- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Same macroscopic fields, different local mechanical loads: An electromechanical closure diagnostic

Bela Schulte Westhoff*

  • *Contact author: schultewesthoff@tu-berlin.de
PDF

Phys. Rev. Applied 26, 054011 – Published 4 November, 2026

DOI: https://doi.org/10.1103/8s4n-1fvh

Abstract

Continuum electromechanical models require bulk forces and surface tractions at the resolution of the target mechanical prediction. Agreement in macroscopic-electromagnetic fields, or even in total force, does not by itself establish that these local loads are determined. Starting from microscopic carrier balances, we formulate an output-first minimum-closure diagnostic that separates two ordered questions: transmission closure CT specifies how Lorentz forces on carriers reach the selected mechanical host, whereas projection closure CP asks whether the retained electromagnetic state determines the required load once transmission is fixed. Two controlled equal-state comparisons isolate these noninterchangeable failure modes. In a uniform prescribed external field, bound dipoles and individually anchored charges have the same retained electromagnetic state and retained projection of the applied-field carrier loading, yet produce different host loads because their support topologies transmit end point forces differently. With transmission fixed, aligned and staggered line-dipole arrangements have the same retained polarization and continuum field, yet produce different boundary tractions because registry-dependent near-field correlations omitted by retention survive as an interfacial load. These witnesses establish structural nonuniqueness within the declared model classes, rather than universal material magnitudes. The diagnostic stops when global balance fixes the requested total force or torque on the receiving system; otherwise, it establishes transmission before testing whether a projection residual affects the selected output above tolerance. Missing closure may be supplied by a support or carrier-kinetic model, targeted reconstruction, or an equivalent validated reduced law. A macroscopic load law is therefore sufficient whenever transmission is fixed or irrelevant, and all output-relevant residuals are negligible or represented.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. X. Xi, J. Ma, Z.-H. Zhou, X.-X. Hu, Y. Chen, C.-L. Zou, C.-H. Dong, and X. Sun, Experimental investigation of the angular symmetry of optical force in a solid dielectric, Optica 8, 1435 (2021).
  2. M. Wang, S. Wang, Q. Zhang, C. T. Chan, and H. B. Chan, Measurement of mechanical deformations induced by enhanced electromagnetic stress on a parallel metallic-plate system, Phys. Rev. Lett. 121, 035502 (2018).
  3. N. G. C. Astrath, G. A. S. Flizikowski, B. Anghinoni, L. C. Malacarne, M. L. Baesso, T. Požar, M. Partanen, I. Brevik, D. Razansky, and S. E. Bialkowski, Unveiling bulk and surface radiation forces in a dielectric liquid, Light: Sci. Appl. 11, 103 (2022).
  4. O. Vizika and D. A. Saville, The electrohydrodynamic deformation of drops suspended in liquids in steady and oscillatory electric fields, J. Fluid Mech. 239, 1 (1992).
  5. A. Ricoeur and M. Kuna, Electrostatic tractions at dielectric interfaces and their implication for crack boundary conditions, Mech. Res. Commun. 36, 330 (2009).
  6. Y. Wan, L. Fan, and Z. Zhong, Finite element modeling of temporal evolution of the quasi-piezoelectric d33 coefficient of cellular piezoelectret polypropylene film, Comput. Mater. Sci. 55, 54 (2012).
  7. M. Torbati, K. Mozaffari, L. Liu, and P. Sharma, Coupling of mechanical deformation and electromagnetic fields in biological cells, Rev. Mod. Phys. 94, 025003 (2022).
  8. Z. Suo, X. Zhao, and W. H. Greene, A nonlinear field theory of deformable dielectrics, J. Mech. Phys. Solids 56, 467 (2008).
  9. Y. M. Shkel, Electrostriction: Material parameters and stress/strain constitutive relations, Philos. Mag. 87, 1743 (2007).
  10. X. Zhao and Z. Suo, Theory of dielectric elastomers capable of giant deformation of actuation, Phys. Rev. Lett. 104, 178302 (2010).
  11. A. R. Balakrishna, J. E. Huber, and C. M. Landis, Nano-actuator concepts based on ferroelectric switching, Smart Mater. Struct. 23, 085016 (2014).
  12. L. Daniel, O. Hubert, N. Buiron, and R. Billardon, Reversible magneto-elastic behavior: A multiscale approach, J. Mech. Phys. Solids 56, 1018 (2008).
  13. Z. Cao and J. Cai, Design of a giant magnetostrictive motor driven by elliptical motion, Sens. Actuat. A 118, 332 (2005).
  14. R. Toupin, The elastic dielectric, J. Ration. Mech. Anal. 5, 849 (1956).
  15. L. D. Landau and E. M. Lifshitz, Electrodynamics of continuous media, in Course of Theoretical Physics, edited by E. M. Lifshitz and L. P. Pitaevskii, 2nd ed. (Pergamon Press, Oxford, 1984), Vol. 8.
  16. H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy (Prentice Hall, Englewood Cliffs, NJ, 1989).
  17. J. R. Melcher, Continuum Electromechanics (MIT Press, Cambridge, MA, 1981).
  18. R. M. McMeeking and C. M. Landis, Electrostatic forces and stored energy for deformable dielectric materials, J. Appl. Mech. 72, 581 (2005).
  19. L. Liu, An energy formulation of continuum magneto-electro-elasticity with applications, J. Mech. Phys. Solids 63, 451 (2014).
  20. L. Dorfmann and R. W. Ogden, Nonlinear electroelasticity: Material properties, continuum theory and applications, Proc. R. Soc. A 473, 20170311 (2017).
  21. J. Marshall and K. Dayal, Atomistic-to-continuum multiscale modeling with long-range electrostatic interactions in ionic solids, J. Mech. Phys. Solids 62, 137 (2014).
  22. H. S. Park, M. Devel, and Z. Wang, A new multiscale formulation for the electromechanical behavior of nanomaterials, Comput. Methods Appl. Mech. Eng. 200, 2447 (2011).
  23. W. Sun, S. B. Wang, J. Ng, L. Zhou, and C. T. Chan, Analytic derivation of electrostrictive tensors and their application to optical force density calculations, Phys. Rev. B 91, 235439 (2015).
  24. S. Wang, J. Ng, M. Xiao, and C. T. Chan, Electromagnetic stress at the boundary: Photon pressure or tension?, Sci. Adv. 2, e1501485 (2016).
  25. V. A. Markel, Numerical investigation of electrostatic force density in ionic crystals such as NaCl, Phys. Rev. B 107, 104307 (2023).
  26. F. A. Reich, Coupling of continuum mechanics and electrodynamics: An investigation of electromagnetic force models by means of experiments and selected problems, Ph.D. thesis, Technische Universität Berlin, 2017.
  27. W. Rickert, An investigation of the electromagnetic coupling problem by means of a rational framework and selected experiments, Ph.D. thesis, Technische Universität Berlin, 2023.
  28. S. R. de Groot and L. G. Suttorp, Foundations of Electrodynamics (North-Holland Publishing Company, Amsterdam, 1972).
  29. A. C. Eringen and G. A. Maugin, Electrodynamics of Continua I: Foundations and Solid Media (Springer-Verlag, New York, 1990).
  30. C. Rinaldi and H. Brenner, Body versus surface forces in continuum mechanics: Is the Maxwell stress tensor a physically objective Cauchy stress?, Phys. Rev. E 65, 036615 (2002).
  31. A. W. Behnke, T. J. Pollei, and K. J. Webb, Einstein–Laub and Lorentz optical force densities with a planar interface, Phys. Rev. A 108, 033708 (2023).
  32. N. C. Admal and E. B. Tadmor, A unified interpretation of stress in molecular systems, J. Elast. 100, 63 (2010).
  33. H. J. H. Clercx and G. Bossis, Electrostatic interactions in slabs of polarizable particles, J. Chem. Phys. 98, 8284 (1993).
  34. N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations, Phys. Rev. B 98, 045426 (2018).
  35. L. Cui, N. Wang, and J. Ng, Computation of internal optical forces using the Helmholtz tensor, Phys. Rev. A 104, 013508 (2021).
  36. M. Mansuripur, A. R. Zakharian, and E. M. Wright, Electromagnetic-force distribution inside matter, Phys. Rev. A 88, 023826 (2013).
  37. B. S. Park, H. S. Choi, J. O. Park, J. H. Wang, and I. H. Park, Equality of the Kelvin and Korteweg–Helmholtz force densities inside dielectric materials, IEEE Trans. Magn. 56, 7515004 (2020).
  38. V. V. Datsyuk and O. R. Pavlyniuk, Maxwell stress on a small dielectric sphere in a dielectric, Phys. Rev. A 91, 023826 (2015).
  39. J. R. Melcher and G. I. Taylor, Electrohydrodynamics: A review of the role of interfacial shear stresses, Annu. Rev. Fluid Mech. 1, 111 (1969).
  40. D. A. Saville, Electrohydrodynamics: The Taylor–Melcher leaky dielectric model, Annu. Rev. Fluid Mech. 29, 27 (1997).
  41. P. Penfield, Jr., and H. A. Haus, Electrodynamics of Moving Media (MIT Press, Cambridge, MA, 1967).
  42. A. Zangwill, Modern Electrodynamics (Cambridge University Press, Cambridge, 2013).
  43. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Colloquium: Momentum of an electromagnetic wave in dielectric media, Rev. Mod. Phys. 79, 1197 (2007).
  44. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  45. S. M. Barnett and R. Loudon, On the electromagnetic force on a dielectric medium, J. Phys. B 39, S671 (2006).
  46. B. Anghinoni, M. Partanen, and N. G. C. Astrath, The microscopic Ampère formulation for the electromagnetic force density in linear dielectrics, Eur. Phys. J. Plus 138, 1034 (2023).
  47. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  48. H. A. Lorentz, The Theory of Electrons and its Applications to the Phenomena of Light and Radiant Heat, 2nd ed. (Dover Publications, New York, 1952), republication of the 2nd edition originally published by Teubner, Leipzig, 1916.
  49. S. P. Xiao and T. Belytschko, A bridging domain method for coupling continua with molecular dynamics, Comput. Methods Appl. Mech. Eng. 193, 1645 (2004).
  50. R. E. Miller and E. B. Tadmor, A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods, Model. Simul. Mater. Sci. Eng. 17, 053001 (2009).
  51. N. Wang, S. Wang, and J. Ng, Electromagnetic stress tensor for an amorphous metamaterial medium, Phys. Rev. A 97, 033839 (2018).
  52. M. Partanen, B. Anghinoni, N. G. C. Astrath, and J. Tulkki, Time-dependent theory of optical electro- and magnetostriction, Phys. Rev. A 107, 023525 (2023).
  53. D. Katusele, C. Majidi, P. Sharma, and K. Dayal, Exploiting instabilities to enable large shape transformations in dielectric elastomers, Phys. Rev. Appl. 23, 014007 (2025).
  54. S. Torza, R. G. Cox, and S. G. Mason, Electrohydrodynamic deformation and burst of liquid drops, Philos. Trans. R. Soc. A 269, 295 (1971).
  55. B. Schulte Westhoff, Reproducibility code for electromagnetic local-load non-closure witnesses: common-grid correction, Zenodo (2026), version 0.2.0, 10.5281/zenodo.22903443

Outline

Information

Phys. Rev. Applied 26, 054011– Published 4 November, 2026
  • Received 19 May 2026
  • Revised 22 September 2026
  • Accepted 8 October 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation