PSI - Issue 73

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2025) 000 – 000 Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 73 (2025) 14–18

23rd International Conference on Modelling in Mechanics 2025 Approximation of a compressed member under large strain Petr Frantík * a a Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology and FEM Consulting s.r.o., Veve ří 331/95, 602 00 Brno, Czech Republic Abstract This article presents the derivation of analytical expressions for describing the response of an elastically compressed prismatic bar made of a linear material under large strains. The expressions are used to approximate the response of numerical models solved by the finite element method with variable dimensionality. © 202 5 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 23rd International Conference on Modelling in Mechanics 2025 organizers Keywords: large deformations; large strain; compressed member 1. Introduction Even for the simplest elastic materials, accounting for large displacements transforms basic loading conditions into a highly complex problem. In this study, we analyze a bar subjected to constant normal stress. The challenge arises from the fact that large displacements introduce geometric nonlinearity — specifically, the dependence of bar stiffness on the magnitude of the applied load. Consequently, the continuous kinematic description must include nonlinear strain measures, despite the linearity of the constitutive law. A central aspect of such formulations is the use of nonlinear strain tensors, such as the Green – Lagrange strain tensor in the total Lagrangian formulation and the Euler – Almansi strain tensor in the updated Lagrangian approach. These strain measures enable accurate representation of finite kinematics, which is essential for capturing geometric effects induced by large displacements. © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the event organizers

* Corresponding author. E-mail address: kitnarf@centrum.cz

2452-3216 © 202 5 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 23rd International Conference on Modelling in Mechanics 2025 organizers

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the event organizers 10.1016/j.prostr.2025.10.003