Professor Daya Reddy
"Some perspectives on strain-gradient plasticity"
Daya Reddy was born in Port Elizabeth, South Africa. He completed a degree in civil engineering at the University of Cape Town, a Ph.D. degree at Cambridge University in the UK, and a post-doctoral year at University College London. He currently holds the South African Research Chair in Computational Mechanics, in the Department of Mathematics and Applied Mathematics at the University of Cape Town. He served as executive dean of the faculty of science at UCT between 1999 and 2005.
Professor Reddy’s research lies in the domain of mathematical modelling, analysis and simulation in mechanics. He has made significant contributions to the theory of plasticity and to the development of stable and convergent mixed finite element methods. He maintains an active engagement in biomechanics, including research into aspects of cardiovascular mechanics.
Daya Reddy is a recipient of the Award for Distinguished Service from the South African Association for Computational and Applied Mechanics, and the Order of Mapungubwe from the President of South Africa. He is an elected Fellow of the International Association for Computational Mechanics. He has held numerous visiting positions, including those of Visiting Faculty Fellow at the Institute for Computational Sciences and Engineering at the University of Texas at Austin and the Timoshenko Lecturer at Stanford University. In 2012 he received the Georg Forster Research Award from the Alexander von Humboldt Foundation.
The key features of the classical theory of elastoplasticity were well established by the middle of the last century and a major part of subsequent developments have been concerned with algorithmic and computational aspects. As a result, highly efficient approaches are now in place for computational solution of complex problems of plasticity.
More recent activity over the last few decades has focused on understanding and modelling the behaviour of elastic-plastic materials at the meso- and microscales. At these scales the classical theory is inadequate as it does not incorporate a length scale. As a result, features such as size-dependent strengthening and hardening, which are clearly evident in experimental studies, are unable to be captured by a classical approach. This shortcoming has led to various extensions of the classical theory.
A key model has been strain-gradient plasticity, a class of extensions of classical elastoplasticity in which size-dependent effects are accommodated through the introduction of a length scale, and the inclusion of gradients of plastic strain, in the constitutive model. The area has received sustained interest, with multiple theoretical, experimental and computational contributions (see for example  and the references therein). This presentation is devoted firstly to an overview of models of strain-gradient plasticity, together with an illustration of experimental results that have motivated the theoretical developments. The subsequent part of the presentation then turns to a treatment of some of the most commonly used models, including their properties and variational formulations, and some numerical examples with justification for the evidence of strengthening and hardening behaviour, which refer respectively to an increase in the initial yield, and alternatively an increase in the rate of hardening, with increase in length scale.
The final part of the talk deals with approaches to determining approximations to the elastic threshold or first yield, which is not straightforward in what is referred to as the dissipative model of strain-gradient plasticity. Here it is shown how the threshold may be approximated by adopting approaches closely associated with the classical theory of limit analysis, to establish upper and lower bounds to the threshold . Again, various numerical examples are presented to illustrate the quality of the bounds.
 W. Han and B.D. Reddy. Plasticity: Mathematical Theory and Numerical Analysis (Second Edition), Springer, 2013.
 B.D. Reddy and S. Sysala. Bounds on the elastic threshold for problems of dissipative strain-gradient plasticity. J. Mech. Phys. Solids, 143, 104089, 2020.