关于微极弹性基础
On Micropolar Elastic Foundations
AI总结：
本文提出一种基于应力势函数和独特归一化方法的微极材料弹性基础理论，推导出应力、偶应力反力及恢复刚度的闭式解，并通过双悬臂梁构型验证，为异质材料分析提供了通用框架。
摘要：
异质材料和构造材料的建模构成一项重大挑战，需要先进的均匀化技术。然而，通过应用微极弹性，这一任务的复杂性可以得到显著简化。另一方面，弹性基础理论被广泛应用于断裂力学以及复合材料中分层扩展的分析。本研究旨在融合这两种框架，增强弹性基础理论以适用于表现出微极行为的材料。具体而言，我们提出了一种新的微极材料弹性基础理论，采用应力势函数表述和一种独特的归一化方法。针对此类材料固有的应力反力和偶应力反力以及相关的恢复刚度，推导出了闭式解。通过使用双悬臂梁构型进行验证，确立了所提出理论的有效性。作为本研究的结论，我们通过量化已知表现出微极行为的材料的导出参数，阐明了所发展理论的优点和局限性。将微极弹性融入弹性基础理论，不仅增进了我们对材料响应的理解，还为各种工程应用中异质材料的分析提供了一个通用的框架。
英文摘要：
The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar elasticity. Conversely, elastic foundation theory is widely employed in fracture mechanics and the analysis of delamination propagation in composite materials. This study aims to amalgamate these two frameworks, enhancing the elastic foundation theory to accommodate materials exhibiting micropolar behaviour. Specifically, we present a novel theory of elastic foundation for micropolar materials, employing stress potentials formulation and a unique normalisation approach. Closed-form solutions are derived for stress and couple stress reactions inherent in such materials, along with the associated restoring stiffness. The validity of the proposed theory is established through verification using the double cantilever beam configuration. Concluding our study, we elucidate the benefits and limitations of the developed theory by quantifying the derived parameters for materials known to exhibit micropolar behaviour. This integration of micropolar elasticity into the elastic foundation theory not only enhances our understanding of material responses but also provides a versatile framework for the analysis of heterogeneous materials in various engineering applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
