Loading and Unloading of Hypo‐Elastic Materials with Internal Variable

The work‐hardening and the hysteresis of two special hypo‐elastic materials with an internal variable are analyzed. The materials have the modified Huber‐Mises yield criterion and the modified Tresca yield criterion as their singularity relations. The loading and the unloading responses in simple shear and in uniaxial stress extension are illustrated. The phenomenon of the rounding of the corner of the stress‐strain reloading curve is shown, and the loading‐unloading cycles show remarkable work‐hardening character. A fracture law for a material is proposed on the basis of the concept that the non‐decreasing internal variable has an ultimate intrinsic value.