A formulation based on Flory’s decomposition for thermomechanical analysis of thermo-elastic solids

Resumo

In several engineering fields, thermomechanical analysis is crucial for the analysis of materials and structures, due to the importance of considering the degradation of mechanical properties and behavior under significant thermal loads. Examples include fire problems, ballistics, and metal forming. In these high-temperature situations, large displacements and strains of bodies are frequently observed, exhibiting an intrinsic geometric and physical nonlinear behavior. Given the importance of the constitutive model for the proper simulation of material behavior, an alternative thermo-elastic constitutive model was developed and implemented in a proprietary computational program. The mechanical simulation is performed through a computational code developed using the Finite Element Method as the numerical solution strategy, which intrinsically considers the exact geometric nonlinearity in its formulations, and triangular-based prismatic solid finite elements were used to discretize the domain of analyzed bodies into approximate subdomains. Initially, the Saint-Venant-Kirchhoff constitutive model was used to define the stress-strain relationship of the materials. However, this model is only suitable for small-strain simulations. To overcome this limitation, a second hyperelastic constitutive model – a combination of the Rivlin-Saunders and Hartmann-Neff formulations – was implemented. This model is well-suited for large-strain analysis and was developed using the Flory’s multiplicative decomposition of the deformation gradient tensor into volumetric and isochoric components. The thermal analysis code was developed from the transient heat conduction differential equation. The thermomechanical model was built using one-way explicit coupling, also referred to as the uncoupled thermomechanical model. The combination of mentioned implementations resulted in the alternative thermo-elastic model, which is appropriate for large strain problems. The developed computational code was successfully validated by comparing it with examples from the scientific literature. It was found that the computational code can satisfactorily simulate the thermo-elastic behavior of structures subjected to thermal variations.