Straightening: existence, uniqueness and stability.
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.
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Republic of Ireland ; School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Republic of Ireland.
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Destrade
School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK.
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Ogden
Dipartimento di Matematica e Fisica 'Ennio De Giorgi', Università del Salento, Lecce, Italy.
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Sgura
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Republic of Ireland ; School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK.
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Vergori
nonlinear elasticity; stiffening; straightening instability