUDY OF WAVE DISPERSION AND PROPAGATION IN PERIDYNAMICS

近场动力学是一类基于非局部思想的新固体力学方法,其采用积分形式的控制方程,自然地适用于极端载荷下材料破碎和裂纹发展的模拟,被广泛用于国防安全等领域的研究.但是,非局部性会引入色散效应,对波的传播产生不利影响,制约其对断裂等固体行为的捕捉能力.为此,采用谱分析方法,对近场动力学系统的色散行为进行了全面的研究.发现相比于低频成分,高频成分的色散关系呈现出振荡趋势和零能模式,色散问题更为严重.高频域的色散行为还随波的传播方向发生改变,呈现出沿45°的对称性.而近场动力学系统本身缺乏数值耗散,无法抑制色散问题带来的不利影响.因此,从引入数值耗散的角度出发,在合理保留传统近场动力学理论框架的基础上,建立了黏性引入的控制方程.并考虑固体中常见的体积变形和对高频成分的选择性抑制,构造了相应的黏性力态.最后,在数值研究中模拟了极端载荷下激波的产生,以探究波的间断性对色散行为的影响.发现间断性强的波表现出更为显著的色散行为,呈现出Gibbs不稳定性.这些均能有效地被黏性力态所抑制,验证了所提方法的正确性.这为在近场动力学系统中实现对波传播过程的正确捕捉,获得正确的固体行为提供了重要参考,从而为国防安全领域研究提供了技术支撑和借鉴.

Periydnamics(PD)is a new nonlocal method reformulated from solid mechanics.It adopts the integral form of governing equation and is naturally suitable to model fragments and cracks under extreme events,thus widely applied in the field of national defense security.However,the nonlocality in PD introduces the dispersion effect and imposes adverse effect on wave propagation,which will greatly restrict its capability in capturing solid behaviors,especially the fractures.For this purpose,we employ the spectral analysis method to study the dispersion behavior of PD system comprehensively.It is found that compared to the low frequencies,the dispersion relation of high frequency components shows an oscillation trend and zero-energy modes,leading to more serious dispersion problems.The dispersion behavior of high frequencies changes with the wave propagation direction and shows 45°symmetry in the spatial wave propagation.As the PD system itself is non-dissipative,the adverse effect of the dispersion problem can not be suppressed.As a result,the simulation accuracy may be greatly influenced.To introduce the numerical dissipation for dispersion effect suppression,the governing equation of viscosity introduction is proposed as a minimum variation of conventional PD.Both the typical deformation in solids and the selective suppression on high frequencies are considered then the corresponding viscous force state is constructed.Finally,a numerical study is conducted to model the shock waves under extreme events and investigate the influence of wave discontinuity.It is indicated that the wave discontinuity aggravates the dispersion problem and shows Gibbs instability in the wave propagation.These can be effectively suppressed by the viscous force state,which verifies the proposed method.This provides an important reference to reproduce the correct wave propagation process and obtain the reasonable solid behavior in PD,thus helps to support and guide the research of national defense security field.