An hp-fem framework for the simulation of electrostrictive and magnetostrictive materials

• Previous work is extended to handle more complex coupled phenomena.
• Electrostriction and magnetostriction of elastic solids.
• Electrostriction and magnetostriction of incompressible Newtonian viscous fluids.
• Newton–Raphson strategy with consistent linearisation and hp finite elements.
• Numerical examples demonstrate the influence of the electromagnetic phenomena.

The physical understanding of coupled electro-magneto-mechanics has long been a topic of particular importance for scientists. However, it is only in more recent times that the computational mechanics community has been involved, due to the particularly demanding nature of these coupled problems. In this paper, we extend our previous work (Gil AJ, Ledger PD. A coupled hp finite element scheme for the solution of two-dimensional electrostrictive materials. Int J Numer Methods Eng 2012;91:1158–1183) to make it possible to capture more complex coupled phenomena, namely electrostriction and magnetostriction of elastic solids and incompressible Newtonian viscous fluids. From the formulation standpoint, a total Cauchy stress tensor is introduced combining the effects of the mechanical deformation and the ponderomotive force and, for the case of conservative materials, the weak form is obtained from the stationary points of a suitable enthalpy energy formulation. In order to ensure accuracy of results hp-finite elements are employed. Moreover, for computational efficiency, the scheme is implemented in a monolithic manner via a Newton–Raphson strategy with consistent linearisation. A series of well known numerical examples are presented to demonstrate the influence of the electromagnetic phenomena when fully coupled with fluid and solid fields.