Sentence examples for by the strain gradient from inspiring English sources

The calculation formula of non-linear error caused by the strain gradient was derived.

To calculate the flexural crack width in the surface of the concrete w c, the width of the crack in the width at the reinforcement w s shall be multiplied by the strain gradient amplification coefficient β s (Eq. 2).

It is also found that the lower bound and the upper bound for the frequencies of nanotubes are, respectively, provided by the strain gradient model provides and the stress gradient theory.

Finally, discussions of size effect induced by the strain gradient terms reveal that the present model is more accurate since size effect play an important role when beam in nanoscale.

Exact solutions are established and comparisons with pertinent results obtained by the Eringen strain-driven two-phase mixture and by the strain gradient theory of elasticity are carried out.

When the inward flux induced by the surface energy minimization at the rim compensates the outward flux by the strain gradient, the trench is formed and in thermal equilibrium, as shown in Figure 3b. Figure 3 Cross-sectional schematic diagrams of strain distribution in the Si capping layer and Si migration during annealing.

This paper comments on the recently published work dealing with the static and dynamic analysis of micro beams by using the strain gradient elasticity theory (International Journal of Engineering Science, 47, 487 498, 2009) by Kong et al. (2009).

Since the average flexural crack width that is calculated using Eq. (18) is assumed to be in the concrete close to the tensile reinforcement, it can be used to calculate the average width of flexural cracks at the concrete surface by applying the strain gradient amplification coefficient β s, as defined in Eqs.

Plastic flow localization in ductile materials subjected to pure shear loading and uniaxial tension is investigated respectively in this paper using a reduced strain gradient theory, which consists of the couple-stress (CS) strain gradient theory proposed by Fleck and Hutchinson (1993) and the strain gradient hardening (softening) law (C W) proposed by Chen and Wang (2000).

Macroscopic quantities of interest such as the Piola Kirchhoff stress tensor can be approximated for any value of the strain gradient by numerically solving a nonlinear PDE.

It is shown that implementation of the strain gradient elasticity by incorporating inertia gradients yields more reliable results especially for shorter length SWCNTs on account of two small scale factors corresponding to the inertia and strain gradients.