AI 中文总结
本文构建满足量纲一致等三项要求的张量物理分量归一化框架，将其应用于非线性弹性与非弹性领域，得出物理分量既非内禀也不唯一的结论。
AI 中文摘要
物理分量广泛应用于力学与数学物理领域，可消除曲线坐标系中固有的依赖坐标的标度，得到具有一致物理量纲的分量。在正交坐标系中，物理分量通过归一化坐标标架与余标架构造；但在一般坐标系中，其构造需要额外的非平凡选择。本文通过坐标标架的正交归一化，提取任意黎曼流形上任意张量的物理分量，进一步构建区分三项要求的通用归一化框架：量纲一致性、对偶标架-余标架兼容性、单位归一化。研究表明，仅量纲一致性会为逆变与协变分量留下独立的一般线性规范自由度；进一步要求对偶兼容性会将其锁定为单一一般线性规范；当且仅当对偶兼容的标架与余标架均为单位长度时，二者正交归一。因此，正交归一变换的选择成为满足三项要求的唯一物理分量框架。将该框架应用于非线性弹性与非弹性（广义指涉及内部畸变的本构响应，本文研究滞弹性、黏弹性、黏滞滞弹性），考察变形梯度、非弹性畸变、应变度量与应力张量，最终指出物理分量既非内禀也不唯一。
英文摘要
Widely used in mechanics and mathematical physics, physical components remove the inherent coordinate-dependent scaling in curvilinear coordinates, yielding components of consistent physical dimension. In orthogonal coordinates, they are constructed by normalizing the coordinate frame and coframe; in general coordinates, however, their construction requires additional, non-trivial choices. In this paper, we extract physical components of arbitrary tensors on arbitrary Riemannian manifolds by orthonormalization of the coordinate frame. We further formulate a general normalization framework distinguishing three requirements: dimensional consistency, dual frame-coframe compatibility, and unit normalization. We show that dimensional consistency alone leaves independent general linear gauge freedoms for the contravariant and covariant components. Further requiring dual compatibility locks these into a single general linear gauge; a dual-compatible frame and coframe are both of unit length if and only if they are orthonormal. Thus, the choice of orthonormal transformations emerges as the only physical-components framework that satisfies all three requirements. We apply this framework to nonlinear elasticity and inelasticity, referring broadly to constitutive responses involving internal distortions, of which we study anelasticity, viscoelasticity, and visco-anelasticity. We examine the deformation gradient, inelastic distortions, strain measures, and stress tensors. We conclude by arguing that physical components remain neither intrinsic nor unique.
