Peridynamic Simulation Of ECC Dynamic Damage Considering The Effect Of Fiber Matrix Interface

Material property studies on Engineered cementitious composites(ECC)are faced with discontinuities such as fracture and damage.When internal crack initiation and propagation,the originally continuous displacement and stress fields are no longer continuous,leading to stress singularities at the crack tip and at the interface,etc.The existing mechanical models and numerical simulation methods are based on the traditional continuous medium mechanics theory,which have major limitations in dealing with fracture and damage.Based on the non-local idea,the PD theory uses the spatial integral equation to express the motion of material points without the derivation process of the displacement field,thus avoiding the difficulties of the traditional continuous medium mechanics theory in dealing with discontinuities,enabling analytical modeling in the same framework,and having unique advantages in dealing with fractures and damages.In this paper,a bond-based PD theory is explained in detail,including the motion equation of the material point,the constraints,the critical elongation of the bond and the formulation of the damage and fracture criterion in the bond-based PD theory.Then the construction of the PD model is presented.The damage correction factor of the bond is introduced by considering the progressive damage caused by microcracks in the modeling of the cement matrix,in the fiber matrix interaction modeling,the constitutive force function of PD theory is modified considering the influence of fiber matrix interface.The simulation results of ECC under tension and compression are compared with the experimental results and the finite element simulation results in literature to verify the validity and accuracy of the model,and the appropriate the PD horizon size and the mesh spacing ratio are obtained through the convergence study of PD.The results are compiled as follows:(1)Considering the influence of fiber matrix interface,the constitutive force function of PD theory is modified,and the PD model of ECC is improved.The corresponding MATLAB program code is written,and the numerical calculation of the theoretical model of PD is realized.(2)Convergence analysis of the PD model for ECC is carried out.The suitable PD horizon size and mesh spacing ratio are obtained by a simulation study of crack expansion in a cement matrix plate,and finally the PD horizon size δ=4.0 mm and the mesh spacing ratio m=4 are selected for subsequent numerical simulations based on the simulation results and time cost.(3)Under tensile load,when the fiber volume fraction is 1%,the cracks of ECC plate are firstly produced at the place where the initial cracks are located.As the fiber volume fraction in the ECC plate increases,the cracks are no longer concentrated at the initial cracks of the ECC plate.When the fiber volume fraction in the ECC plate increases further,the number of small cracks in the ECC plate does not change much,and the ECC plate is no longer sensitive to the existence of the initial cracks.(4)Three-point bending simulation of the ECC beam containing the initial crack is carried out,and the stress cloud of crack extension at different stages is analyzed and it is found that cracks usually occur at the tip of the initial crack or around the initial crack.(5)The wedge splitting simulation of ECC plates with the initial crack is carried out to study the effect of different fiber volume fractions on the crack expansion.It is found that for ECC plates with different fiber volume fractions,the crack initiation time is the same,however,with the increase of fiber volume fraction,the crack no longer shows a single crack propagation,and the crack branches increase significantly.Moreover,the final crack paths of ECC plates with different fiber volume fraction are basically the same and all of them are multiple-crack cracking.