arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.02867cond-mat.soft
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刚性和高变形颗粒混合物的压实:细观力学模型

Compaction of mixtures of rigid and highly deformable particles: a micro-mechanical model

Manuel Cárdenas-Barrantes, David Cantor, Jonathan Barés, Mathieu Renouf, Emilien Azéma

摘要:

采用非光滑接触动力学方法分析了刚性和可变形不可压缩颗粒混合物的各向同性压实问题。通过经典的有限元方法,使用超弹性的新胡克本构律的变形体进行模拟。对于从完全刚性到完全可变形颗粒的混合物,我们表征了填充分数,弹性模量和连通性的演变,作为所施加的应力的函数,当改变颗粒间的摩擦系数时。我们首先表明,包装分数的增加,并趋于渐近的最大值$ϕ_{max}$,这取决于混合比和颗粒间的摩擦。体积模量也被证明是增加与包装分数和发散,因为它接近$ϕ_{max}$。从颗粒应力张量的微观力学表达式,我们开发了一个模型来描述压实行为作为施加的压力,可变形颗粒的杨氏模量,和混合比的函数。从压实方程导出了体积方程。该模型基于单个可变形颗粒在压缩下的特性以及连通性和填充分数之间的幂律关系。这种压实模型,由定义明确的物理量,结果在突出的预测从堵塞点到非常高的密度,并允许我们给出一个直接的预测$ϕ_{max}$作为一个函数的混合比和摩擦系数。

英文摘要:

We analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles by the non-smooth contact dynamics approach (NSCD). The deformable bodies are simulated using a hyper-elastic neo-Hookean constitutive law by means of classical finite elements. For mixtures that varied from totally rigid to totally deformable particles, we characterize the evolution of the packing fraction, the elastic modulus, and the connectivity as a function of the applied stresses when varying inter-particle 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 inter-particle friction. The bulk modulus is also shown to increase with the packing fraction and to diverges as it approaches $ϕ_{max}$. From the micro-mechanical 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.

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