Fatigue mathematical models

Zhao H, Wang L, Li Y, Liu X, King MW. The mathematical model for evaluating fatigue resistance of SG tubular fabric relationship between textile parameters and fatigue performance./. Biomater. Appl. 24 579-590,2010. 

For the mathematical modelling of the sonic fatigue process of PAN monofilaments, the following equation was considered ... 

Some criteria are presented for evaluating the various tyre design theories that are based on the equilibrium shape of the sidewall and on the rolling contour of a tyre. Tyre failure types and the mathematical models by which they can be predicted by modem theories of mbber/cord fatigue are also described. A tyre design theory based on stress-strain optimisation of its elements is proposed as is a hierarchic system of complicated tyre models for calculation of stress-strain cycles. Influence of the cross-section geometry and of the iimer stmcture of the tyre on stress-strain cycles in the belt and bead of radial tyres is investigated. 21 refs. 

Ray A., Tangirala S., Phoha S. 1998. Stochastic modeling of fatigue crack propagation. Applied Mathematical Modelling 11 197-204. 

Note Wear, aging, fatigue, and corrosion are processes, the spreading of which may, on many occasions, be described by mathematical models. 

The present fatigue life model, expressed by Eqs. (5-7), is based on three existing fatigue life theories. The basic concept of fatigue integral is due to loannides and Harris [18]. The incorporation of fatigue limit stress, the mathematical form of the depth factor, and the use of the Mises stress as the equivalent stress are also part of the loannides-Harris theory [17-18]. 

The plastic strain energy density can be physically interpreted as the energy of distortion associated with the change in shape of a volume elanent and is related to failure, particularly under conditions of ductile behavior, as it often occurs in many of the polymeric materials submitted to cyclic mechanical solicitation (Kanchanomai and Mutoh, 2004). According to the mathematical model proposed by Morrow (American Society for Testing and Materials, 1965), the strain energy density can be evaluated numerically as the inner area of the saturated hysteresis loop for the uniaxial fatigue experiments (Fig. 7.6), and is expressed mathematically as ... 

Lardner, R. W. (1968) A dislocation model of fatigue crack growth in metals. Philos. Mag. 17, 71-82 Lardner, R.W. (1974) Mathematical Theory of Dislocations and Fracture (University of Toronto Press, Toronto)... 

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