FE-based assessment of the resistance of steel joints using strain averaging

Strain, defined as deformation per unit length, is, by nature, an averaged magnitude. Experimental values of strain, linked to the actual length of samples (coupon tests), are accepted as representative of the material and used for modelling. These constitutive values are inherently different from the point values retrieved from finite element (FE) models, highly dependent on mesh type and size. Moreover, strain is not a primary analysis variable on the FE method, so mesh refinement resulting in displacement convergence may not necessarily yield peak strain convergence. This paper proposes a methodology to determine peak strains that are invariant across different mesh discretizations satisfying global convergence criteria. Such a methodology is required because of the increasing use of advanced numerical design calculations using the finite element method that require resistance criteria based on local maximum peak strains, such as part 1–14 of Eurocode 3. This work presents a novel averaging procedure for strains (‘bubble averaging’), based on a weighted average on increasingly large volumes, surfaces, or lines around a point of interest. The procedure is formulated for solid models, and its specific application is demonstrated for a steel connection component, both isolated and integrated on a joint, and shown to result in stable, mesh-independent values.