Federico C. Buroni

Three-dimensional Green's function and its derivative for materials with general anisotropic magneto-electro-elastic coupling

Explicit expressions of Green’s function and its derivative for three-dimensional infinite solids are presented in this paper. The medium is allowed to exhibit a fully magneto-electro-elastic (MEE) coupling and general anisotropic behaviour. In particular, new explicit expressions for the first-order derivative of Green’s function are proposed. The derivation combines extended Stroh formalism, Radon transform and Cauchy’s residue theory. In order to cover mathematical degenerate and non-degenerate materials in the Stroh formalism context, a multiple residue scheme is performed. Expressions are explicit in terms of Stroh’s eigenvalues, this being a feature of special interest in numerical applications such as boundary element methods. As a particular case, simplifications for MEE materials with transversely isotropic symmetry are derived. Details on the implementation and numerical stability of the proposed solutions for degenerate cases are studied.

Unique and Explicit Formulas for Green's Function in Three-Dimensional Anisotropic Linear Elasticity

Unique, explicit, and exact expressions for the firstand second-order derivatives of the three-dimensional Green’s function for general anisotropic materials are presented in this paper. The derived expressions are based on a mixed complex-variable method and are obtained from the solution proposed by Ting and Lee (Ting and Lee, 1997,“The Three-Dimensional Elastostatic Green’s Function for General Anisotropic Linear Elastic Solids,” Q. J. Mech. Appl. Math. 50, pp. 407–426) which has three valuable features. First, it is explicit in terms of Stroh’s eigenvalues pa (a 1⁄4 1; 2; 3) on the oblique plane with normal coincident with the position vector; second, it remains well-defined when some Stroh’s eigenvalues are equal (mathematical degeneracy) or nearly equal (quasi-mathematical degeneracy); and third, they are exact. Therefore, both new proposed solutions inherit these appealing features, being explicit in terms of Stroh’s eigenvalues, simpler, unique, exact and valid independently of the kind of degeneracy involved, as opposed to previous approaches. A study of all possible degenerate cases validate the proposed scheme. [DOI: 10.1115/1.4023627]

Quasistatic Electro-Elastic Contact Modeling Using the Boundary Element Method

A three-dimensional boundary element methodology to study frictionless indentation response of piezoelectric (PE) materials is presented. The boundary element method (BEM) is used in order to compute the electro-elastic influence coeffcients of fully anisotropic piezoelectric solids. The proposed contact formulation is based on the augmented Lagrangian method presented in [33, 34, 35] and makes it possible to consider piezoelectric materials under different mechanical and electrical boundary conditions (i.e. insulating indenter and conducting indenter). The methodology is validated by comparison with theoretical solutions presented in the literature.

Boundary element analysis of the frictionless indentation of piezoelectric films

The boundary element method is used for studying frictionless indentation response of piezoelectric (PE) films under spherical indenter (i.e. sphere) and circular cylindrical indenter (i.e. punch). An augmented Lagrangian formulation is employed to solve PE films of finite thickness under contact conditions. The methodology is validated by comparison with theoretical solutions presented in the literature for the two limiting cases: infinitely thick and infinitely thin PE films closed-form solutions. Furthermore, the formulation is applied to compute the indentation response of those cases in between.