We present Deep Mechanician, a closed loop framework that integrates large language models (LLMs) into constitutive modeling workflows for computational mechanics. A key barrier to trustworthy LLM assisted scientific code generation is the frequent mismatch between fluent text and physics valid, verifiable mathematical structure, particularly for thermodynamically consistent formulations. Deep Mechanician addresses this gap by combining physics embedded curriculum design with an action layer that translates model outputs into executable forms and validates them through neuro symbolic checks. We fine-tune a 70B parameter Llama family model using supervised learning and train at scale with PyTorch Fully Sharded Data Parallel on AMD MI250X GPUs; for evaluation, we run a three stage pipeline over 63 benchmark prompts: model inference, LLM assisted equation extraction, and symbolic and numerical verification of dissipation and free energy conditions derived from the Clausius--Duhem inequality. On this thermodynamic consistency benchmark, the fine tuned model yields substantially higher extraction success (96.8% parseable equations) than the base model (61.9%), and increases the rate of fully passing samples by roughly 5x relative to the base model. These results indicate that physics aware training and verification can convert LLM outputs into measurable scientific artifacts, while exposing remaining failure modes that motivate tighter symbolic constraints and simulation in the loop refinement.