The «materialization» of forces: Why confounding mathematical concept and physical entity makes the design of metamaterials arduous. Issue 2 (8th November 2022)

• Record Type: Journal Article
• Authors: dell'Isola, Francesco; Stilz, Maximilian
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 103:Issue 2(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-11-08
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202200433
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: In this paper we show why the postulation scheme based on forces and couples is detrimental when designing novel metamaterials. Instead, the most effective postulation scheme for mechanics is that based on the Principle of Virtual Work formulated by, for example, d'Alembert, Lagrange, Piola, and Paul Germain. In fact, generalized continuum mechanics can be formulated in a coherent way only by basing its foundations on the Principle of Virtual Work while the problem of synthesis of novel metamaterials can be efficiently confronted only when introducing generalized continua as their model at macroscopic level. Once work functionals are postulated, the set of involved generalized forces are identified using the representation theorem for distributions by Laurent Schwartz, forces in particular being zeroth order distributions. Actually, only when limiting the class of considered internal work functionals to first order distributions is the Principle of Virtual Work equivalent to the balances of forces and couples. The predominant Role of the Principle of Virtual Work has been denied by those inductivist scholars who claim that balance laws can be induced by experimentation. The Principle of Virtual Work postulation more truly fits in a falsificationist approach to epistemology. Abstract : In this paper we show why the postulation scheme based on forces and couples is detrimental when designing novel metamaterials. Instead, the most effective postulation scheme for mechanics is that based on the Principle of Virtual Work formulated by, for example, d'Alembert, Lagrange, Piola, and Paul Germain. In fact, generalized continuum mechanics can be formulated in a coherent way only by basing its foundations on the Principle of Virtual Work while the problem of synthesis of novel metamaterials can be efficiently confronted only when introducing generalized continua as their model at macroscopic level.…