A space–time conformal gauge theory is used to develop a unified continuum model describing myriad electromechanical and magnetomechanical coupling effects observed in solids. Using the pseudo-Riemannian Minkowski metric in a finite-deformation setup and exploiting the Lagrangian’s local conformal symmetry, we derive Cauchy–Maxwell (CM) equations that seamlessly combine, for the first time, Cauchy’s elasto-dynamic equations with Maxwell’s equations for electromagnetism. Maxwell’s equations for vacuum are recoverable from our model, which in itself also constitutes a new derivation of these equations. With deformation gradient and material velocity coupled in the Lagrange density, various pseudo-forces appear in the Euler–Lagrange equations. These forces, not identifiable through classical continuum mechanics, should have significance under specific geometric or loading conditions. As a limited illustration on how the CM equations work, we carry out semi-analytical studies, viz. on an infinite body subject to isochoric deformation and a finite membrane under both tensile and transverse loading, considering piezoelectricity and piezomagnetism. Our results show that under specific loading frequencies and tension, electric and magnetic potentials may increase rapidly in some regions of the membrane. Explorations of this nature via the CM model may have implications in future studies on efficient energy harvesting.

时空共形规范理论用于建立一个统一的连续模型，该模型描述了在固体中观察到的多种机电耦合效应。在有限变形设置中使用伪黎曼Minkowski度量并利用Lagrangian局部共形对称性，我们推导出了Cauchy-Maxwell（CM）方程，该方程首次将Cauchy的弹性动力学方程式与Maxwell电磁方程式无缝结合。麦克斯韦的真空方程可以从我们的模型中恢复，它本身也构成了这些方程的新推导。当变形梯度和材料速度与拉格朗日密度耦合时，在欧拉-拉格朗日方程中会出现各种伪力。这些力（通过经典的连续体力学无法识别）在特定的几何或载荷条件下应具有重要意义。作为关于CM方程如何工作的有限说明，我们进行了半分析研究。考虑压电和压磁作用，在等速变形的无限​​物体和受拉和横向载荷作用下的有限膜上的振动。我们的结果表明，在特定的加载频率和张力下，膜某些区域的电势和磁势可能会迅速增加。通过CM模型进行的这种性质的探索可能对未来有关有效能量收集的研究产生影响。考虑压电和压磁作用，在等速变形的无限​​物体和受拉和横向载荷作用下的有限膜上的振动。我们的结果表明，在特定的加载频率和张力下，膜某些区域的电势和磁势可能会迅速增加。通过CM模型进行的这种性质的探索可能会对未来有关有效能量收集的研究产生影响。考虑压电和压磁作用，在等速变形的无限​​物体和受拉和横向载荷作用下的有限膜上的振动。我们的结果表明，在特定的加载频率和张力下，膜某些区域的电势和磁势可能会迅速增加。通过CM模型进行的这种性质的探索可能对未来有关有效能量收集的研究产生影响。