Folding and faulting of an elastic continuum.
Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called 'chevrons') and seashell patterns (for instanceLopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures.
DICAM , University of Trento , via Mesiano 77, 38123 Trento, Italy.
Davide
0000-0001-5423-6033
D
Bigoni
DICAM , University of Trento , via Mesiano 77, 38123 Trento, Italy.
Panos A
PA
Gourgiotis
Cosserat elasticity; Green's functions; dilation/compaction; ellipticity; extreme orthotropy; stress channelling