An uncertain thermo-mechanical constitutive model for metals with inherent defects

Obtaining accurate constitutive models for metals has long been a fundamental objective in solid mechanics. However, constitutive models derived from micro-defect analyses inherently involve uncertainties, rendering their development particularly challenging. Moreover, increasingly demanding service environments impose higher performance requirements on these models. To address these challenges, this study proposes a novel uncertain thermo-mechanical constitutive model that explicitly accounts for defect-related uncertainties and enhances the expressive capability of the constitutive framework by incorporating thermal effects as an additional dimension. A multiscale interval neural network architecture is developed to improve the efficiency of uncertainty propagation, with data sets generated through molecular dynamics and crystal plasticity finite element simulations. To further support the multiscale uncertainty-modeling framework, an adaptive constitutive curve segmentation strategy is introduced, enabling the construction of performance envelope surfaces for metallic materials. Finally, the proposed approach is validated through numerical simulations and high-temperature experiments on pure titanium.