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In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material. [ 1 ] [ 2 ] [ 3 ] It provides a theoretical upper- and lower-bound on properties such as the elastic modulus , ultimate tensile strength , thermal conductivity , and electrical conductivity . [ 3 ]
In crystallography, materials science and metallurgy, Vegard's law is an empirical finding (heuristic approach) resembling the rule of mixtures.In 1921, Lars Vegard discovered that the lattice parameter of a solid solution of two constituents is approximately a weighted mean of the two constituents' lattice parameters at the same temperature: [1] [2]
Richmann's law, [1] [2] sometimes referred to as Richmann's rule, [3] Richmann's mixing rule, [4] Richmann's rule of mixture [5] or Richmann's law of mixture, [6] is a physical law for calculating the mixing temperature when pooling multiple bodies. [5]
Voigt [4] (1887) - Strains constant in composite, rule of mixtures for stiffness components. Reuss (1929) [5] - Stresses constant in composite, rule of mixtures for compliance components. Strength of Materials (SOM) - Longitudinally: strains constant in composite, stresses volume-additive. Transversely: stresses constant in composite, strains ...
The existence of the velocity gradient in the functional relationship for non-Newtonian fluids says that viscosity is generally not an equation of state, so the term constitutional equation will in general be used for viscosity equations (or functions). The free variables in the two equations above, also indicates that specific constitutive ...
The Lorentz rule was proposed by H. A. Lorentz in 1881: [5] = + The Lorentz rule is only analytically correct for hard sphere systems. Intuitively, since , loosely reflect the radii of particle i and j respectively, their averages can be said to be the effective radii between the two particles at which point repulsive interactions become severe.
Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity.
The basic assumption is that, at any instant of time, all phases are present at every material point, and momentum and mass balance equations are postulated. Like other models, mixture theory requires constitutive relations to close the system of equations. Krzysztof Wilmanski extended the model by introducing a balance equation of porosity. [2 ...