On Force Interactions for Electrodynamics-Like Theories

Reuven Segev¹^*, Vladimir Gol'dshtein²

¹ Ben-Gurion University of the Negev, Department of Mechanical Engineering, Beer-Sheva, Israel; ² Ben-Gurion University of the Negev, Department of Mathematics, Beer-Sheva, Israel

Constitutive Foundations & Mathematical Material Modeling · C223

Tuesday, 1 September 2026, 14:25–14:50 · Chair: Martin Horák

Keywords: electrodynamics, field theory, geometric continuum mechanics, stress, potential energy, forces

In earlier works (see [1, 2, 3]), a framework for premetric $p$ -form electrodynamics is proposed. Independently of particular constitutive relations, the generalized Maxwell equations are derived as a special case of stress theory in geometric continuum mechanics. In the proposed setting, generalized velocities are modeled mathematically as $p$ -differential forms, interpreted physically as potential forms. In addition, for the expression of the mechanical power/potential energy, the stress field is assumed to have a particularly simple form. In this work (see [4]), we extend the theory to propose expressions for the force and stress interactions acting on a charged/magnetized body due to external electromagnetic fields. The expression for the force distribution, viewed as a linear functional of virtual velocity fields, is obtained by computing the rate of change of the proposed potential energy under a virtual motion of the region. The expressions we obtain differ from those appearing in the standard references. For example, in the case of electrostatics in $ℝ^{3}$ , letting $F$ , $w$ , $D$ , and $E$ , denote the force functional, virtual velocity of the material, electric displacement, and the electric field, respectively, the force functional is of the form $F (w) = \int_{Ω} D_{j, j} E_{i} w_{i} d V + \int_{Ω} D_{j} E_{i, j} w_{i} d V + \int_{Ω} D_{j} E_{i} w_{i, j} d V .$ It is noted that the last integral includes stress-like and torque-like interactions. The cases of electrostatics and magnetostatics in $ℝ^{3}$ are presented as examples.

References

R. Segev, Continuum mechanics, stresses, currents and electrodynamics, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2066):20150174, 2016, https://doi.org/10.1098/rsta.2015.0174.
R. Segev, Foundations of geometric continuum mechanics, Birkhauser, 2023.
R. Segev, Electrodynamics and geometric continuum mechanics, Continuum Mechanics and Thermodynamics, 37:33, 2025, https://doi.org/10.1007/s00161-025-01364-1.
V. Goldshtein and R. Segev, On force interaction for electrodynamics-like theories, 2026.