Abstract
This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics. From a thermodynamical viewpoint, it is only necessary to know the two macroscopic potentials (macroscopic free energy and macroscopic potential of dissipation) to describe the state of the body and its quasistatic evolution. These global potentials are the averages of the local ones. We point out some particular cases of non-linearities, especially the case of damaged materials.
Highlights
This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics
This paper proposes some extensions of classical relations to nonlinear mechanics in small perturbations
This paper shows how local mechanical behaviour can influence the global behavior of an heterogeneous medium
Summary
This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics. The macroscopic elastic modulus has not the same value when macrohomogeneous strain or stress conditions are prescribed on the boundary ∂Ω. The macroscopic behaviour has variable elastic moduli When both materials are elastoplastic or with initial strains, because of the existence of incompatible strains, a self equilibrated stress field r appears, and the local stress can be decomposed as σ = A : Σ + r = σE + r (45). E(t) ≥ ET , Ri (t) = Re and the answer can be plotted as in Fig. we consider the macroscopic behaviour of a composite spheres assemblage when two families exist in the structure, with volume fraction of phase 2 denoted by cI and cII (cI > cII ). This shows the necessity to study stability and bifurcation of each equilibrium path in homogeneization of nonlinear mechanical behaviour to ensure the existence of the macroscopic law
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
