Molecular Approaches for Multifield Continua: origins and current developments

The mechanical behaviour of complex materials, characterised at finer scales by the presence of heterogeneities of significant size and texture, strongly depends on their microstructural features. Attention is centred on multiscale approaches which aim to deduce properties and relations at a given macroscale by bridging information at proper underlying microlevel via energy equivalence criteria. Focus is on physically–based corpuscular–continuous models originated by the molecular models developed in the 19th century to give an explanation per causas of elasticity. In particular, the ‘mechanistic–energetistic’ approach by Voigt and Poincare who, when dealing with the paradoxes deriving from the search of the exact number of elastic constants in linear elasticity, respectively introduced molecular models with moment and multi–body interactions is examined. Thus overcoming the experimental discrepancies related to the so–called central–force scheme, originally adopted by Navier, Cauchy and Poisson.