Electrostatic theory preserves charges, but allows dipolar excitations. Elasticity theory preserves dipoles, but allows quadrupolar (Eshelby like) plastic events. Charged amorphous granular systems are interesting in their own right; here we focus on their plastic instabilities and examine their mechanical response to external strain and to external electric field, to expose the competition between elasticity and electrostatics. In this paper a generic model is offered, its mechanical instabilities are examined and a theoretical analysis is presented. Plastic instabilities are discussed as saddle-node bifurcations that can be fully understood in terms of eigenvalues and eigenfunctions of the relevant Hessian matrix. This system exhibits moduli that describe how electric polarization and stress are influenced by strain and electric field. Theoretical expression for these moduli are offered and compared to the measurements in numerical simulations.

中文翻译：

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带电颗粒系统中的塑料不稳定性：弹性和静电之间的竞争

静电理论保留电荷，但允许偶极激发。弹性理论保留了偶极子，但允许四极（类似于埃舍尔比）塑性事件。带电的无定形颗粒系统本身就很有趣。在这里，我们关注它们的塑性不稳定性，并检查它们对外部应变和外部电场的机械响应，以揭示弹性和静电之间的竞争。在本文中，提供了一个通用模型，研究了其机械不稳定性，并进行了理论分析。塑性不稳定性被视为鞍节点分叉，可以根据相关Hessian矩阵的特征值和特征函数完全理解。该系统的模量描述了应变和电场如何影响极化和应力。