Linear Elastic Solid with Linear Strain Hardening
Linear elastic, plastic with linear strain hardening material model is defined by a combination of the two precedent models. This behaviour is also known as bilinear, and it could be representative to describe the elasto-plastic behaviour of many materials.
This behaviour is defined by an initial range in the curve where linear elastic behaviour is assumed (so this part is described by an elastic modulus an a Poisson's ratio), until yield stress σ0 is reached. From this point on, the plastic deformation follows a hardening law described by the slope of the curve in the second part of the curve (&deltaE), being 0 < &delta < 1.
The mechanical model that represents this behaviour is a serial connection of a spring with constant E1 (linear elastic behaviour) and a second component which controls the second part of the curve, being a parallel connection of a spring E2 and a friction plane σ0.
The relationships E=E1 and &deltaE=E1E2(E1+E2) can be obtained by parameter identification between the material law and the mechanical model. So, the general material law is as stated