Abstract
Using a numerical approach based on the coupling of the discrete and finite element methods, we explore the variation of the bulk modulusKof soft particle assemblies undergoing isotropic compression. As the assemblies densify under pressure-controlled boundary conditions, we show that the non-linearities ofKrapidly deviate from predictions standing on a small-strain framework or the, so-called, Equivalent Medium Theory (EMT). Using the granular stress tensor and extracting the bulk properties of single representative grains under compression, we propose a model to predict the evolution ofKas a function of the sample’s solid fraction and a reference state as the applied pressureP→0. The model closely reproduces the trends observed in our numerical experiments confirming the behavior scalability of soft particle assemblies from the individual particle scale. Finally, we present the effect of the interparticle friction onK’s evolution and how our model easily adapts to such a mechanical constraint.
Highlights
1 Introduction the behavior of individual representative particles, we propose an analytical equation for the bulk modulus evolution
To simulate assemblies of soft particles, we used the coupling of the discrete method known as contact dynamics (CD) [13, 14] and classic finite elements in the framework coined as non-smooth contact dynamics (NSCD) by M
We studied the bulk modulus behavior of two-dimensional particle grain assemblies undergoing isotropic compression using a coupled discrete-finite element simulation platform
Summary
We can track the deformations of the servo-controlled boundary walls. That approach adopts an analogue model considering a set of springs joining the center of mass of bodies in contact and whose deformation represents the relative approaching of their centers as they deform Using this type of approach, it is possible to integrate the set of springs’ deformation and deduce a stress-strain relation for the whole system; a bulk equation can be deduced. Considering that = P, we can deduce a microscopic definition of the bulk modulus upon the derivative of Eq (1) as It is necessary to track the evolution of K for the multi-particle system using an alternative approach
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