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Straightening: existence, uniqueness and stability. (English) Zbl 1371.74041
Summary: One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and stability are addressed. Particular attention is paid to the system of forces required to sustain the large static deformation, including by the application of end couples. The influence of geometric parameters and constitutive models on the appearance of wrinkles on the compressed face of the block is also studied. Different numerical methods for solving the incremental stability problem are compared and it is found that the impedance matrix method, based on the resolution of a matrix Riccati differential equation, is the more precise.

MSC:
74B20 Nonlinear elasticity
74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
74G60 Bifurcation and buckling
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