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Chapter 7. Environmental, special loading, and manufacturing effects 321

Here, t is the current time, z is some moment of time in the past (0 < z 6 t) at which
stress a(z) acts and C(t - z) is the creep compliance (or creep kernel) depending on
time passing from the moment z to the moment t. Constitutive equation of the
hereditary theory, Eq. (7.31), is illustrated in Fig. 7.13 from which it follows that
the total strain ~(t)is composed of the elastic strain governed by the current stress
a(t) and the viscous strain cv depending on the loading process as if the material
“remembers” this process. Within the frame work of this interpretation, the creep
compliance C(8), where 8 = t - t can be treated as some “memory function” which
should, naturally, be infinitely high at 8 = 0 and tend to zero while 8 --f m as in
Fig. 7.14.

H

Fig. 7.13. Geometric interpretation of the hereditary constitutive theory.

Fig. 7.14. Typical form of the creep compliance function.