Three-Dimensional Continuum Point Cloud Method for Finite-Strain Thermoelasticity

We present applications of the Continuum Point Cloud Method (CPCM) to three-dimensional, geometrically nonlinear thermoelastic problems. A set of partial differential equations that govern the mechanical and thermal responses of a continuous medium was established by employing the conservation of mass, momentum, and energy, enabling analysis of a body and the interacting thermal field. The partial differential equations for the resulting nonlinear field were directly linearized and discretized using CPCM differential operators, yielding a system of algebraic equations. This system was solved incrementally using the Newton–Raphson approach. Performance of the CPCM for a coupled thermomechanical Neo-Hookean model was assessed through numerical examples. Holding one field fixed while solving for the other allowed kinematic quantities computed in the previous phase to be reused, thereby circumventing the need to explicitly recompute differential operators, with observed linear-to-superlinear convergence within the mechanical stages. Among the tested tensile configurations, the coarser uniform discretization required fewer mechanical iterations. The computed axial nominal stress differed by approximately 0.8% from the value evaluated using the constitutive relation at the computed Jacobian and prescribed stretch, providing an internal consistency check at the reference-temperature state.