线性黏弹性球面波的特征线分析

基于ZWT黏弹性本构方程建立了体现高应变率效应的黏弹性球面波的控制方程组,包含5个偏微分方程,解5个未知量v、σr、σθ、εr和εθ。采用特征线法,问题转化为解3族特征线上的5个常微分方程,物理上图像清晰,数学上易于求解。特征线数值分析显示,黏弹性球面波的衰减和弥散效应超过线弹性球面波。球面扩散引起的环向拉应力是导致介质拉伸破坏的主因。进一步还针对强间断黏弹性球面波得出其衰减特性的解析表达式,表明这种更强的衰减特性是几何扩散效应和本构黏性效应两者共同作用的后果。

Characteristics analyses of linear viscoelastic spherical waves

Based on the ZWT viscoelastic constitutive relation, the governing equations which reflect high-strain-rate effects, for viscoelastic spherical waves are established, including five partial differential equations to solve five unknown variables such as v, σ_r, σ_θ, ε_r and ε_θ. By using the characteristics method, the problem is reduced to solve five ordinary differential equations along three sets of characteristics. The numerical results by the characteristics method show that the degree of attenuation and dispersion for viscoelastic spherical waves are more remarkable than those of linear elastic spherical waves. The tangential tensile stress/strain induced by the surface extension of spherical wave front plays a significant role in tensile failure of medium, while the constitutive viscosity can relieve the tensile stress/strain. An analytic expression for the attenuation of strong discontinuous viscoelastic spherical wave front is further derived, which analytically illustrates that the more remarkable attenuation of strong discontinuous viscoelastic spherical wave front is resulted from the combined effects of both the geometrical extension effect and the constitutive viscosity effect.