An article co-authored by Dr Andrew McBride, Mebratu Fenta & Daya Reddy has been published in Computer Methods in Applied Mechanics and Engineering.

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 dis- continuous 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. 

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An article co-authored by Dr Andrew McBride and Jean-Paul Pelteret, Denis Davydov, Andrew McBride, Duc Khoi Vu & Paul Steinmann has been published in the International Journal for Numerical Methods in Engineering.

In this work a mixed variational formulation to simulate quasi-incompressible electro- or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media.

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