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Piezoelectric balance presented by Pierre Curie to Lord Kelvin, Hunterian Museum, Glasgow. Piezoelectricity [note 1] is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress.
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 converse piezoelectric effect (CPE) describes how an applied electric field will create a resultant strain which in turn leads to a physical deformation of the material. This effect can be described through the constitutive equations. [4] The CPE can be written as =
The piezoelectric coefficient or piezoelectric modulus, usually written d 33, quantifies the volume change when a piezoelectric material is subject to an electric field, or the polarization on the application of stress.
Piezoelectric polymers (PVDF, 240 mV-m/N) possess higher piezoelectric stress constants (g 33), an important parameter in sensors, than ceramics (PZT, 11 mV-m/N), which show that they can be better sensors than ceramics. Moreover, piezoelectric polymeric sensors and actuators, due to their processing flexibility, can be readily manufactured ...
The above equation is a vector form of the most general equation for fluid flow in porous media, and it gives the reader a good overview of the terms and quantities involved. Before you go ahead and transform the differential equation into difference equations, to be used by the computers, you must write the flow equation in component form.
All non-relativistic balance equations, such as the Navier–Stokes equations, can be derived by beginning with the Cauchy equations and specifying the stress tensor through a constitutive relation. By expressing the deviatoric (shear) stress tensor in terms of viscosity and the fluid velocity gradient, and assuming constant viscosity, the ...
The compressible Euler equations consist of equations for conservation of mass, balance of momentum, and balance of energy, together with a suitable constitutive equation for the specific energy density of the fluid. Historically, only the equations of conservation of mass and balance of momentum were derived by Euler.