Flow relations and yield functions for dissipative strain-gradient plasticity

Carstensen, C., Ebobisse, F., McBride, A. T. , Reddy, B. D. and Steinmann, P. (2017) Flow relations and yield functions for dissipative strain-gradient plasticity. In: dell'Isola, F., Sofonea, M. and Steigmann, D. (eds.) Mathematical Modelling in Solid Mechanics. Series: Advanced structured materials (69). Springer Singapore, pp. 31-42. ISBN 9789811037634 (doi: 10.1007/978-981-10-3764-1_3)

Abstract

In this work we carry out a theoretical investigation of a dissipative model of rate-independent strain-gradient plasticity. The work builds on the investigation in [1], which in turn was inspired by the investigations in [4] of responses to non-proportional loading in the form of surface passivation. We recall the global nature of the flow relation when expressed in terms of the Cauchy stress and dissipation function. We highlight the difficulties encountered in attempts to obtain dual forms of the flow relation and associated yield functions, for the continuous and discrete problems, and derive upper bounds on the global yield function.

• Item Type: Book Sections
• Status: Published
• Glasgow Author(s) Enlighten ID: McBride, Professor Andrew and Steinmann, Professor Paul
• Authors: Carstensen, C., Ebobisse, F., McBride, A. T., Reddy, B. D., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Publisher: Springer Singapore
• ISSN: 1869-8433
• ISBN: 9789811037634