Franco Navarro Pedro, Benson David J, Nesterenko Vitali F
Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California 92093-0411, USA.
Department of Structural Engineering, University of California, San Diego, La Jolla, California 92093-0085, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062917. doi: 10.1103/PhysRevE.92.062917. Epub 2015 Dec 18.
We study the evolution of high-amplitude stress pulses in periodic dissipative laminates taking into account the nonlinear constitutive equations of the components and their dissipative behavior. Aluminum-tungsten laminate was selected due to the large difference in acoustic impedances of components, the significant nonlinearity of the aluminum constitutive equation at the investigated range of stresses, and its possible practical applications. Laminates with different cell size, which controls the internal time scale, impacted by plates with different thicknesses that determine the incoming pulse duration, were investigated. It has been observed that the ratio of the duration of the incoming pulse to the internal characteristic time determines the nature of the high-amplitude dissipative propagating waves-a triangular oscillatory shock-like profile, a train of localized pulses, or a single localized pulse. These localized quasistationary waves resemble solitary waves even in the presence of dissipation: The similar pulses emerged from different initial conditions, indicating that they are inherent properties of the corresponding laminates; their characteristic length scale is determined by the scale of mesostructure, nonlinear properties of materials, and the stress amplitude; and a linear relationship exists between their speed and amplitude. They mostly recover their shapes after collision with phase shift. A theoretical description approximating the shape, length scale, and speed of these high-amplitude dissipative pulses was proposed based on the Korteweg-de Vries equation with a dispersive term determined by the mesostructure and a nonlinear term derived using Hugoniot curves of components.
我们研究了周期性耗散层合材料中高振幅应力脉冲的演化，同时考虑了各组分的非线性本构方程及其耗散行为。选择铝 - 钨层合材料是因为其组分的声阻抗差异大，在所研究的应力范围内铝本构方程具有显著的非线性，以及其可能的实际应用。研究了具有不同单元尺寸（控制内部时间尺度）的层合材料，这些层合材料受到不同厚度平板的冲击（平板厚度决定入射脉冲持续时间）。据观察，入射脉冲持续时间与内部特征时间的比值决定了高振幅耗散传播波的性质——三角形振荡激波状轮廓、一系列局部脉冲或单个局部脉冲。即使在存在耗散的情况下，这些局部准稳态波也类似于孤立波：从不同初始条件出现相似的脉冲，表明它们是相应层合材料的固有属性；它们的特征长度尺度由细观结构尺度、材料的非线性特性和应力振幅决定；并且它们的速度和振幅之间存在线性关系。它们在碰撞后大多会恢复形状并伴有相移。基于Korteweg - de Vries方程提出了一种理论描述，该方程的色散项由细观结构决定，非线性项通过各组分物质的冲击绝热线导出，用于近似这些高振幅耗散脉冲的形状、长度尺度和速度。
