Analysis of bimaterial singular regions for orthotropic and isotropic materials under thermal loading

F. Ernesto Penado

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A method to formulate an asymptotic elasticity solution for bimaterial singular regions in orthotropic materials is presented for the thermal case. In the vicinity of material and geometric singularities, approximate methods such as finite elements fail to converge and procedures to improve these solutions become necessary. The results presented herein can be used in conjunction with approximate numerical techniques for the determination of stresses and stress intensity factors in composite bonded joints, cracked bimaterial interfaces, or a junction of dissimilar materials under thermal loading. The thermal displacement and stress fields at the tip of a bimaterial wedge are developed by means of eigenfunction expansions including both singular and nonsingular terms. The thermal elasticity solution for isotropic materials as the limiting case of the orthotropic solution is also obtained. The formulations obtained are applicable to bonded joints with interfacial or interlaminar cracks, geometric and material discontinuities, and uniform thermal loading. The detailed formulation presented provides an essential component in the application of finite elements for the determination of generalized intensity factors and stresses in composites, bonded joints, or other dissimilar materials under thermal loading. Formulation results for orthotropic materials, including the limiting case of isotropic materials, are compared with published and closed form results that use different formulations, and excellent agreement is observed. Furthermore, the existence of logarithmic stress singularities of the form (k⋅ΔT⋅lnr) is investigated and discussed.

Original languageEnglish (US)
Article number107527
JournalEngineering Fracture Mechanics
StatePublished - Feb 15 2021


  • Bimaterial interface
  • Composite materials
  • Eigenfunction expansion
  • Orthotropic materials
  • Singular stresses
  • Thermoelasticity

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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