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      Generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength

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          Abstract

          We present generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength. The proposed mechanistic contact laws are continuous at the onset of unloading by means of a regularization term, in the spirit of a cohesive zone model, that introduces a small and controllable error in the conditions for interparticle breakage. This continuity property is in sharp contrast with the behavior of standard mechanistic loading and unloading contact theories, which exhibit a discontinuity at the onset of unloading when particles form solid bridges during plastic deformation. The formulation depends on five material properties, namely two elastic properties (Young's modulus and Poisson's ratio), two plastic properties (a plastic stiffness and a power-law hardening exponent) and one fracture mechanics property (fracture toughness), and its predictions are in agreement with detailed finite-element simulations. The numerical robustness and efficiency of the proposed formulation are borne out by performing three-dimensional particle mechanics static calculations of microstructure evolution during the three most important steps of powder die-compaction, namely during compaction, unloading, and ejection. These simulations reveal the evolution, up to relative densities close to one, of microstructural features, process variables and compact mechanical attributes which are quantitatively similar to those experimentally observed and in remarkable agreement with the (semi-)empirical formulae reported in the literature.

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          Computing a Trust Region Step

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            On Brinell and Boussinesq indentation of creeping solids

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              Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic

              We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates \(r\) and initial packing fractions followed by compression and decompression in small steps to reach packing fractions \(\phi_J\) at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to \(\phi_J\). We find that amorphous, isostatic packings exist over a finite range of packing fractions from \(\phi_{\rm min} \le \phi_J \le \phi_{\rm max}\) in the large-system limit, with \(\phi_{\rm max} \approx 0.853\). In agreement with previous calculations, we obtain \(\phi_{\rm min} \approx 0.84\) for \(r > r^*\), where \(r^*\) is the rate above which \(\phi_J\) is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, bond orientational order, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered, whereas bond-orientational and compositional order increase with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies of the static packings to understand the extent to which the mechanical properties of amorphous, isostatic packings are different from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.
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                Author and article information

                Journal
                20 March 2018
                Article
                1803.07456
                b6284886-4b58-48a0-a6b8-0895488c785c

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                36 pages, 21 figures
                cond-mat.soft cond-mat.mtrl-sci physics.comp-ph

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