Natural materials achieve adaptive behavior through hierarchical organization and coupled mechanisms across scales. Their translation into engineering, however, remains largely heuristic. What is missing is a formal translation framework that carries biological design logic into engineered realization while preserving physical consistency across levels of abstraction. Here we present a category theoretic compositional framework for verified nature-derived design. The framework defines a category of stimulus response dynamical systems with natural and artificial subcategories. It introduces a structure preserving implementation functor from biological mechanics to engineered systems. It also formalizes a machine agnostic specification layer that links behavioral intent to executable fabrication programs. We instantiate the framework on the hygromorphic pinecone hierarchy as a representative biological case. We implement the full pipeline in Grasshopper, where formal specifications are translated into modular parametric scripts that preserve the compositional structure of the model. The resulting designs are fabricated by fused filament fabrication, evaluated experimentally, and tested against model predictions derived from the pipeline. The current implementation generates four actuator classes spanning two stimulus types and two kinematic responses. One actuator arises purely through composition from previously validated components, without additional manual derivation. The results show that compositionality can function not just as a descriptive language, but as a generative and system level verifiable method for mechanical material design. More broadly, the work provides a concrete route for embedding formal multiscale reasoning within increasingly computational, generative, and physics-driven design workflows.

翻译：天然材料通过层级组织结构和跨尺度耦合机制实现自适应行为。然而，将其工程化转化仍主要依赖启发式方法。当前缺失的是能将生物设计逻辑转化为工程实现、同时保持跨抽象层级物理一致性的形式化转化框架。本文提出了一个经范畴论形式化构建的、源自自然的设计验证框架。该框架定义了包含自然子范畴与人工子范畴的刺激-响应动力系统范畴，引入了从生物力学到工程系统的结构保持实现函子，并形式化了联结行为意图与可执行制造程序的机器无关规范层。我们以湿热形态松果层级结构为代表性生物案例对该框架进行实例化，并在Grasshopper平台上实现完整工作流——形式化规范被转化为保持模型组合结构的模块化参数化脚本。最终设计通过熔融沉积成型制造、实验评估，并与工作流推导的模型预测进行对比验证。当前实现生成了跨越两种刺激类型与两种运动学响应的四类致动器，其中一类致动器完全通过已有验证组件的组合推导得出，无需额外人工推导。研究结果表明，组合性不仅可作为描述性语言，更能成为兼具生成性与系统级可验证性的机械材料设计方法。更广泛而言，本工作为将形式化多尺度推理嵌入日益计算化、生成化与物理驱动的设计流程提供了具体路径。