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Fundamental topics in continuum mechanics: grand ideas, errors and horrors
Received date: 2025-12-18
Revised date: 2026-03-21
Online published: 2026-05-06
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Shortly after the middle of the past century, a comprehensive presentation of continuum mechanics was written under the supervision of Clifford Ambrose Truesdell III in two volumes of Siegfried Flügge’s Handbuch der Physik; a first volume in 1960 with Richard Toupin on The Classical Field Theories (the monster), including an Appendix on Tensor Analysis by Jerald LaVerne Ericksen, and a second volume in 1965 with Walter Noll on The Non-Linear Field Theories of Mechanics (the monsterino). Both nicknames were due to Truesdell. These contributions were gradually taken as turning points by the mechanics community worldwide, due to the completeness of the analysis and the profoundness of the documentation. However, the vastness of the treatment acted as a shield against careful reasoning on delicate but basic notions. In the wake of some 19th-century scholars, these notions were taken to be worthy of belief and incorporated into the presentation with a valuable historical background. A lack of engineering perspective discouraged the necessary caution when addressing a number of issues. Scholars in continuum mechanics, fascinated by the monumental work conceived and carried out by Truesdell and his associates, did not dare to make any accurate revisions. The analysis is here centered on unsatisfactory formulations that are presently disseminated in the literature by followers of Truesdell’s magnum opus. The geometric approach in four-dimensional (4D) Euclidean spacetime adopted here is self-contained even in the classical context, providing clarity of notions, methods, and results unachievable via the more familiar but less powerful and error-prone three-dimensional (3D) treatment.
G. ROMANO , R. BARRETTA . Fundamental topics in continuum mechanics: grand ideas, errors and horrors[J]. Applied Mathematics and Mechanics, 2026 , 47(5) : 1131 -1156 . DOI: 10.1007/s10483-026-3385-7
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