A key challenge for implementation of a circular economy model in manufacturing systems is the functional dependence of downstream processes on upstream byproducts. Design principles provide a framework for mapping goals to solutions by decomposing complex engineering problems into structured sets of requirements to be satisfied and embodied by design parameters and process variables. Large Language Models can computationally represent such textually-described design elements to quantify interconnections between problems, solutions, and processes. We present a Functional Digital Twin concept, powered by AI language modeling and guided by principles of manufacturing systems design, to identify functionally coupled process variables in an industrial symbiosis and automatically push alerts to stakeholders in a circular manufacturing system. Changes in byproduct composition are pushed downstream, and upstream decision-makers are guided to balance satisfying their design requirements with maintaining circularity of the system. The presented method is demonstrated in a case study of bio-based absorbent materials for intended use in disposable sanitary articles developed from byproducts of the agro-food industry.