Cárdenas-Barrantes Manuel, Cantor David, Barés Jonathan, Renouf Mathieu, Azéma Emilien
LMGC, Université de Montpellier, CNRS, Montpellier, France.
Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, Québec, Canada.
Phys Rev E. 2020 Sep;102(3-1):032904. doi: 10.1103/PhysRevE.102.032904.
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 ϕ_{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 ϕ_{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 ϕ_{max} as a function of both the mixture ratio and the friction coefficient.
我们采用非光滑接触动力学方法分析了由刚性和可变形不可压缩颗粒组成的混合物的各向同性压实。通过经典有限元方法，使用超弹性新胡克本构定律对可变形体进行模拟。当改变颗粒间摩擦系数时，我们将堆积分数、弹性模量和连通性的演化表征为所施加应力的函数。我们首先表明，堆积分数增加并渐近趋于最大值ϕ_max，该值取决于混合比和颗粒间摩擦。体积模量也随堆积分数增加而增加，并在接近ϕ_max时发散。从颗粒应力张量的微观力学表达式出发，我们建立了一个模型来描述压实行为与所施加压力、可变形颗粒的杨氏模量和混合比之间的函数关系。还从压实方程导出了一个体积方程。该模型基于单个可变形颗粒在压缩下的表征以及连通性与堆积分数之间的幂律关系。这个由明确的物理量设定的压实模型，从堵塞点到非常高的密度都能给出出色的预测，并使我们能够直接预测ϕ_max作为混合比和摩擦系数的函数。
