An RVE-based multiscale theory of solids with micro-scale inertia and body force effects

E.A. DE SOUZA NETO; P.J. BLANCO; P.J. SÁNCHEZ; R.A. FEIJÓO

MECHANICS OF MATERIALS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2015 vol. 80 p. 136 - 144

0167-6636

A multiscale theory of solids based on the concept of representative volume element (RVE) and accounting for micro-scale inertia and body forces is proposed. A simple extension of the classical Hill?Mandel Principle together with suitable kinematical constraints on the micro-scale displacements provide the variational framework within which the theory is devised. In this context, the micro-scale equilibrium equation and the homogenisation relations among the relevant macro- and micro-scale quantities are rigorously derived by means of straightforward variational arguments. In particular, it is shown that only the fluctuations of micro-scale inertia and body forces about their RVE volume averages may affect the micro-scale equilibrium problem and the resulting homogenised stress. The volume average themselves are mechanically relevant only to the macro-scale.