A fast and non-degenerate scheme for the evaluation of the 3D fundamental solution and its derivatives for fully anisotropic magneto-electro-elastic materials

A new expression for the fundamental solution is introduced, presenting three relevant characteristics: (i ) it is explicit in terms of the Stroh's eigenvalues, (ii ) it remains well-defined when some Stroh’s eigenvalues are repeated, and (iii ) it is exact. A fast and robust numerical scheme for the evaluation of the fundamental solution and its derivatives developed from double Fourier series representations is presented. The Fourier series representation is possible due to the periodic nature of the solution. The attractiveness of this series solution is that the information of the material properties is contained only in the Fourier coefficients, while the information of the dependence of the evaluation point is contained in simple trigonometric functions. This implies that any order derivatives can be determined by spatial differentiation of the trigonometric functions. Moreover, Fourier coefficients need to be obtained only once for a given material, leading to an efficient methodology

3D coupled multifield magneto-electro-elastic contact modelling

The present work deals with the general contact problem for coupled magneto-electro-elastic materials. Despite of the relevant technological applications, this topic of research has been treated only in some analytical works. But analytical solutions lack the generality of numerical methodologies, being restricted typically to simple geometries, loading conditions, idealized contact conditions and mostly taking into account transversely isotropic material symmetry with the symmetry axis normal to the contact surface. In this work, a numerical procedure for the three-dimensional frictional contact modelling of anisotropic coupled magneto-electro-elastic materials in presence of both electric and magnetic fields is presented for the first time. An orthotropic frictional law is considered, so anisotropy is present both in the bulk and in the surface. The methodology uses the boundary element method with explicit evaluation of the fundamental solutions in order to compute the magneto-electro-elastic influence coefficients. The contact model is based on an augmented Lagrangian formulation and it uses an iterative Uzawa scheme of resolution. Conducting, semi-conducting and insulated electric and/or magnetic indentation conditions, as well as orthotropic frictional contact conditions are considered. The methodology is validated by comparison with benchmark analytical solutions. Then, additional exploration examples are presented and discussed in detail, revealing that magneto-electric material coupling, conductivity contact conditions lead to a significant effect on the indentation force and contact pressure distributions. The influence of friction in electric and magnetic potential responses has been also proved to be very significant. Moreover, tangential loads exhibit an important influence both on the maximum values of the electric and magnetic potentials as well as on their distributions

A fast and non-degenerate scheme for the evaluation of the 3D fundamental solution and its derivatives for fully anisotropic magneto-electro-elastic materials

A new expression for the fundamental solution is introduced, presenting three relevant characteristics: (i ) it is explicit in terms of the Stroh's eigenvalues, (ii ) it remains well-defined when some Stroh’s eigenvalues are repeated, and (iii ) it is exact. A fast and robust numerical scheme for the evaluation of the fundamental solution and its derivatives developed from double Fourier series representations is presented. The Fourier series representation is possible due to the periodic nature of the solution. The attractiveness of this series solution is that the information of the material properties is contained only in the Fourier coefficients, while the information of the dependence of the evaluation point is contained in simple trigonometric functions. This implies that any order derivatives can be determined by spatial differentiation of the trigonometric functions. Moreover, Fourier coefficients need to be obtained only once for a given material, leading to an efficient methodology