The chevron folding instability in thermoplastic elastomers and other layered materials

When thermoplastic elastomers (TPEs) such as styrene-isoprene-styrene or st yrene-butadiene-stryrene copolymers in an aligned lamellar or hexagonal mor phology are stretched perpendicularly to the plates or rods, then above a c ritical stress the lamellae or cylinders buckle to form a chevron or zig-za g structure. We examine this instability both analytically and using finite element analysis. In the analytic work we treat the elastomer as if it wer e a homogeneous anisotropic material and describe the chevron formation in terms of strain fields at length scales larger than that of the microphase pattern. We find that in order to do this one must respect the underlying m icrophase structure in two respects: (i) in terms of a statement as to how the material anisotropy rotates with the material; and (ii) in terms of add itional 'material moduli' which represent couplings between the macroscopic strain fields and deformations that occur at the microphase length scale. We define moduli which relate to hard phase bending and to displacement of the soft phase relative to the hard phase. The analytical results are teste d by comparison with finite element models which solve for the microscopic strain held, and which allow the examination of post-buckling behaviour. We find that for perfectly aligned TPEs there is a geometric instability towa rds a sinusoidal buckling profile, which evolves into the chevron shape on further strain beyond the instability. The buckling is associated with a sh arp turnover in the stress-strain curve. We also set our work in the contex t of treatments of similar buckling instabilties found in the fields of str uctural geology and liquid crystals.