caa a22 4500 445812583 CHVBK 20180317145216.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00419-010-0502-z doi (NATIONALLICENCE)springer-10.1007/s00419-010-0502-z Voigt and Poincaré's mechanistic-energetic approaches to linear elasticity and suggestions for multiscale modelling [Elektronische Daten] [Danilo Capecchi, Giuseppe Ruta, Patrizia Trovalusci] Many modern theories for "complex” materials rely on the construction of specific potentials for inner actions by resorting to mechanistic/corpuscular descriptions of the matter at different length scales. Techniques allowing the dialogue among different material scales on the basis of energetic equivalence criteria play a central role in mechanics of materials. These multiscale techniques can be seen as originated from the molecular theories of the nineteenth century and in particular by the suggestions of Voigt and Poincaré, to deal with the paradoxes coming from the search of the exact number of elastic constants in linear elasticity. In this paper, we examine both Voigt and Poincaré's mechanistic-energetic approaches to the standard linear theory of elasticity in contrast with the mechanistic molecular model by Navier, Cauchy and Poisson. We also try to provide some conceptual guidelines among these approaches and the contemporary theories of complex material behaviour. Springer-Verlag, 2011 Constitutive models nationallicence Molecular theory of elasticity nationallicence Energy-based homogenization nationallicence Atomistic-continuum models nationallicence Capecchi Danilo Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via A. Gramsci 53, 00197, Rome, Italy aut Ruta Giuseppe Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via Eudossiana 18, 00184, Rome, Italy aut Trovalusci Patrizia Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via A. Gramsci 53, 00197, Rome, Italy aut Archive of Applied Mechanics Springer-Verlag 81/11(2011-11-01), 1573-1584 0939-1533 81:11<1573 2011 81 419 https://doi.org/10.1007/s00419-010-0502-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-010-0502-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Capecchi Danilo Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via A. Gramsci 53, 00197, Rome, Italy aut NATIONALLICENCE 700 1- Ruta Giuseppe Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via Eudossiana 18, 00184, Rome, Italy aut NATIONALLICENCE 700 1- Trovalusci Patrizia Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via A. Gramsci 53, 00197, Rome, Italy aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/11(2011-11-01), 1573-1584 0939-1533 81:11<1573 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer