A study by researchers from the International Center for Numerical Methods in Engineering (CIMNE) and Swansea University has concluded that constitutive models can satisfy the first and second laws of thermodynamics while being incompatible with the third. The research, published in the scientific journal Journal of the Mechanics and Physics of Solids, analyzes the influence of specific heat on the mathematical description of materials subjected to extreme deformations and temperature changes.
The article, titled Finite strain thermoelasticity and the Third Law of thermodynamics, is authored by Professor Javier Bonet, CEO and researcher at CIMNE, and Dr. Antonio J. Gil, a professor at the Zienkiewicz Institute for Modelling, Data and AI at Swansea University. Constitutive models are fundamental for simulating complex thermomechanical behaviors, as they describe how materials respond to external conditions such as stress, strain, and temperature.
Bonet and Gil mathematically demonstrate that common assumptions about constant specific heat or heat dependent only on temperature impose significant restrictions when considering the third law of thermodynamics, potentially compromising the models' coherence. The third law states that entropy tends to zero as temperature approaches absolute zero (0 K), but conventional models with positive, constant specific heat predict entropy tending towards negative infinity.
"The third law imposes constraints on thermomechanical coupling that conventional constitutive models do not always account for," explains Bonet. As an alternative, the researchers propose an analytical constitutive framework where specific heat is expressed as a multiplicative combination of temperature and deformation functions. This formulation complies with the third law and maintains consistency with the first and second laws, also incorporating polyconvexity for model stability.
These findings could have implications for simulating materials like rubber-like substances, with applications in sectors such as automotive, construction, and health. They also develop formulations to represent thermal softening and melting, relevant for aerospace engineering, nuclear energy, and additive manufacturing. Bonet notes that a more complete thermodynamic description would improve the physical coherence of the models.
Although the research is theoretical and requires experimental validation, it lays the groundwork for future investigations into material simulation, with potential repercussions in advanced computing, industrial processes, and clean energy.
