NONLINEAR ELASTICITY AND PRESSURE-DEPENDENT WAVE SPEEDS IN GRANULAR MEDIA
NONLINEAR ELASTICITY AND PRESSURE-DEPENDENT WAVE SPEEDS IN GRANULAR MEDIA
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DOI：
10.1098/rspa.1990.0083
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发表时间：
1990-07-09
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影响因子：
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通讯作者：
GODDARD, JD
中科院分区：
文献类型：
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作者：
GODDARD, JD
以下是零应力状态附近粒状介质的小应变非线性弹性的分析，因为它与压力相关的增量线性弹性和波速有关。主要目的是阐明增量弹性模量对压力p的p ½依赖性，在许多实验中观察到的依赖性，但发现与基于赫兹接触的各种微力学模型预测的p ½标度不一致。在提出了一个幂律连续介质模型的小应变非线性弹性，目前的工作发展的微观力学模型的基础上的两个替代机制的异常压力标度，即：（1）偏离单接触水平的赫兹接触，由于点状或圆锥形的非球面性;（2）在赫兹接触的数量密度的变化，由于颗粒链的屈曲。这两种机制在低压下导致p ½压力缩放，并且在特征过渡压力p * 下都表现出高压过渡顶部1/2缩放。对于几乎相等的球体组合，机制（1）的非赫兹接触模型和机制（2）的扩散型模型产生p * 的估计，形式为p * =cμ π ι 3。这里是一个无量纲系数，仅取决于颗粒接触几何形状，而α ε 1是一个小参数，代表球形缺陷，μ ε是颗粒的适当弹性模量。然后，用R代表颗粒半径和一个特征球面公差或粗糙高度，发现对于机制（1），α=（h/R）½，而对于机制（2），α=h/R。Duffy & Mindlin关于球体组合的经典实验的有限数据倾向于支持机制（1），但需要更详尽的实验。除了上述的可逆弹性效应的分析，非弹性的“安定”或固结的渗流模型。它用于描述长时间的机械振动如何导致点状或非活动接触被更硬的赫兹接触取代，从而改变颗粒介质的压力缩放行为。目前的分析表明，压力依赖性的弹性可以提供一个有用的手段表征状态的固结和稳定的致密颗粒介质。
Following is an analysis of the small-strain nonlinear elasticity of granular media near states of zero stress, as it relates to the pressure-dependent incremental linear elasticity and wave speeds. The main object is elucidation of thep½dependence of incremental elastic moduli on pressurep, a dependence observed in numerous experiments but found to be at odds with thep½scaling predicted by various micromechanical models based on hertzian contact. After presenting a power-law continuum model for small-strain nonlinear elasticity, the present work develops micromechanical models based on two alternative mechanisms for the anomalous pressure scaling, namely: (1) departures at the single-contact level from the hertzian contact, due to point-like or conical asphericity; (2) variation in the number density of hertzian contacts, due to buckling of particle chains. Both mechanisms result inp½pressure scaling at low pressure and both exhibit a high-pressure transition top½scaling at a characteristic transition pressurep*. For assemblages of nearly equal spheres, a non-hertzian contact model for mechanism (1) and percolation-type model for (2) yield estimates ofp* of the formp* =cμˆ∝3. Herecis a non-dimensional coefficient depending only on granular-contact geometry, whileα≪ 1 is a small parameter representing spherical imperfections andμˆis an appropriate elastic modulus of the particles. Then, withRrepresenting particle radius andha characteristic spherical tolerance or asperity height, it is found thatα= (h/R)½for mechanism (1) as opposed toα=h/Rfor (2). Limited data from the classic experiments of Duffy & Mindlin on sphere assemblages tend to support mechanism (1), but more exhaustive experiments are called for. In addition to the above analysis of reversible elastic effects, a percolation model of inelastic ‘shake-down’ or consolidation is given. It serves to describe how prolonged mechanical vibration, leading to the replacement of point-like or inactive contacts by stiffer Hertz contacts may change the pressure-scaling behaviour of particulate media. The present analysis suggests that pressure-dependence of elasticity may provide a useful means of characterizing the state of consolidation and stability of dense particulate media.