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The value of σ g determines the slope of the least-squares regression curve. α: Relative standard deviation or degree of polydispersity. This value is also determined mathematically. For values less than 0.1, the particulate sample can be considered to be monodisperse. α = σ g /D 50. Re (P) : Particle Reynolds Number. In contrast to the ...
Absement changes as an object remains displaced and stays constant as the object resides at the initial position. It is the first time-integral of the displacement [3] [4] (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement.
Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.
If the material is linearly elastic, the computation of its energy release rate can be much simplified. In this case, the Load vs. Load-point Displacement curve is linear with a positive slope, and the displacement per unit force applied is defined as the compliance, [3] =.
In physics and continuum mechanics, deformation is the change in the shape or size of an object. It has dimension of length with SI unit of metre (m). It is quantified as the residual displacement of particles in a non-rigid body, from an initial configuration to a final configuration, excluding the body's average translation and rotation (its rigid transformation). [1]
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
The particle deformation can be measured by the deflection of the cantilever tip over the sample. The resulting force-displacement curves can be used to calculate elastic modulus. [75] However, it is unclear whether particle size and indentation depth affect the measured elastic modulus of nanoparticles by AFM. [75]
An example indentation image, from which the area may be determined, is shown at right. Some nanoindenters use an area function based on the geometry of the tip, compensating for elastic load during the test. Use of this area function provides a method of gaining real-time nanohardness values from a load-displacement graph.