Smart Polymer‐Integrated IoT Systems: A Mathematical Framework for Real‐Time Sensing and Adaptive Material Behavior

ABSTRACT New frontiers of innovative material application based on the convergence of the Internet of Things and polymer science have come from real‐time sensing, adaptability, and response to environmental changes. This work presents a novel mathematical framework for integrating IoT‐enabled sensors with polymer‐based material to improve dynamic material properties like self‐healing and shape memory and to improve its conductivity properties. The work is based on modelling and optimizing the interaction of polymeric materials with IoT‐driven sensor networks utilizing advanced differential equations, machine learning algorithms and finite element analysis to assess the predictive behavior. Embedded microcontrollers and wireless sensor networks (WSNs) are employed to collect, process, and analyze polymeric substrates' data for real‐time monitoring of mechanical, thermal, and electrical properties. We also introduce a computational model of polymer responses in different environments based on a mathematical basis for the prediction and optimization performance. This work demonstrates the effectiveness of IoT‐assisted polymer systems for enhancing material intelligence with today's common approaches. It has potential technology applications in biomedical engineering, aerospace, and structural health monitoring. By creating this methodology and offering it as a quantitative approach to the interaction of polymer science and IoT, this study further contributes to an interdisciplinary field of innovative materials.