Application Of Two-scale Asymptotic Homogenization Method In Masonry Structure

Two-scale asymptotic homogenization is one of the most popular methods tostudy the mechanical behavior of composite material with periodicity. As formasonry structure, the characteristic dimension of brick is much smaller thanthe dimension of masonry walls. As a result of that, masonry walls can beregarded as a composite material made up of brick and mortar, which isperiodically arranged. So two-scale asymptotic homogenization method can beapplied to study the mechanical behavior of masonry walls.With two-scale asymptotic homogenization method, displacement functionis approximated in terms of two-scale asymptotic expansions with a smallparameter of. Stress and strain function can be obtained by insertingdisplacement function into geometry and constitutive equations.By importingdisplacement infuence function, coarse-scale stress, strain and consititutivetensor can be solved in a unit cell, which connecct coarse-scale quantities withfine-scale quantities.Based on the theory mentioned above, asymptotic homogenization equations can be solved with the help of FEM method. In ABAQUS, the processof solving homogenization equations is simplified with thermal-stress method.The effective properties of masonry structure is solved in a unit cell with the useof this numerical method. To evaluate the invalidity of this method, the obtainedresults are compared with the results calculated by other methods.A material constitutive model for a masonry shear-wall is presented in thispaper using the calculated masonry equivalent Young’s modulus in combinationwith Rankine failure criterion. To simulate masonry shear-walls under shear andpressure force, it is simulated in ABAQUS with the constitutive model. Thefailure mode and force-displacement diagram obtained in simulation iscompared with the experimental results, which can be found that usinghomogenized constitutive model to analyze the shear wall failure mechanismand macroscopic mechanical behavior is effective.In addition, based on the homogenization theory, the selection of unit cellfor masonry walls with different masonry patterns is analyzed. A plug-in isdeveloped to calculate macroscopic effective properties of masonry walls thatconsist of mortar and bricks with different elasticity modulus.