Mean Stress and Mean Strain

Mean Stress and Mean Strain Подпись: £ Подпись: AL ' L Подпись: (8.1.1)

Whatever the nature of the foregoing elements, we can define the mean uniaxial stress as the load per unit representative area of the cross section, and the mean strain of each element and the mean strain of the whole coupling as the elongation per unit initial length, i. e., w’e set, in general,

where A is the representative area.

Подпись: є = Подпись: (L,£,U + L2Sh2)/(L -I- In) - і for hardening (I,esi + Ыm)Кіл + Рг) - Єи Т 5(^1 - £ut) for softening Подпись: (8.1.2)

The advantage of this representation is that the hardening portions of the (mean) stress-strain curves are identical for each of the elements and for the series coupling. This is not so, however, for the softening part of the curves. Let £h be the mean strain on the hardening branch of the curve for any one of the two elements. Further, let eu be the strain at the same stress level on the unloading branch emanating from the peak, and let es be the strain at the same stress level on the softening part of the curve, as indicated in Fig. 8.1.3c-d. The curves in this figure are the same as those in Fig. 8.1.1, with a change of scale. The resulting (mean) stress-strain curve is shown in Fig. 8.1.3d, in which the mean strain at the given stress level is given by

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