References
179
Fig. 13.5 Ideal
elastic–plastic body
Fig. 13.6 Material with
linear strengthening
between stresses and strains. Figure 13.6 shows that the same stress σ A can
correspond to different strains ε A , ε B , or ε C . Everything depends on how we
reached the stress σ A . The strain ε A is obtained during the elastic work of the
material and is unambiguously defined by the stress σ A . The strains ε B and ε C are
obtained by the elongation of the material beyond the yield strength and further
unloading along the trajectories BB and CC to the stress σ A . As we see, each of
these cases corresponds to their own strain values; however, the stress is the same.
In this connection, the concept of “loading history” is introduced in the mechanics
of non-elastic deformations. They also say that materials have memory.
References
1. P. Bridzhmen, Issledovaniya bol’shikh plasticheskikh deformatsii i razryva : Vliyanie vysokogo
gidrostaticheskogo davleniya na mekhanicheskie svoistva materialov [Studies of large plastic
deformations and impact of high hydrostatic pressure on the mechanical properties of
materials] (Izdatel’skaya gruppa URSS Publ., Moskow, 2010)
179
Fig. 13.5 Ideal
elastic–plastic body
Fig. 13.6 Material with
linear strengthening
between stresses and strains. Figure 13.6 shows that the same stress σ A can
correspond to different strains ε A , ε B , or ε C . Everything depends on how we
reached the stress σ A . The strain ε A is obtained during the elastic work of the
material and is unambiguously defined by the stress σ A . The strains ε B and ε C are
obtained by the elongation of the material beyond the yield strength and further
unloading along the trajectories BB and CC to the stress σ A . As we see, each of
these cases corresponds to their own strain values; however, the stress is the same.
In this connection, the concept of “loading history” is introduced in the mechanics
of non-elastic deformations. They also say that materials have memory.
References
1. P. Bridzhmen, Issledovaniya bol’shikh plasticheskikh deformatsii i razryva : Vliyanie vysokogo
gidrostaticheskogo davleniya na mekhanicheskie svoistva materialov [Studies of large plastic
deformations and impact of high hydrostatic pressure on the mechanical properties of
materials] (Izdatel’skaya gruppa URSS Publ., Moskow, 2010)