Transformer neural networks show promising capabilities, in particular for uses in materials analysis, design, and manufacturing, including their capacity to work effectively with human language, symbols, code, and numerical data. Here, we explore the use of large language models (LLMs) as a tool that can support engineering analysis of materials, applied to retrieving key information about subject areas, developing research hypotheses, discovery of mechanistic relationships across disparate areas of knowledge, and writing and executing simulation codes for active knowledge generation based on physical ground truths. Moreover, when used as sets of AI agents with specific features, capabilities, and instructions, LLMs can provide powerful problem-solution strategies for applications in analysis and design problems. Our experiments focus on using a fine-tuned model, MechGPT, developed based on training data in the mechanics of materials domain. We first affirm how fine-tuning endows LLMs with a reasonable understanding of subject area knowledge. However, when queried outside the context of learned matter, LLMs can have difficulty recalling correct information and may hallucinate. We show how this can be addressed using retrievalaugmented Ontological Knowledge Graph strategies. The graph-based strategy helps us not only to discern how the model understands what concepts are important but also how they are related, which significantly improves generative performance and also naturally allows for injection of new and augmented data sources into generative AI algorithms. We find that the additional feature of relatedness provides advantages over regular retrieval augmentation approaches and not only improves LLM performance but also provides mechanistic insights for exploration of a material design process. Illustrated for a use case of relating distinct areas of knowledge, here, music and proteins, such strategies can also provide an interpretable graph structure with rich information at the node, edge, and subgraph level that provides specific insights into mechanisms and relationships. We discuss other approaches to improve generative qualities, including nonlinear sampling strategies and agent-based modeling that offer enhancements over singleshot generations, whereby LLMs are used to both generate content and assess content against an objective target. Examples provided include complex question answering, code generation, and execution in the context of automated force-field development from actively learned density functional theory (DFT) modeling and data analysis.