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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.
Schematic diagram of Burgers material, Kelvin representation. Given that the Kelvin material has an elasticity and viscosity , the spring has an elasticity and the dashpot has a viscosity , the Burgers model has the constitutive equation
Although this type of fluid is non-Newtonian (i.e. non-linear) in nature, its constitutive equation is a generalised form of the Newtonian fluid. Generalised Newtonian fluids satisfy the following rheological equation: = (˙) ˙
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 ...
Constitutive may refer to: In physics, a constitutive equation is a relation between two physical quantities In ecology , a constitutive defense is one that is always active, as opposed to an inducible defense
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.
The properties are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics. For non-Newtonian fluid's viscosity, there are pseudoplastic, plastic, and dilatant flows that are time-independent, and there are thixotropic and rheopectic flows that are time-dependent.
This definition assumes that the effect of temperature can be ignored, and the body is homogeneous. This is the constitutive equation for a Cauchy-elastic material. Note that the function depends on the choice of reference configuration. Typically, the reference configuration is taken as the relaxed (zero-stress) configuration, but need not be.