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@ -179,7 +179,7 @@ The model requires the following inputs:
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1. *Young's modulus* :math:`E > 0` : The Young's modulus is commonly reported
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for various powders.
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2. *Poissons ratio* :math:`0 \le \nu \le 0.5` : The Poisson's ratio is commonly
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2. *Poisson's ratio* :math:`0 \le \nu \le 0.5` : The Poisson's ratio is commonly
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reported for various powders.
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3. *Yield stress* :math:`Y \ge 0` : The yield stress is often known for powders
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@ -191,12 +191,12 @@ The model requires the following inputs:
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relation to the more commonly reported critical stress intensity factor
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:math:`K_{Ic} = \sqrt{2\Delta\gamma E/(1-\nu^2)}`.
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5. *Critical confinement ratio* :math:`0 \le \psi_b \le 1` : The critical confinment
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5. *Critical confinement ratio* :math:`0 \le \psi_b \le 1` : The critical confinement
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ratio is a tunable parameter that determines when the bulk elastic response is
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triggered. Lower values of :math:`\psi_b` delay the onset of the bulk elastic
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response.
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6. *Coefficient of restiution* :math:`0 \le e \le 1` : The coefficient of
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6. *Coefficient of restitution* :math:`0 \le e \le 1` : The coefficient of
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restitution is a tunable parameter that controls damping in the normal direction.
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.. note::
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@ -229,11 +229,11 @@ begin with an initial radius, however as compaction occurs and plastic
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deformation is accumulated, a new enlarged apparent radius is defined to
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ensure that that volume change due to plastic deformation is not lost.
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This apparent radius is stored as the *atom radius* meaning it is used
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for subsequent neighbor list builds and contact dectection checks. The
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for subsequent neighbor list builds and contact detection checks. The
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advantage of this is that multi-neighbor dependent effects such as
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formation of secondary contacts caused by radial expansion are captured
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by the *mdr* model. Setting *atom_style sphere 1* ensures that updates to
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the particle radius are properly reflected throughout the simulation.
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the particle radii are properly reflected throughout the simulation.
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.. code-block:: LAMMPS
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@ -242,7 +242,7 @@ the particle radius are properly reflected throughout the simulation.
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Newton's third law must be set to *off*. This ensures that the neighbor lists
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are constructed properly for the topological penalty algorithm used to screen
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for non-physical contacts occurring through obstructing particles, an issue
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prevelant under large deformation conditions. For more information on this
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prevalent under large deformation conditions. For more information on this
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algorithm see :ref:`Zunker et al. <Zunker2025>`.
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.. code-block:: LAMMPS
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@ -258,7 +258,7 @@ in damping model.
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The definition of multiple *mdr* models in the *pair_style* is currently not
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supported. Similarly, the *mdr* model cannot be combined with a different normal
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model in the *pair_style*. Phyiscally this means that only one homogenous
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model in the *pair_style*. Physically this means that only one homogenous
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collection of particles governed by a single *mdr* model is allowed.
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The *mdr* model currently only supports *fix wall/gran/region*, not
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@ -279,9 +279,8 @@ adhesive behaviors between particle-particle and particle-wall interactions.
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In addition to contact forces the *mdr* model also tracks the following
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quantities for each particle: elastic volume change, the average normal
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stress components for each particle, and total surface area involved in
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contact. In the input script these quantities can be accessed by first
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calling *run 0* to initialize the values then through subsequent
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*compute* commands.
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contact. In the input script, these quantities are initialized by calling
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*run 0* and can then be accessed using subsequent *compute* commands.
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.. code-block:: LAMMPS
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@ -1003,20 +1002,20 @@ solids. Proc. R. Soc. Lond. A, 324(1558), 301-313.
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.. _DMT1975:
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**Derjaguin et al, 1975)** Derjaguin, B. V., Muller, V. M., & Toporov,
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**(Derjaguin et al, 1975)** Derjaguin, B. V., Muller, V. M., & Toporov,
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Y. P. (1975). Effect of contact deformations on the adhesion of
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particles. Journal of Colloid and interface science, 53(2), 314-326.
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.. _Zunker2024I:
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**(Zunker et al, 2024)** Zunker, W., & Kamrin, K. (2024).
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**(Zunker and Kamrin, 2024)** Zunker, W., & Kamrin, K. (2024).
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A mechanically-derived contact model for adhesive elastic-perfectly
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plastic particles, Part I: Utilizing the method of dimensionality
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reduction. Journal of the Mechanics and Physics of Solids, 183, 105492.
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.. _Zunker2024II:
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**(Zunker et al, 2024)** Zunker, W., & Kamrin, K. (2024).
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**(Zunker and Kamrin, 2024)** Zunker, W., & Kamrin, K. (2024).
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A mechanically-derived contact model for adhesive elastic-perfectly
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plastic particles, Part II: Contact under high compaction—modeling
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a bulk elastic response. Journal of the Mechanics and Physics of Solids,
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