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Strain Gradient Plasticity
In physics and materials science, plasticity describes the change in the shape or size of a material undergoing non-
reversible changes in response to an applied force or change in temperature. Perfect plasticity is a property of materials
to undergo irreversible deformation without any increase in stresses or loads. Plastic materials with hardening require
increasingly higher stresses in order for further plastic deformation to occur. Generally plastic deformation is also
dependent on the speed of the deformation; such materials are said to deform visco-plastically.
Because the constitutive relations of classical plasticity
do not possess a natural length scale, they are therefore
unable to account for size effects. Gradient theories
represent a popular and well-established extension
which allows for physically relevant length scales to be
introduced.
Current research in this area is devoted to problems of
single- and polycrystal plasticity. A crystal has atoms
in a near-perfect arrangement where a ‘pattern’ is
repeated in regular intervals, whereas a polycrystal is
composed of many microscopic crystals. However, the
arrangement of atoms or molecules in most crystalline
materials is not perfect. The regular patterns are
interrupted by crystallographic defects. One focus has
been on the development of variational formulations,
where the role of particular choices of defect energy
and of dissipation functions has been investigated.
Also of interest are new hardening relations.
Another area of research is on modelling the influence
of the grain boundary on the overall response of the
continuum. A grain boundary is the interface between two
crystallites in a polycrystalline material. Grain boundaries
are defects in the crystal structure, and tend to decrease
the electrical and thermal conductivity of the material.
Computational work has been concerned with the
development and implementation of finite element
approximations for visco-plastic crystal problems involving
large deformations, and in which both energetic and
dissipative microstresses are present. Both single crystals
and ensembles of crystal grains are considered.
This large, multi-institution project, led by Professor
Daya Reddy, spans a network of five institutions across
the globe, and has already produced one master’s
Perfect plasticity is a property of
materials to undergo irreversible
deformation without any increase
in stresses or loads.
student. Two doctoral students and a second master’s
student are currently engaged in research in this
area, while Professor Reddy’s collaborators include
Dr Francois Ebobisse and Dr Andrew McBride from
UCT, Professor Swantje Bargmann (Technische
Universität Hamburg-Harburg), Emeritus Professor
Morton Gurtin (Carnegie-Mellon University), Dr
Britta Hirschberger (Leibniz Universität Hannover),
Professor Paul Steinmann (Friedrich-Alexander-
Universität Erlangen-Nürnberg) and Professor Ali
Javili (Friedrich-Alexander-Universität Erlangen-
Nürnberg).
Research Project