Elastoplastic material, stress-strain relationship

Fig. 2.14 Schematic view of the stress-strain relationship for an elastoplastic material. The symbols Yp and yr denote the yield strain, the plastic strain and the failure strain, respectively. The same notation is used for the stress a.

Besides linear viscoelastic behavior, elastoplastic behavior is also often encountered for food products. In Fig. 2.14, the stress-strain behavior of an elastoplastic material is shown schematically. Because the stress-strain relationship is not linear and the strain does not recover if the yield stress is exceeded, the equations to describe this behavior are much more complicated. 

In contrast to the simplicity of elastic deformation, plastic deformation occurs in diverse ways. Figure 1.9 illustrates the stress-strain curves for two typical elastoplastic materials (hardened metal and polymer). Both materials show similar linear relationships between stress and strain for the elastic deformation (i.e., before yield strength) but quite different correlations in the yielding processes before fracture. 

Elastoplastic materials Elastoplastic materials deform elastically for small strains, but start to deform plastically (permanently) for larger ones. In the small-strain regime, this behavior may be captured by writing the total strain as the sum of elastic and plastic parts (i.e., e = e -I- gP, where e and gP are the elastic and plastic strains, respectively). The stress in the material is generally assumed to depend on the elastic strain only (not on the plastic strain or the strain rate), and hence, no unique functional relationship exists between stress and strain. This fact also implies that energy is dissipated during plastic deformation. The point at which the material starts to deform plastically (the yield locus) is usually specified via a yield condition, which for one-dimensional plasticity may be stated as (38)... 

---