Non-metric connection and metric anomalies in materially uniform elastic solids

TL;DR

This paper introduces a geometric framework for representing metric anomalies in crystalline elastic solids, linking defects and growth to internal stress via a quasi-plastic deformation approach and Weyl geometry.

Contribution

It develops a multiplicative decomposition of deformation gradients that accounts for metric anomalies and dislocations within a unified geometric framework.

Findings

Derived a form of metric anomalies producing zero stress in ideal conditions.

Linked metric anomalies to Weyl geometry and quasi-plastic strain formulations.

Provided a representation for internal stresses caused by defects and growth.

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.