Two-Dimensional Static Problems: Stroh Formalism
The two-dimensional configuration has had its unique position in boundary value problems since people developed various analytical concepts and procedures from it. The focus of the present chapter is to introduce the Stroh formalism in the two-dimensional piezoelectric boundary value problem. Historically, the scheme was originally proposed by Eshelby et al.  for linear elasticity in anisotropic solids. The formulation has been considered to be elegant and neat for studies of dislocation , wave propagation , and interfacial cracks . Then, the scheme was extended to the piezoelectric solids which are intrinsically anisotropic. Barnett and Lothe  extended this formalism to the piezoelectricity when a dislocation in an infinite piezoelectric medium was studied. Most important configurations of boundary value problems in piezoelectricity via Stroh formalism were studied in the 1990s after their corresponding problems in anisotropic elasticity had been worked out in the 1980s and early 1990s.
KeywordsStress Intensity Factor Piezoelectric Material Anisotropic Elasticity Hilbert Problem Elliptic Inclusion
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