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Theory Manual Version 3.6
 Subsection 2.8.1: Mixture Kinematics Up Section 2.8: Constrained Reactive Mixture of Solids Subsection 2.8.3: Mixture Free Energy and Stress 

2.8.2 Mixture Composition

Each constituent has an apparent mass density which may evolve due to deformation, or due to reactive processes which alter the mixture composition. Following [41, 42], we define the referential apparent mass density of each constituent as Equation (2.8.2-1) expresses the mass of constituent per referential volume of the master constituent ; thus may only evolve if the mass content changes via reactions, making it a suitable state variable for tracking composition in a reactive framework. The axiom of mass balance for each constituent may be written as where the dot operator represents the material time derivative and is the referential mass supply density for constituent , representing the rate at which mass (per referential volume) is added to due to reactions with all other mixture constituents [8, 77]. A constitutive relation must be provided for for various types of reactions. The mixture referential mass density is given by This summation is carried out over all constituents. When a constrained mixture of solid constituents represents a closed system, remains constant over time. Taking the material time derivative of eq.(2.8.2-3) and using eq.(2.8.2-2) shows that the referential mass density supplies must satisfy
 Subsection 2.8.1: Mixture Kinematics Up Section 2.8: Constrained Reactive Mixture of Solids Subsection 2.8.3: Mixture Free Energy and Stress