Exact and complete fundamental solutions for penny-shaped crack in an infinite transversely isotropic thermoporoelastic medium: mode I problem

Xiang-Yu LI , J. Wu , W.Q. Chen , Hui-Ying Wang , Z.Q. Zhou

Abstract

This paper examines the problem of a penny-shaped crack in a thermoporoelastic body. On the basis of the recently developed general solutions for thermoporoelasticity, appropriate potentials are suggested and the governing equations are solved in view of the similarity to those for pure elasticity. Exact and closed form fundamental solutions are expressed in terms of elementary functions. The singularity behavior is then discussed. The present solutions are compared with those in literature and an excellent agreement is achieved. Numerical calculations are performed to show the influence of the material parameters upon the distribution of the thermoporoelastic field. Due to its ideal property, the present solution is a natural benchmark to various numerical codes and simplified analyses.

Key Words

thermoporoelasticity; transversely isotropic; fundamental solution; potential theory method; penny-shaped crack

Address

Xiang-Yu LI — School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, P.R. China; UPMC Sisyphe, Boite 105, 4 Place Jussieu, 75252 Paris, Cedex 05, France
J. Wu — Laboratoire d\'Etudes Aerodynamiques, Universite de Poitiers, Bd Marie et Pierre Curie, BP 30179, Teleport 2, Chasseneuil, Cedex, France
W.Q. Chen — Department of Engineering Mechanics, Zhejiang University, Yuquan Campus, Hangzhou 310027, P.R. China
Hui-Ying Wang — E.N.S.M.A., University of Poitiers, B.P., B.P. 109-Chasseneuil du Poitou 86960 Futuroscope, Cedex, France
Z.Q. Zhou — Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL 33124, USA

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