Fracture Simulation of Nanostructured Porous Polymers Using a Boundary Element Method With Fractional Heat Conduction and Pyrolysis Coupling

ABSTRACT This paper introduces a new boundary element formulation to simulate fracture response in nanostructured porous polymer composites exposed to extreme heat environments. The model integrates three coupled physical mechanisms: (i) time‐fractional heat conduction by multiterm Caputo derivatives to represent thermal memory effects, (ii) pyrolysis‐driven internal heating by temperature‐dependent chemical kinetics, and (iii) size‐dependent thermoelasticity by consistent couple‐stress theory to account for microstructural mechanical responses. The analysis is performed in the Laplace domain for efficient solution of the time‐dependent and nonlocal field equations and is numerically inverted to derive the transient mechanical and thermal responses. Fracture is assessed by direct calculation of Mode I and Mode II stress intensity factors (SIFs) and path‐independent J‐integral, derived from near‐tip BEM fields. The model accurately captures the generation of thermal gradients, deformation, and crack‐driving stresses with impulsive heating, as verified by comparison with analytical, finite difference, and finite element solutions. The proposed method provides an effective computational scheme for modeling thermally induced fracture in advanced polymer composites, particularly for aerospace and high‐temperature structural applications.