Plastic Simulation Of Elliptical Hole With Two Cracks In Quasicrystal

The problem of orifice with crack in solid has been paid close attention to by the mathematical and mechanical circles.As a new solid structure material,quasicrystals will attract the attention of many scholars.It is found that to explore the elastic problem of quasicrystals,we need not only to explore the phonon field,but also to explore the phase field coupled with phonon field.Since quasicrystals have been discovered,the study of plastic simulation of quasicrystals with cracks has become very active.The method of establishing physical model has become the choice of most scholars.Many scholars have made meaningful research on the quasicrystal orifice problems with cracks by using the conformal mapping method,complex potential method and Fourier transform in the complex function,and combining with the physical model,and gradually formed a systematic knowledge network in this knowledge field.In this paper,the plastic simulation of the crack tip in one-dimensional hexagonal quasicrystals and two-dimensional quasicrystals with two cracks is carried out.Firstly,the conformal mapping method is used to transform the difficult physical plane problem into a regular mathematical plane problem.At the same time,their basic equations: generalized Hooke's law,equilibrium equation and so on are discussed.Then,the problem is decoupled into the same plane problem as the classical plane elastic problem and an anti plane elastic problem.For the former problem,this paper does not do research,but mainly studies the phonon phasor coupling anti plane elastic problem of the latter;Based on the existing theoretical basis,the size of the plastic region at the tip of the double crack at the elliptical orifice of the one-dimensional hexagonal Quasicrystal and the two-dimensional quasicrystal with a point group of 10 mm decagonal symmetry is calculated,and it is verified that the results are consistent with the existing results in the limit case.