A B S T R A C T Cold expansion of fastener holes creates compressive residual stresses around the hole.This well-known technique improves fatigue life by reducing tensile stress around the holes. However, cyclic loading causes these compressive residual stresses to relax, thus reducing their beneficial effect. Estimation of the fatigue life without considering the residual stress relaxation might lead to inaccurate results. In this research, numerical studies were carried out using 2D finite element (FE) models to determine the initial tangential and radial residual stress distributions generated by cold expansion and their relaxation under cyclic loading. To predict the stress relaxation, four nonlinear kinematic hardening models were applied in simulation of stress/strain path. The results obtained from the FE analysis were compared with available experimental results. A good agreement between the numerical and experimental results was observed.Keywords cold expansion; fastener hole; finite element simulation; residual stress relaxation. N O M E N C L A T U R Eā = current centre of the yield surface in the deviatoric stress spacē a 4 = threshold term C i = nonlinear kinematic hardening model parameter E = elastic modulus H = plastic modulus m = nonlinear kinematic hardening model parameter M = number of segments required for multilinear representation of the uniaxial stress-strain R = stress ratio s¯= deviatoric stress tensor S u = tensile strength ᾱ = current centre of the yield surface in total stress space δ = multiaxial parameter in the kinematic hardening rule ε p = plastic strain tensor γ i = nonlinear kinematic hardening model parameters ν = Poisson's ratio σ = stress tensor σ y = yield stress σ 0 = size of the yield surface

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Concrete is a complex heterogeneous material, and thus, it is important to develop numerical modeling methods to enhance the prediction accuracy of the fracture mechanism. In this study, a two-dimensional mesoscale model is developed using a non-ordinary state-based peridynamic (NOSBPD) method. Fracture in a concrete cube specimen subjected to pure tension is studied. The presence of heterogeneous materials consisting of coarse aggregates, interfacial transition zones, air voids and cementitious matrix is characterized as particle points in a two-dimensional mesoscale model. Coarse aggregates and voids are generated using uniform probability distributions, while a statistical study is provided to comprise the effect of random distributions of constituent materials. In obtaining the steady-state response, an incremental and iterative solver is adopted for the dynamic relaxation method. Load-displacement curves and damage patterns are compared with available experimental and finite element analysis (FEA) results. Although the proposed model uses much simpler material damage models and discretization schemes, the load-displacement curves show no difference from the FEA results. Furthermore, no mesh refinement is necessary, as fracture is inherently characterized by bond breakages. Finally, a sensitivity study is conducted to understand the effect of aggregate volume fraction and porosity on the load capacity of the proposed mesoscale model.