Its linear part is used to determine shear modulus
where [[alpha].sub.e], [r.sub.e1], and [r.sub.e2] are material parameters and [G.sup.E.sub.0] the initial elastic shear modulus
. [[gamma].sup.P*.sub.ap] denotes the accumulative plastic deviatoric strain after the stress ratio reaches the phase transformation [M.sup.*.sub.m], and [[gamma].sup.E*.sub.r] is the reference strain which can be obtained by fitting to liquefaction resistance curve.
Symbols ILSS: Interlaminar shear strength I[Lss.sub.max]: Maximum interlaminar shear stress [DELTA][[alpha].sub.max]: Maximum difference of axial coefficients of thermal expansion between carbon fiber and epoxy [DELTA][T.sub.max]: Maximum temperature variation between stress-free temperature and ambient temperature [G.sub.max]: Maximum shear modulus
in axial direction [[alpha].sub.CFACTE]: Carbon fiber's axial coefficient of thermal expansion [[alpha].sub.epoxy]: Epoxy's axial coefficient of thermal expansion [T.sub.s]: Stress-free temperature [T.sub.coldest]: Coldest temperature [G.sub.CFASM]: Carbon fiber's axial shear modulus
N: Cycle numbers to failure [DELTA]T: Temperature variation.
The effects of the shear modulus
ratio [G.sup.SL] of the soil and die, the Poisson ratio [v.sup.s] of the soil material, the fractional-derivative order [alpha], the material parameter ratio [T.sub.[sigma]]/[T.sub.[epsilon]] on the radial displacement, and the hoop stress amplitude were investigated.
The first one is the maximum shear modulus
, [G.sub.0], which can be measured in the order of ~10-5-10-3% cyclic strain range.
Solving Equation 1 and 2, both derived from bending tests, it leads to values of longitudinal modulus of elasticity and shear modulus
, Equation 3 and 4, respectively.
Caption: FIGURE 1: Shear modulus
[[mu].sub.x]; a = 2, b = 1; [k.sub.1] = [k.sub.3] = 1, [k.sub.2] = 2.
TABLE 1: Mean grain size, grain centre distribution, grain boundary atomic fraction [eta], bulk modulus B, shear modulus
[mu], Young's modulus E, and Poisson's ratio v, calculated from the above values of B and [mu], and average values of Young's modulus resulting from uniaxial strain tests, for each of the 8 samples studied in this paper.
In the formula mentioned above (see (1)), E is Young's modulus, G is shear modulus
, [rho] is the density, and [mu] refers to Poisson's ratio.
where [K.sub.w] and [K.sub.G] are Winkler modulus for normal load and shear modulus
for transverse shear loads, respectively.
The shear modulus
[micro] of the measured muscle can then be calculated via the following equation:
Keywords: Normalized shear modulus
Damping ratio Hyperbolic model Nonlinear multiple regression model Rockfill material