forked from lijiext/lammps
fix spelling and record false positives
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@ -111,8 +111,7 @@ For the {hertz/material} model, the force is given by:
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Here, \(E_\{eff\} = E = \left(\frac\{1-\nu_i^2\}\{E_i\} + \frac\{1-\nu_j^2\}\{E_j\}\right)^\{-1\}\)
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is the effective Young's modulus,
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with \(\nu_i, \nu_j \) the Poisson ratios of the particles of types {i} and {j}. Note that
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if the elastic and shear moduli of the
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two particles are the same, the {hertz/material}
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if the elastic modulus and the shear modulus of the two particles are the same, the {hertz/material}
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model is equivalent to the {hertz} model with \(k_N = 4/3 E_\{eff\}\)
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The {dmt} model corresponds to the "(Derjaguin-Muller-Toporov)"_#DMT1975 cohesive model,
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@ -188,7 +187,7 @@ for all models except {jkr}, for which it is given implicitly according to \(del
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In this case, \eta_\{n0\}\ is in units of 1/({time}*{distance}).
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The {tsuji} model is based on the work of "(Tsuji et al)"_#Tsuji1992. Here, the
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damping coefficient specified as part of the normal model is intepreted
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damping coefficient specified as part of the normal model is interpreted
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as a restitution coefficient \(e\). The damping constant \(\eta_n\) is given by:
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\begin\{equation\}
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@ -242,7 +241,7 @@ The tangential damping force \(\mathbf\{F\}_\mathrm\{t,damp\}\) is given by:
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\mathbf\{F\}_\mathrm\{t,damp\} = -\eta_t \mathbf\{v\}_\{t,rel\}
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\end\{equation\}
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The tangetial damping prefactor \(\eta_t\) is calculated by scaling the normal damping \(\eta_n\) (see above):
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The tangential damping prefactor \(\eta_t\) is calculated by scaling the normal damping \(\eta_n\) (see above):
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\begin\{equation\}
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\eta_t = -x_\{\gamma,t\} \eta_n
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\end\{equation\}
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@ -292,7 +291,7 @@ duration of the contact:
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\mathbf\{\xi\} = \int_\{t0\}^t \mathbf\{v\}_\{t,rel\}(\tau) \mathrm\{d\}\tau
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\end\{equation\}
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This accumlated tangential displacement must be adjusted to account for changes
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This accumulated tangential displacement must be adjusted to account for changes
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in the frame of reference
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of the contacting pair of particles during contact. This occurs due to the overall motion of the contacting particles
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in a rigid-body-like fashion during the duration of the contact. There are two modes of motion
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@ -304,7 +303,7 @@ made by rotating the accumulated displacement into the plane that is tangential
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to the contact vector at each step,
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or equivalently removing any component of the tangential displacement
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that lies along \(\mathbf\{n\}\), and rescaling to preserve the magnitude.
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This folllows the discussion in "Luding"_#Luding2008, see equation 17 and
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This follows the discussion in "Luding"_#Luding2008, see equation 17 and
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relevant discussion in that work:
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\begin\{equation\}
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@ -350,7 +349,7 @@ see discussion above. To match the Mindlin solution, one should set \(k_t = 8G\)
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\(G\) is the shear modulus, related to Young's modulus \(E\) by \(G = E/(2(1+\nu))\), where \(\nu\)
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is Poisson's ratio. This can also be achieved by specifying {NULL} for \(k_t\), in which case
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a normal contact model that specifies material parameters \(E\) and \(\nu\) is required (e.g. {hertz/material},
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{dmt} or {jkr}). In this case, mixing of shear moduli for different particle types {i} and {j} is done according
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{dmt} or {jkr}). In this case, mixing of the shear modulus for different particle types {i} and {j} is done according
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to:
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\begin\{equation\}
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1/G = 2(2-\nu_i)(1+\nu_i)/E_i + 2(2-\nu_j)(1+\nu_j)/E_j
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@ -381,7 +380,7 @@ If the {rolling} keyword is not specified, the model defaults to {none}.
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For {rolling sds}, rolling friction is computed via a spring-dashpot-slider, using a
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'pseudo-force' formulation, as detailed by "Luding"_#Luding2008. Unlike the formulation
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in "Marshall"_#Marshall2009, this allows for the required adjustment of
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rolling displacement due to changes in the frame of referenece of the contacting pair.
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rolling displacement due to changes in the frame of reference of the contacting pair.
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The rolling pseudo-force is computed analogously to the tangential force:
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\begin\{equation\}
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@ -487,7 +486,7 @@ Finally, the twisting torque on each particle is given by:
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:line
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LAMMPS automatically sets pairwise cutoff values for {pair_style granular} based on particle radii (and in the case
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of {jkr} pulloff distances). In the vast majority of situations, this is adequate.
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of {jkr} pull-off distances). In the vast majority of situations, this is adequate.
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However, a cutoff value can optionally be appended to the {pair_style granular} command to specify
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a global cutoff (i.e. a cutoff for all atom types). Additionally, the optional {cutoff} keyword
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can be passed to the {pair_coeff} command, followed by a cutoff value.
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@ -533,7 +532,7 @@ Mixing of coefficients is carried out using geometric averaging for
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most quantities, e.g. if friction coefficient for type 1-type 1 interactions
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is set to \(\mu_1\), and friction coefficient for type 2-type 2 interactions
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is set to \(\mu_2\), the friction coefficient for type1-type2 interactions
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is computed as \(\sqrt\{\mu_1\mu_2\}\) (unless explictly specified to
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is computed as \(\sqrt\{\mu_1\mu_2\}\) (unless explicitly specified to
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a different value by a {pair_coeff 1 2 ...} command. The exception to this is
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elastic modulus, only applicable to {hertz/material}, {dmt} and {jkr} normal
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contact models. In that case, the effective elastic modulus is computed as:
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@ -542,7 +541,7 @@ contact models. In that case, the effective elastic modulus is computed as:
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E_\{eff,ij\} = \left(\frac\{1-\nu_i^2\}\{E_i\} + \frac\{1-\nu_j^2\}\{E_j\}\right)^\{-1\}
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\end\{equation\}
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If the {i-j} coefficients \(E_\{ij\}\) and \(\nu_\{ij\}\) are explictly specified,
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If the {i-j} coefficients \(E_\{ij\}\) and \(\nu_\{ij\}\) are explicitly specified,
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the effective modulus is computed as:
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\begin\{equation\}
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@ -155,6 +155,8 @@ ba
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Babadi
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backcolor
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Baczewski
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Bagi
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Bagnold
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Bal
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balancer
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Balankura
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@ -343,6 +345,7 @@ Cij
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cis
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civ
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clearstore
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Cleary
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Clebsch
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clemson
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Clermont
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@ -369,6 +372,7 @@ Coeff
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CoefficientN
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coeffs
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Coeffs
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cohesionless
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Coker
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Colberg
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coleman
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@ -442,6 +446,7 @@ cuda
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Cuda
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CUDA
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CuH
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Cummins
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Curk
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customIDs
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cutbond
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@ -485,6 +490,7 @@ darkturquoise
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darkviolet
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Das
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Dasgupta
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dashpot
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dat
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datafile
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datums
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@ -521,6 +527,7 @@ Dequidt
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der
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derekt
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Derjagin
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Derjaguin
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Derlet
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Deserno
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Destree
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@ -1065,6 +1072,7 @@ Hyoungki
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hyperdynamics
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hyperradius
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hyperspherical
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hysteretic
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Ibanez
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ibar
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ibm
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@ -1124,6 +1132,7 @@ interconvert
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interial
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interlayer
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intermolecular
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Interparticle
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interstitials
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Intr
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intra
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@ -1141,6 +1150,7 @@ IPython
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Isele
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isenthalpic
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ish
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Ishida
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iso
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isodemic
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isoenergetic
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@ -1430,6 +1440,7 @@ logfile
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logfreq
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logicals
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Lomdahl
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Lond
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lookups
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Lookups
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LoopVar
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@ -1444,6 +1455,7 @@ lsfftw
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ltbbmalloc
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lubricateU
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lucy
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Luding
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Lussetti
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Lustig
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lwsock
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@ -1482,6 +1494,7 @@ manybody
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MANYBODY
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Maras
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Marrink
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Marroquin
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Marsaglia
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Marseille
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Martyna
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@ -1493,6 +1506,7 @@ masstotal
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Masuhiro
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Matchett
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Materias
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mathbf
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matlab
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matplotlib
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Mattox
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@ -1580,6 +1594,7 @@ Mie
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Mikami
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Militzer
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Minary
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Mindlin
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mincap
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mingw
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minima
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@ -2260,6 +2275,7 @@ rg
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Rg
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Rhaphson
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rheological
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rheology
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rhodo
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Rhodo
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rhodopsin
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@ -2572,6 +2588,7 @@ Tait
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taitwater
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Tajkhorshid
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Tamaskovics
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Tanaka
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tanh
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Tartakovsky
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taskset
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@ -2659,6 +2676,7 @@ tokyo
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tol
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toolchain
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topologies
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Toporov
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Torder
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torsions
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Tosi
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@ -2703,6 +2721,7 @@ Tsrd
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Tstart
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tstat
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Tstop
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Tsuji
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Tsuzuki
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tt
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Tt
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