This paper investigates a hygrothermoelastic material containing a penny-shaped crack. The purpose is to determine the effect of coupled moisture transfer and heat conduction on local displacements and stresses near the crack. The crack is modeled as a soft inclusion within the material, with either known moisture content and temperature or prescribed moisture transfer and heat flux on the crack faces. The governing equations for temperature, moisture content, and elastic displacements are solved using the dual integral equation method. Closed-form solutions for the problem are obtained. The analytical derivation presented herein is relatively concise and mathematically compact. These closed-form solutions provide a benchmark for rapid evaluation of the material performance and validation of other theoretical and numerical approaches in fracture mechanics under hygrothermal loading conditions. To demonstrate the application of the proposed solutions, a case study regarding a T300/5208 graphite/epoxy composite material is presented.
Li et al. (2026) studied this question.