Title: Non-metric connection and metric anomalies in materially uniform elastic solids Show Chinese title

Title: 非度量联络与物质均匀弹性固体中的度量异常

Abstract: Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By emphasizing the geometric nature of such anomalies we seek their representations for materially uniform crystalline elastic solids. In particular, we introduce a quasi-plastic deformation framework where the multiplicative decomposition of the total deformation gradient into an elastic and a plastic deformation is established such that the plastic deformation is further decomposed multiplicatively in terms of a deformation due to dislocations and another due to metric anomalies. We discuss our work in the context of quasi-plastic strain formulation and Weyl geometry. We also derive a general form of metric anomalies which yield a zero stress field in the absence of other inhomogeneities and any external sources of stress. Show Chinese abstract

Abstract: 由点缺陷（内在的间隙原子、空位、点堆垛层错）、热变形、生物生长等因素引起的度量异常是材料非均匀性和内应力的已知来源。 通过强调这些异常的几何性质，我们寻求它们在均匀晶体弹性固体中的表示方法。 特别是，我们引入了一种拟塑性变形框架，在其中总变形梯度被分解为弹性和塑性变形，而塑性变形进一步以位错引起的变形和度量异常引起的变形的乘积形式分解。 我们在拟塑性应变公式化和韦尔几何的背景下讨论我们的工作。 我们还推导出了一种度量异常的一般形式，在没有其他不均匀性和任何外部应力源的情况下，该异常会产生零应力场。