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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.
The constitutive equations describe how the quantity in question responds to various stimuli via transport. Prominent examples include Fourier's law of heat conduction and the Navier–Stokes equations , which describe, respectively, the response of heat flux to temperature gradients and the relationship between fluid flux and the forces ...
For this case only two components of the shear stress became non-zero: = ˙ and = ˙ where ˙ is the shear rate.. Thus, the upper-convected Maxwell model predicts for the simple shear that shear stress to be proportional to the shear rate and the first difference of normal stresses is proportional to the square of the shear rate, the second difference of normal stresses is always zero.
Plastic deformation of a thin metal sheet. Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. [1] Flow plasticity theories are characterized by the assumption that a flow rule exists that can be used to determine the amount of plastic deformation in the material.
Einstein field equations; Einstein–Rosen metric; Electromagnetic wave equation; Elliott formula; Emden–Chandrasekhar equation; Ensemble (mathematical physics) Equation of state; Equations of motion; Euler's laws of motion
A flux in classical mechanics is normally not a governing equation, but usually a defining equation for transport properties. Darcy's law was originally established as an empirical equation, but is later shown to be derivable as an approximation of Navier-Stokes equation combined with an empirical composite friction force term. This explains ...
Betti's theorem, also known as Maxwell–Betti reciprocal work theorem, discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces {P i} i=1,...,n and {Q j}, j=1,2,...,n, the work done by the set P through the displacements produced by the set Q is equal to the work done by the set Q through the displacements produced by the set P.
It is a two-equation model which gives a general description of turbulence by means of two transport equations (PDEs). The original impetus for the K-epsilon model was to improve the mixing-length model, as well as to find an alternative to algebraically prescribing turbulent length scales in moderate to high complexity flows.