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. Author manuscript; available in PMC: 2019 Dec 1.
Published in final edited form as: Z Angew Math Mech. 2018 Mar 23;98(12):2048–2071. doi: 10.1002/zamm.201700302
Mα Partial mass of constituent α within the mixture (usually defined locally) kg
Vα Partial volume of constituent α within the mixture (usually defined locally) m3
Πα Mass production rate of constituent α (usually defined locally) kg · s−1
ρα Apparent spatial mass density of constituent α: current mass of constituent α per unit current volume of mixture kg · m−3
ρRα
Apparent referential mass density of constituent α: current mass of constituent α per unit reference volume of mixture kg · m−3
ΦRα
Referential volume fraction of constituent α: current volume of constituent α per unit reference volume of mixture [−]
Φα Spatial volume fraction of constituent α: current volume of constituent α per unit current volume of mixture [−]
ϕα Spatial mass fraction of constituent α: current mass of constituent α per unit current mass of mixture [−]
mα Spatial mass density production rate of constituent α: current mass production rate of constituent α per unit current volume of mixture kg · s−1 · m−3
mRα
Referential mass density production rate of constituent α: current mass production rate of constituent α per unit reference volume of mixture kg · s−1 · m−3
mNα
Referential nominal mass density production rate of constituent α: current nominal mass production rate of constituent α per unit reference volume of mixture kg · s−1 · m−3
WRα
Referential strain energy function of constituent α: current strain energy of mass of constituent α within the mixture per unit reference volume of mixture J · m−3