Isostress-isostrain approximation

The easiest approximation for the effective material properly calculation is so called isostress-isostrain approximation (Skitmer et al. 1978 Smithetal. 1989). 

Effective material coefficients for the hydrophone application of 1-3 composite (Smith 1983) could be estimated in isostress/isostrain approximation as a function of the ceramic volume content v... 

Effective material properties could be easily calculated using the isostress/isostrain approximation (see parallel connection of phases in Eqs.(7.21), (7.22), and (7.23)). More complicated estimates include also non-homogeneous stress/strain distribution over each phase (Cao et al. 1993). Effective piezoelectric coefficient depends on the aspect ratio (i.e. on the ratio of ID-period length vs. composite thickness). It is much smaller than ceramic s J33 for low ceramics content in PZT/epoxy composite (Cao et al. 1993). On the contraiy, the effective uniaxial figure of merit is higher for aspect ratios lower than 1 and... 

Figure 5.20 Shear modulus C44 as a function of shear strain asxo- (O) MC simulations in grand mixed isostress isostrain ensemble (—) representation of small-strain approximation C44 (asxo) = 00 + 02 (asxo) (see Eqs. (5.113) and (5.114)].

The demonstration of equivalence departs from the observation that partition functions in any statistical physical ensemble comply with the general form given in Eq. (B.52) with individual summands as given in Eq. (B.54). Thus, according to th( discussion in Appendix B.4, wo may approximate the grand mixed isostress isostrain ensemble partition functiou x b (2.70a) b> the maximum terms in the sums appearing on the right side of that equation... 

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