Loss of strong ellipticity in non-associative elastoplasticity

Loss of strong ellipticity is considered for clastoplastic solids in the presence of non-associative flow laws. Reference is made to the two comparison solids introduced by Ramiecki and Bruhns. The loss of strong ellipticity is expressed in terms of a critical value of the hardening modulus. In the context of the infinitesimal theory, the loss of strong ellipticity is shown to occur simultaneously in the two comparison solids. Finally, an explicit form for the critical hardening modulus is given and applications are performed for the Drucker- Prager and Schleicher yield functions.