We analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles by the nonsmooth contact dynamics approach. The deformable bodies are simulated using a hyperelastic neo-Hookean constitutive law by means of classical finite elements. We characterize the evolution of the packing fraction, the elastic modulus, and the connectivity as a function of the applied stresses when varying the interparticle coefficient of friction. We show first that the packing fraction increases and tends asymptotically to a maximum value ${\varphi }_{\max }$, which depends on both the mixture ratio and the interparticle friction. The bulk modulus is also shown to increase with the packing fraction and to diverge as it approaches ${\varphi }_{\max }$. From the micromechanical expression of the granular stress tensor, we develop a model to describe the compaction behavior as a function of the applied pressure, the Young modulus of the deformable particles, and the mixture ratio. A bulk equation is also derived from the compaction equation. This model lays on the characterization of a single deformable particle under compression together with a power-law relation between connectivity and packing fraction. This compaction model, set by well-defined physical quantities, results in outstanding predictions from the jamming point up to very high densities and allows us to give a direct prediction of ${\varphi }_{\max }$ as a function of both the mixture ratio and the friction coefficient.

中文翻译：

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刚性和高变形颗粒混合物的压实：微力学模型

我们通过非光滑接触动力学方法分析了由刚性和可变形的不可压缩颗粒组成的混合物的各向同性压实。借助经典有限元，使用超弹性新霍克本构定律模拟可变形体。当改变颗粒间的摩擦系数时，我们表征了填充分数，弹性模量和连通性随施加应力的变化。我们首先显示出装填率增加并渐近趋于最大值${\varphi }_{\mathrm{最高}}$，这取决于混合比和颗粒间的摩擦力。堆积模量也随着填充率的增加而增加，并且随着其接近而发散${\varphi }_{\mathrm{最高}}$。从颗粒应力张量的微机械表达式，我们建立了一个模型来描述压实行为，该模型是施加压力，可变形颗粒的杨氏模量和混合比的函数。整体方程也从压缩方程中导出。该模型基于压缩下单个可变形颗粒的表征以及连通性和堆积分数之间的幂律关系。该压实模型由定义明确的物理量设定，可得出从阻塞点到非常高的密度的出色预测，并允许我们直接预测${\varphi }_{\mathrm{最高}}$ 作为混合比和摩擦系数的函数。