Development of a finite-strain phase-field formulation for thermo-mechanical brittle fracture in Total Lagrangian SPH and its comparative assessment with pseudo-spring model

Abstract

This work presents the development of a finite-strain phase-field formulation for thermo-mechanical brittle fracture within the Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) framework and its comparative assessment with the pseudo-spring model. The proposed formulation extends TLSPH to coupled thermo-mechanical conditions through a multiplicative decomposition of the deformation gradient into elastic and thermal components, enabling consistent treatment of large deformations and temperature-dependent stresses. A hyperbolic regularization of the phase-field evolution equation is adopted to enhance stability and alleviate time-step restrictions inherent in parabolic formulations. Four representative problems are investigated: thermal cracking in a double-notched specimen, expansion-induced fracture in a two-layer cylindrical rock, dynamic crack branching in a notched plate under combined loading, and thermal-shock-induced fracture in ceramics. Results are validated against experimental and numerical data, with quantitative comparisons of crack paths, crack-tip velocity, branching angle, and strain–energy dissipation. The phase-field TLSPH formulation accurately captures continuous and parallel crack evolution under severe thermal gradients, whereas the pseudo-spring model efficiently reproduces multiple small radial cracks in heterogeneous media but exhibits spurious local damage under abrupt thermal shocks. The study establishes a robust particle-based framework for thermo-mechanical fracture and clarifies the relative strengths and limitations of continuum and discrete fracture representations within TLSPH.