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The modulus is derived by means of a strain energy approach founded on micromechanics.
The overall bulk modulus is derived in a simple form, based on the construction of neutral composite sphere.
We then apply the proposed general methods to the specific case of nanocomposites with monodisperse spherical inclusions, for which a lower bound on the bulk modulus is derived.
An expression for the nonlinear shear modulus is derived based on the assumption of uniform distribution of micro-kinks and fiber misalignment defects.
Using this approach, the elastic modulus is derived based on scaling factors which depend on cartilage thickness, indenter radius and Poisson's ratio, and the cartilage model is assumed isotropic and homogeneous, thereby greatly simplifying the true tissue characteristics.
The effect of nanoparticles on viscosity or, in the case of elastomers, the effect of nanoparticles on the elastic modulus is derived from hydrodynamic [45 47] or elastic equations [48].
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Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived.
The stress was calculated as the force applied divided by the cross-sectional area of the helix, while the Young's modulus was derived from the slope of the stress strain diagram after linear regression fitting.
With the Brazilian test method, the quantity-relationship between the displacement and the elastic modulus was derived.
Explicit formulae for the mass density tensor and bulk modulus are derived in terms of the transformation function.
Using deformation energy equilibrium between sum of individual fibers and the plate of nano-fibrous scaffold, the scaffold effective modulus was derived explicitly.
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