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The internal efforts (N int, M int ) developed by the deformations (δu, δw) are related by the following formulas (Eq. (6)): Open image in new window Fig. 3 Behavior material law representation.
Based on an Ohm's law representation of kinetics, we develop an accurate quasi steady-state (QSS) rate expression for the complete sequence, not possible with the usual QSS approach, which provides only numerical results for the nonlinear sequence.
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It is found that when expressed in this form the exponent of this variant is approximately 2 and, as such, is considerably lower than the exponent in "Paris like" power law representations for delamination growth in composites.
To this end we show that the delamination growth rate da/dN can often be related to (Δ√G − Δ√Gth)α, where α is approximately 2. As such the exponent in this relationship is considerably lower than the exponent in "Paris like" power law representations.
This study has been greatly facilitated by use of the piecewise power-law representation, which was first developed by systems engineers in the 1940s and adapted for biochemical systems in the early 1970s.
The piecewise power-law representation of the rate laws for G6PD and GSR allowed us to define the design space for the NADPH redox cycle.
14 On the other hand, the power-law representation can be employed as a local representation.
By performing Taylor expansion, the power-law representation can be employed as a piecewise expression.
The JAK2-STAT5 pathasy has been modelled using a power-law representation [ 15].
In general, the power-law representation in biological systems can be considered as a canonical nonlinear system.
In addition, we analyse under which conditions the use of a power-law representation for the system is useful.
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