An unconditionally stable algorithm for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods

An efficient time-stepping algorithm is proposed based on operator-splitting and the space–time discontinuous Galerkin finite element method for problems in the non-classical theory of thermoelasticity. The non-classical theory incorporates three models: the classical theory based on Fourier’s law of heat conduction resulting in a hyperbolic–parabolic coupled system, a non-classical theory of a fully-hyperbolic extension, and a combination of the two. The general problem is split into two contractive sub-problems, namely the mechanical phase and the thermal phase. Each sub-problem is discretized using the space–time discontinuous Galerkin finite element method. The sub-problems are stable which then leads to unconditional stability of the global product algorithm. A number of numerical examples are presented to demonstrate the performance and capability of the method

On the Finite Element Method for Mixed Variational Inequalities Arising in Elastoplasticity

We analyze the finite-element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. An abstract variational inequality, of which the elastoplastic problems are special cases, has been previously introduced and analyzed [B. D. Reddy, Nonlinear Anal., 19 (1992), pp. 1071-1089], and existence and uniqueness results for this problem have been given there. In this contribution the same approach is taken ; that is, finite-element approximations of the abstract variational inequality are analyzed, and the results are then discussed in further detail in the context of the concrete problems. Results on convergence are presented, as are error estimates. Regularization methods are commonly employed in variational inequalities of this kind, in both theoretical and computational investigations. We derive a posteriori error estimates which enable us to determine whether the solution of a regularized problem can be taken as a sufficiently accurate approximation of the solution of the original problem

Special SFSA Plenary Debate: ‘The future of transdisciplinarity: How do we relearn to be human in new ways?’

This Structured Conversation took place among Dr Mamphela Ramphele, Prof. Coleen Vogel and Prof. Daya Reddy. Dr Ramphele was invited to deliver a Plenary address at the Science Forum South Africa 2020. Her address was followed by a response from Prof. Vogel, and the discussion was moderated by Prof. Reddy

Some aspects of dynamic computational modelling of direct current plasma arc phenomena

Direct current arc furnaces see considerable use in modern industrial melting and smelting processes. Pyrometallurgical applications for this type of furnace are wide-ranging, and include commodities such as Ferrochrome, Ferronickel, Cobalt, Zinc, Magnesium, Titanium Dioxide, Platinum-group metals1, and others. Central to the operation of such furnaces is the direct current plasma arc, a sustained high temperature jet of ionised gas which is formed between the end of one or more graphite electrodes and the bath of molten process material below. Passage of electric current through the arc inputs energy and maintains the high temperatures necessary for ionisation via ohmic heating. This is balanced by various mechanisms of energy loss from the arc, including volumetric radiation and convection to the molten bath surface below. Much of this energy is delivered to a localised area directly beneath the arc, making it a very efficient means of heating the process material. Flow of plasma in the arc column is driven strongly by electromagnetic Lorentz forces resulting from the constriction of the conduction channel in the vicinity of the electrode. This constriction causes the arc to draw in gas from the surroundings and accelerate it away from the electrode surface, toward the molten bath below (the Maecker effect2). Much research has been conducted in the area of numerical modelling of arc phenomena, starting with Szekely and co-workers3 and becoming increasingly more sophisticated with the advent of better software, property data, and increased computing capability. However, the majority of arc modelling efforts concentrate on steady-state, axisymmetric systems. While valuable from an engineering standpoint these models are not able to describe any transient behaviour exhibited by the arc, or any evolution of the shape and structure of the arc which breaks the symmetry imposed by the model. Both of these aspects are important for a deeper understanding of direct current plasma arc behaviour

The Stored Energy of Cold Work, Thermal Annealing, and Other Thermodynamic Issues in Single Crystal Plasticity at Small Length Scales

This paper develops a thermodynamically consistent gradient theory of single-crystal plasticity using the principle of virtual power as a paradigm to develop appropriate balance laws for forces and energy. The resulting theory leads to a system of microscopic force balances, one balance for each slip system, and to an energy balance that accounts for power expended during plastic flow via microscopic forces acting in concert with slip-rates and slip-rate gradients. Central to the theory are an internal energy and entropy, plastic in nature, dependent on densities that account for the accumulation of glide dislocations as well as geometrically necessary dislocations – and that, consequently, represent quantities associated with cold work. Our theory allows us to discuss – within the framework of a gradient theory – the fraction of plastic stress-power that goes into heating, as well as the reduction of the dislocation density in a cold-worked material upon subsequent (or concurrent) thermal annealing.National Science Foundation (U.S.) (NSF CMMI Award No.1063626)National Research Foundation (South Africa