We study the rate-dependent mechanics of viscoelastic granular packings. Using a two-dimensional, square lattice of particles as a motif mimicking nominally mono-disperse granular packings, we perform a suite of finite element simulations under rate-dependent uniaxial compaction followed by unloading. The focus is on understanding the macroscopic force–displacement relations and the porosity evolution as a function of the viscoelastic relaxation parameters. For the constituent parameters considered here, the force–displacement relations show a two-stage power-law behavior, which is associated with the relative contributions of viscous dissipation and elastic effects at a particular loading rate. For a given loading rate, the nonlinearity of the porosity evolution depends on the constituent parameters and is found to be captured well by a simple analytical model. The heterogeneity of stresses during the compaction and recovery phases provide insights into the emergent complex micromechanics in simple granular motifs. Upon unloading, particles may experience transient tensile pressures, which could have implications on their failure.

中文翻译：

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二维颗粒晶格的粘弹性力学

我们研究粘弹性颗粒填料的速率相关力学。使用二维方形颗粒晶格作为模拟名义上单分散颗粒填料的图案，我们在速率相关的单轴压实和卸载下进行了一系列有限元模拟。重点是理解宏观力-位移关系以及作为粘弹性松弛参数函数的孔隙率演化。对于这里考虑的构成参数，力-位移关系显示出两阶段幂律行为，这与特定加载速率下粘性耗散和弹性效应的相对贡献相关。对于给定的加载速率，孔隙率演化的非线性取决于组成参数，并且发现可以通过简单的分析模型很好地捕获。压实和恢复阶段应力的异质性为简单颗粒图案中出现的复杂微观力学提供了见解。卸载时，颗粒可能会经历瞬态拉伸压力，这可能会对其失效产生影响。