Strain gradient

The stress-strain behavior of plastics in flexure generally follows from the behavior observed in tension and compression for either unreinforced or reinforced plastics. The flexural modulus of elasticity is nominally the average between the tension and compression moduli. The flexural yield point is generally that which is observed in tension, but this is not easily discerned, because the strain gradient in the flexural RP sample essentially eliminates any abrupt change in the flexural stress-strain relationship when the extreme fibers start to yield. 

The details of the rocking ctrrve are extremely sensitive to the strains and strain gradients in the specimen. 

Figure 8.9 Types of extinction contrast, (a) Defect with high strain gradient. Three images, the direct (1), the dynamical (2) and the intermediary (3) are formed, (b) Low strain gradient where the wavefield rays paths are curved...

Gross, T.S., Edwards, J.L., et.al. (1997) Strain gradients correlate with sites of periosteal bone formation. Journal of Bone and Mineral Research 12 982-8... 

N.A. Fleck et al Strain gradient plasticity Theory and experiment. Acta Mater. 42,475 187... 

Active stresses exerted by smooth muscle cells appear to increase the internal stresses that exist in vessel wall. The effects of passive and active muscular contraction on the residual stress in the wall have been considered. Their results suggest that basal muscle tone, which exists under physiological conditions, reduces the strain gradient in the arterial wall and yields a near uniform stress distribution. Increased muscular tone that accompanies elevated blood pressure tends to restore the distribution of circumferential strain in the arterial wall, and to maintain the flow-induced wall shear stress at normal levels. It appears that the active stresses exerted by smooth muscle cells may balance the tension within the vessel wall in a similar manner to the way that active fibroblast tension balances the stress in the dermis. 

Fig.2(b), and this may be as much as 50 times the depth of the surface scratches (7). Experiments with etching techniques t>f varying sensitivies (7) indicate that the strain gradient throughout this zone is of the general form shown in Fig. 5. 

Fig. 5. Estimate of the strain gradient in a brass surface abraded on 600-grade silicon carbide paper.

Rheocalic V2.4. The Bingham mathematic model was used to determine viscosity. The Bingham equation is t = Tq + ly. Where t is the shear stress applied to the material, y is the shear strain rate (also called the strain gradient). To is the yield stress and p is the plastic viscosity. 

Nix W. D. and Gao H., Indentation Size Effects in Crystalline Materials A Faw for Strain Gradient Plasticity, J. Mech. Phys. Solids 46, 411 (1998). 

As an example of such measurements, consider the determination of the Dislocation Density (Nye) Tensor [24], a, from measurements of lattice strain and curvature. Bilby, Gardner and Smith [25] show that this tensor is related to the local lattice curvature and lattice strain gradient by1... 

In a local detailed analysis, the flexible adhesive is modeled with three-dimensional solid elements to enable the refined capture of any local stress or strain gradients. The adhesive material is described as a rabber-like, nearly incompressible, hyperelastic material characterized by a strain energy function. Using U as the strain energy potential per unit of the reference volume, the form of the Ogden strain energy potential is shown in Eq. (1) jii and u are material parameters which are determined from adhesive material test data. 

F. A. Lewis, K. Kandasamy, X. Q. Tong, Lattice strain gradient effects on hydrogen diffusion parameter calculations, Int.J. Hydrogen Energy 2002, 27, 687-694. 

A typical finite element mesh for the joint is shown in Figure 11.6. Five separate parts were meshed — two laminates, two washers and a combined bolt-nut. The meshing of the laminates is similar to that used by Ireman [20], with a relatively high radial mesh density near the hole and under the washer, where high-strain gradients exist. Wedge elements were used to form the core of the bolt. 

During normal steady-state operation, the graphite elements of the core are subjected to stresses induced by the strain gradients resulting from the varying temperature and fluence fields. In addition to stresses created by thermal and irradiation effects, the fuel elements are subject to mechanical loads of gravity, fluid forces and seismic events. Of these mechanical loads only the seismic loads are significant, and even those are small in relation to those due to thermal and irradiation effects. 

Figure 6.26 The flexoelectric effect in BaTiO (a) the evolution of the potential energy curve under a homogeneous stress and in a strain gradient (b) domain switching via mechanical stress imposed by a probe (Original data from Lu et al. (2012))...

Peak distortion by strain gradients, as happens in textile composites. 

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