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This comprehensive review primarily concerns axially moving flexible structures in problems involving distributed structure-to-solid contact. The distinguishing features of axially moving structures are presented in terms of prevalent studies regarding models with simplified support conditions. Subsequent sections focus on the particular difficulties of treating contact problems with classical structural theories, on the appropriate non-material kinematic description for travelling structures, on the proper formulation of established mechanical principles for open systems and on the category of Arbitrary Lagrangian–Eulerian (ALE) approaches, which are frequently applied for the development of application-oriented finite element schemes. Novel analytical and numerical transient solutions for the benchmark problem of an axially moving beam, which is travelling across a rough surface between two misaligned joints, are presented to illustrate particular challenges as well as to highlight perspectives for future research activities. There are 177 references cited in this paper.

The proposed Kirchhoff-Love shell stress resultant plasticity model extends a previously reported model for plates by complementing the constitutive law of elastoplasticity with membrane effects. This enhanced model is designed for bending dominant settings with small to moderate membrane forces. It is thus implemented in a purpose-built nonlinear mixed Eulerian–Lagrangian finite element scheme for the simulation of sheet metal roll forming. Numerical experiments by imposing artificial strain histories on a through-the-thickness element are conducted to test the model against previously reported stress resultant plasticity models and to validate it against the traditional continuum plasticity approach that features an integration of relations of elastoplasticity in a set of grid points distributed over the thickness. Results of actual roll forming simulations demonstrate the practicality in comparison to the computationally more expensive continuum plasticity approach.