On the Nonlinear Continuum Theory of Dislocations: A Gauge Field Theoretical Approach
On the Nonlinear Continuum Theory of Dislocations: A Gauge Field Theoretical Approach
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位错的非线性连续体理论：规范场理论方法
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Lazar
中科院分区：
文献类型：
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作者：
E. Agiasofitou;M. Lazar
基于规范理论方法，提出了含连续分布位错的物质体的非线性连续介质理论。首先，我们利用Noether定理导出了对应于物质空间中平移和旋转群的正则守恒律。这些方程给出了正则Eshelby应力张量和正则角动量张量。正则Eshelby应力张量既不是对称的，也不是规范不变的。基于Belinfante-Rosenfeld方法，我们得到了规范不变的Eshelby应力张量，它只能对各向同性材料相对于参考位形对称。也得到了规范不变的角动量张量。规范不变的Eshelby应力张量在弹性和位错部分的分解引起了著名的Peach-Koehler力的推导。
A nonlinear continuum theory of material bodies with continuously distributed dislocations is presented, based on a gauge theoretical approach. Firstly, we derive the canonical conservation laws that correspond to the group of translations and rotations in the material space using Noether’s theorem. These equations give us the canonical Eshelby stress tensor as well as the total canonical angular momentum tensor. The canonical Eshelby stress tensor is neither symmetric nor gauge-invariant. Based on the Belinfante-Rosenfeld procedure, we obtain the gauge-invariant Eshelby stress tensor which can be symmetric relative to the reference configuration only for isotropic materials. The gauge-invariant angular momentum tensor is obtained as well. The decomposition of the gauge-invariant Eshelby stress tensor in an elastic and in a dislocation part gives rise to the derivation of the famous Peach-Koehler force.