Irwin model

There are two principal theories, or models, that attempt to describe what happens during brittle fracture, the Griffith fracture theory and the Irwin model. Both assume that fracture takes place through the presence of preexisting cracks or flaws in the polymer and are concerned with what happens near such a crack when a load is applied. Each leads to the definition of a fracture-toughness parameter and the two parameters are closely related to each other. The Griffith theory is concerned with the elastically stored energy near the crack, whereas the Irwin model is concerned with the distribution of stresses near the crack. Both theories apply strictly only for materials that are perfectly elastic for small strains and are therefore said to describe linear fracture mechanics. 

The elastic stresses in the outer zone can be calculated from the Irwin model by assigning a fictitious length a -I- Ty to the crack. 

Fig. 13. Irwin model Small plastic zone surrounded by an elastic field.

Linear elastic fracture mechanics (including the Irwin model of confined plasticity, the line-zone or Dugdale model and viscoelastic effects)... 

Figure 7.5 Irwin model of the plastic zone at a crack tip.

Fig. 20-2. Ratio of second highest 24-hr estimated concentrations from the CRSTER model (47) to measured concentrations as a function of the excess of receptor elevation over stack base evaluation A relative to the stack height h. Names with each symbol are power plants. Source From Turner and Irwin (48).

Turner, D. B., and Irwin, J. S., Comparison of sulfur dioxide estimates from the model RAM with St. Louis RAPS measurements, in "Air Pollution Modeling and Its Application 11" (C. de Wispelaere, ed.). Plenum, New York, 1982. 

J.Neter and W.Wasserman, Annlied Linear. Statistical Models. Richard D. Irwin, Homewood, IL (1974). 

Sterman ID. Business dynamics systems thinking and modeling for a complex world. McGraw-Hill/Irwin, 2000. 

More complicated reactions schemes, including first-order reversible consecutive processes and competitive consecutive reactions, are considered in a textbook by Irwin [89]. Professor Irwin s textbook also includes computer programs written in the BASIC language. These programs can be used to fit data to the models described. 

M. H. Kutner, C. J. Nachtsheim, and J. Neter. Applied Linear Regression Models. McGraw-Hill Irwin, 4 edition, 2004. 

Neter, J., Wasserman, W and Kutner, M.H. (1990), Applied Linear Statistical Models Regression, Analysis of Variance, and Experimental Designs, 3rd ed., Irwin, Homewood, IL. 

Irwin, J. J., Shoichet, B.K. ZINC — a free database of commercially available compounds for virtual screening. J. Chem. Inf. Model. 2005, 45, 177-82. 

In Sections 10.3 and 10.4 the R2 value increased from 0.479 to 0.794 and the F-ratio for the significance of regression increased from the 97.3% to the 99.6% level of confidence when the term fl x 2 was added to the model. Is it possible that in some instances R2 will increase, but the significance of regression will decrease If so, why [See, for example, Neter, J., and Wasserman, W. (1974). Applied Linear Statistical Models. Regression, Analysis of Variance, and Experimental Designs, p. 229. Irwin, Homewood, Illinois.]... 

Mroso P, Li Wan Po A, Irwin W. Solid-state stability of aspirin in the presence of excipients kinetic interpretation modeling and prediction. J Pharm Sci 1982 71(10) 1096—1101. 

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