Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and capture some growth phenomena found in Nature, we extend volume growth theory to account for an electro-elasticity coupling. Based on the multiplicative decomposition, we present a general analysis of isotropic growth and pattern formation of electro-elastic solids under external mechanical and electrical fields. As an example, we treat the case of a tubular structure to illustrate an electro-mechanically guided growth affected by axial strain and radial voltage. Our numerical results show that a high voltage can enhance the non-uniformity of the residual stress distribution and induce extensional buckling, while a low voltage can delay the onset of wrinkling shapes and can also generate more complex morphologies. Within a controllable range, axial tensile stretching shows the ability to stabilise the tube and help form more complex 3D patterns, while compressive stretching promotes instability. Both the applied voltage and external axial strain have a significant impact on guiding growth and pattern formation. Our modelling provides a basic tool for analysing the growth of electro-elastic materials, which can be useful for designing a pattern prescription strategy or growth self-assembly in Engineering.

几个实验已经证明了许多生物组织和水凝胶中存在机电效应，以及其对生长，迁移和模式形成的实际影响。在这里，为了模拟这些相互作用并捕获在自然界中发现的一些生长现象，我们扩展了体积增长理论以解释电弹性耦合。基于乘法分解，我们对在外部机械和电场作用下电弹性固体的各向同性生长和图案形成进行了一般分析。例如，我们以管状结构为例，说明受轴向应变和径向电压影响的机电引导生长。我们的数值结果表明，高电压会增强残余应力分布的不均匀性并引起拉伸屈曲，低电压会延迟起皱形状的产生，并且还会生成更复杂的形态。在可控制的范围内，轴向拉伸拉伸显示出稳定管并帮助形成更复杂的3D图案的能力，而压缩拉伸则促进了不稳定性。施加的电压和外部轴向应变都对引导生长和图案形成有重大影响。我们的建模提供了用于分析电弹性材料生长的基本工具，这对于设计模式处方策略或工程中的生长自组装很有用。而压缩拉伸会增加不稳定性。施加的电压和外部轴向应变都对引导生长和图案形成有重大影响。我们的建模提供了用于分析电弹性材料生长的基本工具，这对于设计模式处方策略或工程中的生长自组装很有用。而压缩拉伸会增加不稳定性。施加的电压和外部轴向应变都对引导生长和图案形成有重大影响。我们的建模提供了用于分析电弹性材料生长的基本工具，这对于设计模式处方策略或工程中的生长自组装很有用。