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.
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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.
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.
If the true functions for the processes in the system are unknown, the numerical values of the parameters in the power-law representations (Eq. 1 and Supplement Eq. S1) are not known.
Second, experience has shown that this vicinity can be quite large in biological systems and that power-law representations are often sufficiently accurate for high-percent or even fold variations in system components.
While for conventional models the kinetic orders are decided a priori, in power-law representations the number of parameters that must be extracted from data is therefore larger.
The simplification of mathematical modeling using power-law representations, such as saturable and synergistic (S -system or generalized maS -system (GMA)-system representatiors in the framework of biochemical systems theory (BST) (Savageneralized b, 1970; Shiraishi and Savageau 1992; Voit 2013), probably has the potential to overcomasshe actionproblems.
Within the conceptual framework of power-law representations, the rate of the association reaction between molecules of species S1 and S2 is given as k [ X 1 (t ) ] f 1 [ X 2 (t ) ] f 2. Here, k is the rate constant and f1 and f2 are real-valued kinetic orders, which are no longer necessarily positive integers as it is assumed in a mass action law.
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.
