A closed-form solution for the 3D steady-state thermoporoelastic field in an infinite transversely isotropic rock weakened by an elliptical crack

Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

“…whose expressions are provided in [38]; ζ i and ρ i are related to the generalized loads and are specified by…”

“…With the help of equation (37) and the definition of f 3 ( z ) and g 3 ( z ) in [38], the expressions of f 3 ( 0 ) and g 3 ( 0 ) can be written as…”

“…Substituting equation (38) into the expression of k in equation ( 32) and taking advantage of the following equations:…”

“…Furthermore, Fabrikant’s potential theory method has been applied to analyze the elliptical crack problem [36] and the obtained complete solution was more concise than that of Kassir and Sih [32]. Recently, the potential theory method [37] has been extended to solve elliptical crack problems in the context of multiphysics [38, 39].…”

Non‐local stress and electric displacement solution of a 3D semi‐permeable rectangular crack in infinite orthotropic piezoelectric materials

“…Recently, 3D fracture behaviors of piezoelectric materials have received concerned under different electrical boundary condition (such as electrically permeable crack condition [10][11][12], the electrically impermeable crack condition [13][14][15] and the electrically semi-permeable condition [3,[16][17][18]). In order to acquire analytical solutions to 3D problems, the shape of crack was generally considered to be rectangular crack [12,[19][20][21], penny crack [22][23][24], elliptical crack [25][26][27]. In previous article, the material properties are considered to be general isotropic or transversely isotropic.…”