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The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
This constitutive equation is also called the Newton law of viscosity. The total stress tensor σ {\displaystyle {\boldsymbol {\sigma }}} can always be decomposed as the sum of the isotropic stress tensor and the deviatoric stress tensor ( σ ′ {\displaystyle {\boldsymbol {\sigma }}'} ):
For completion, one must make hypotheses on the forms of τ and p, that is, one needs a constitutive law for the stress tensor which can be obtained for specific fluid families and on the pressure. Some of these hypotheses lead to the Euler equations (fluid dynamics) , other ones lead to the Navier–Stokes equations.
The constitutive relation is expressed as a linear first-order differential equation: = + ˙ This model represents a solid undergoing reversible, viscoelastic strain. Upon application of a constant stress, the material deforms at a decreasing rate, asymptotically approaching the steady-state strain.
Newton's law of viscosity is the simplest relationship between the flux of momentum and the velocity gradient. It may be useful to note that this is an unconventional use of the symbol τ zx ; the indices are reversed as compared with standard usage in solid mechanics, and the sign is reversed.
Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, and molecule activation.
Mendeleev's law allowed him to build up a systematic periodic table of all the 66 elements then known based on atomic mass, which he published in Principles of Chemistry in 1869. His first Periodic Table was compiled on the basis of arranging the elements in ascending order of atomic weight and grouping them by similarity of properties.
The history of scientific method considers changes in the methodology of scientific inquiry, as distinct from the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the ...