Strain energy spectral density and information content of materials deformation
Strain energy spectral density and information content of materials deformation
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DOI：
10.1016/j.ijmecsci.2018.09.018
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发表时间：
2018-11-01
影响因子：
7.3
通讯作者：
Danso, Larry A.
中科院分区：
文献类型：
--
作者：
Karpov, Eduard G.;Danso, Larry A.
更广泛的分析工具可以增强对元材料和其他先进材料系统的不寻常机械性能的理解。在这里，我们讨论了Parseval能量定理的力学模拟，它导致了倒易空间中应变能的密度。它反映了弹性介质在空间两点之间转换静态变形模式的方式。归一化谱密度也提供了这些点上变形的信息熵。讨论了香农型的微分熵和离散熵（数值）。谱熵是材料内部关于表面载荷的信息的基本度量，或者是由变形引入弹性介质的无序度量。导出了各向同性平面固体在高斯分布和点载荷作用下的精确解析熵函数。讨论了计算固体力学中谱熵的数值计算方法。弹性连续体的能谱密度和谱熵在逻辑上与圣维南原理一致。然而，它也变得清楚，微结构介质可能表现出应变能谱的异常演化途径，使工程材料系统的有趣的转变力学研究成为可能。
A broader range of analytical tools can enhance understanding of the unusual mechanical properties of meta materials and other advanced material systems. Here, we discuss a mechanics analogue of the Parseval's energy theorem that leads to a density of the strain energy in the reciprocal space. It reflects the ways for an elastic medium to translate static deformation patterns between two points in space. A normalized spectral density also provides an information entropy of deformation at those points. Both differential and discrete (numerical) entropies of the Shannon's type are discussed. Spectral entropy is a basic measure of information available in the material interior about surface loads, or a measure of disorder introduced into elastic medium by the deformation. An exact analytical entropy function is derived for an isotropic plane solid under Gauss-distributed and point loads. Approaches to numerical calculation of spectral entropy in computational solid mechanics are also discussed. Energy spectral density and spectral entropy of an elastic continuum is shown to translate, logically, in agreement with the Saint-Venant's principle. However, it also becomes clear that microstructured media may demonstrate anomalous pathways of evolution of the strain energy spectrum, enabling interesting transformation mechanics studies of engineered material systems.