🤖 AI Summary
This study addresses the challenge of accurately calibrating strongly coupled thermomechanical materials under finite strains using only surface experimental data. To this end, the authors propose a full-field calibration framework that leverages boundary displacements, reaction forces, and surface temperature measurements. The forward problem is formulated as a nearly incompressible thermo-hyperelastic system based on a Helmholtz free energy constitutive model, and the inverse problem is solved via PDE-constrained optimization. Innovatively relying solely on surface observables—without requiring volumetric measurements—the method integrates weighted multi-source observational terms and exploits automatic differentiation for efficient computation of adjoint gradients. Validation on both synthetic and real experimental data demonstrates the framework’s ability to accurately identify key coupling parameters, such as thermal expansion and directional contraction coefficients.
📝 Abstract
Calibrating thermomechanical material models from experiments is challenging because deformation, temperature, and force responses are strongly coupled, while measurements are usually restricted to specimen surfaces. We present a full-field calibration framework for coupled finite-strain thermomechanical material models using boundary displacement, reaction-force data, and temperature. The forward model is formulated as a near-incompressible thermo-hyperelastic problem with thermomechanical coupling derived from a Helmholtz free energy, and the inverse problem is posed as a PDE-constrained optimization problem with weighted observation terms for the available data streams.
Reduced gradients are computed with adjoint sensitivities that are obtained by automatic differentiation, enabling gradient-based calibration of nonlinear transient thermomechanical systems. The formulation is first verified on synthetic examples involving uniform thermal preconditioning and localized transient rod contact, where the ground-truth parameters are recovered from full-field measurements and force observations. The same workflow is then applied to experimental thermomechanical data by first calibrating a hyperelastic mechanical baseline from cyclic equibiaxial loading and subsequently identifying thermal expansion and directional shrinkage parameters from surface-temperature and boundary-force histories. The results demonstrate that coupled thermomechanical parameters can be inferred from experimentally accessible surface data without requiring volumetric observations.