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Plenary Lecture

Plenary 3

Daya Reddy (U Cape Town): Some variational and computational aspects of problems for gradient plasticity

Monday, April 18, 2011, 14:15 – 15:00

There has been a proliferation of gradient theories of plasticity over the last decade. These generally address the inability of classical theories to account for size effects such as grain size and lattice defects at the microscale level. Of particular interest are those gradient theories that incorporate higher-order stresses or microstresses which are conjugate to plastic strain gradients. With regard to these theories there has been extensive theoretical and computational work aimed at gaining a better understanding of their physical underpinnings and their relationships to each other. Nevertheless there remain open questions: these concern, for example, the conditions under which different formulations of gradient theories are well-posed, and also the manner in which computational approximations can be obtained efficiently and accurately. These questions are especially pertinent in the rate-independent case though they apply equally to viscoplastic formulations.

The purpose of my presentation is, first, to review some of the key gradient theories and to present a variational framework which is sufficiently general to include a broad class of theories as special cases. I will use the analysis of these formulations to shed light on the implications of adopting various alternative forms for defect energies, and will show how the variational framework allows for the construction of computational algorithms that are stable, accurate and efficient. Theories for both single- and polycrystal plasticity are considered.