Bridging the gap between small scale phenomena and large scale beams strengthened with FRP – A 1D XFEM high order approach

• The size dependency of stress concentration in large scale FRP strengthened beams is studied.
• A high order model is combined with the XFEM to create a specially tailored enriched finite element.
• The tailored XFEM is used for the combined local–global analysis of beams up to 40 m long.
• Localized effects with length scales much smaller than the element length are explored.
• The existence of a size effect on the localized stress concentration is revealed.

The structural behavior, inter-laminar stresses, and potential size effect in large concrete beams strengthened with fiber reinforced polymer (FRP) composite materials are investigated. The purpose of this paper is to face the problems that arise while modeling large FRP strengthened beams (with length to thickness of the bonded layer ratio in the order of 104) due to the considerable scatter of elastic and geometrical scales. The paper develops a specially tailored finite element that combines the eXtended Finite Element Method (XFEM) along with the high order approach in order to overcome the scales problem. The capabilities and limitations of the proposed high order XFEM are then studied. The numerical study focuses on the analysis of large scale beams, compares the localized effects that evolve in such beams with the ones that evolve in small scale ones, and studies the scalability of the observations on the gap between the small scale phenomena and the size of the beam.