非均匀超弹性的等价群
Equivalence Groups of Inhomogeneous Hyperelasticity
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中文总结 AI 辅助
本文研究非均匀超弹性固体运动场方程的等价群，推导无穷小生成元并施加约束以保证变换后方程有应变能函数，探讨了均匀/非均匀及各向同性/各向异性材料间的映射，并用实例说明。
中文摘要 AI 辅助
研究了非均匀超弹性固体任意运动场方程所关联的等价群。推导了无穷小生成元（即与等价群相关的等矢量场的分量）的显式形式。建立了对等矢量分量的附加约束，以确保变换后的方程由应变能函数支持。考察了不同性质材料方程之间可能的映射。不仅研究了均匀与非均匀超弹性方程之间的变换，还研究了各向同性与各向异性材料的方程和应变能函数之间的变换。结果通过多个示例加以说明。
英文摘要
Equivalence groups associated with the field equations of arbitrary motions of inhomogeneous hyperelastic solids are investigated. The explicit forms of the infinitesimal generators, namely the components of the isovector field associated with the equivalence groups are derived. Additional constraints on the isovector components are established to ensure that the transformed equations are supported by a strain energy function. Possible mappings between the equations of materials with different properties are examined. Not only the transformations between homogeneous and inhomogeneous hyperelasticity equations, but also the transformations between the equations and strain energy functions of isotropic and anisotropic materials are investigated. The results are illustrated with several examples.
发表机构
- Istanbul Technical University（伊斯坦布尔理工大学）
机构由 AI 辅助整理，请以论文原文为准。
