Strain potential

Carvalho, R.S., Scott, J.E., Suga, D.M., et al. (1994) Stimulation of signal transduction pathways in osteoblasts by mechanical strain potentiated by parathyroid hormone. Journal of Bone and Mineral Research 9 999-1011... 

For one of our carbons we estimate that in some cases < a and C are of the order of 20% of the adsorption potential, assuming a Poisson ratio of 1/3. In these cases one may regard the adsorption potential as arising from a release of a compressive stress potential (80%) and a shear strain potential (20%). 

Under standard conditions, reaction (a) is 108 times faster than reaction (b). The explanation is that the cyclic compound in (a) has considerable bond strain (potential energy in this configuration is high), which is released on ring opening during hydrolysis. This type of strain is not present in the diester in (b). 

Agents that are found to be constrained by fastidious culture requirements, too strict epidemiological parameters, or inadequate virulence or that are too labile must be the subject of more nutritional, genetic or physiological research to enhance strain potential. Understanding the molecular basis for these sorts of... 

From experiments in our laboratory on biaxial deformations of thin sheets, it is found that in some materials cracks are formed without any evidence of necking, while at the same levels of strain in uniaxial extension necking had already occurred. This is not surprising since the potential function w depends on the strain Invariants and for biaxial experiments, the solution given in section III has to be modified because the strain potential now has to be differentiated with respect to the first and second strain invariants. More work in biaxial deformations will lead to a better description of the failure mechanism In general. 

Potential strain Not required Total a. Seismic b. Wave Strain potential of individual elements Seed (1966)... 

Knowing the F.S. at each element based on failure defined by a specified strain in a laboratory test makes possible the evaluation of the equivalent cycUc strain at each element. These strains are strains that would develop in a laboratory test specimen, which is subjected to the same static and seismic stresses imposed on a field element. However, an element in the field cannot strain like the test specimen because it is constrained by the deformations of adjacent elements. Thus, with reference to the field loading case, the cyclic strains are referred to as potential strains. Judgment is again required to interpret the meaning of strain potential in terms of the overall dynamic stability of the slope. 

Lee (1974) developed a more rigorous method of estimating the permanent deformations experienced by earth structures during a dynamic loading. This method followed the basic Seed approach for calculating the F.S. and strain potential for individual elements (Seed, 1966). Differences between the two methods depend on procedures used to calculate deformations from the strain potential values. 

The K-BKZ Theory Model. The K-BKZ model was developed in the early 1960s by two independent groups. Bernstein, Kearsley, and Zapas (70) of the National Bureau of Standards (now the National Institute of Standards and Technology) first presented the model in 1962 and published it in 1963. Kaye (71), in Cranfield, U.K., published the model in 1962, without the extensive derivations and background thermodynamics associated with the BKZ papers (82,107). Regardless of this, only the final form of the constitutive equation is of concern here. Similar to the idea of finite elasticity theory, the K-BKZ model postulates the existence of a strain potential function U Ii, I2, t). This is similar to the strain energy density function, but it depends on time and, now, the invariants are those of the relative left Cauchy-Green deformation tensor The relevant constitutive equation is... 

Torsional Experiments. The geometry and equations for torsion of an elastic cylinder are presented above. For the viscoelastic K-BKZ material, the equations look similar. For isochronal values of the strain potential function, one can define what looks like a time-dependent strain-energy ftinction Wi(Ii, I2, t) ... 

Issues of Material Compressibility. There is a full theory of compressible and nonlinear viscoelastic materials that would be equivalent to the compressible finite deformation elasticity theory described above (eq. 39), but more complicated because of the need to develop an expansion of the time-dependent strain potential function as a series of multiple integrals (108,109). One such formahsm is discussed briefiy under Lustig, Shay and Caruthers Model. Here a simphfied model that is based upon the K-BKZ framework with a VL-like kernel function (98) is examined. 

The strain potential function of the solid phase used here was assumed to be an additive function of isotropic (properties arising from proteoglycans and ions) and... 

The isotropic part was taken from Holmes Mow s strain potential function [17] while the anisotropic part was modeled based on concepts introduced by Holzapfel et al. 2000 ... 

Similar to the idea of finite elasticity theory, the K-BKZ model postulates the existence of a strain potential function U(Ji, I2, i). This is similar to the strain energy density function, but it depends on time and, now, the invariants are those of the relative left Cauchy-Green deformation tensor The relevant constitutive equation is... 

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