SOME BASIC PROBLEMS IN NUMERICALLY SIMULATING EFFECTIVE PROPERTIFS AND LOCAL FIELDS OF COMPOSITE MATERIALS

摘要

It is pointed out that to numerically estimate the effective properties and local fields ofmatrix-inclusion composites,a commonly adopted method is accompanied with some serious draw-backs.We call this method the nominal loading scheme(NLS),which considers the actual inclusiondistribution inside a finite domain,Ω say,treats the external domain of Ω to be of the pure matrix ma-terial,and imposes the actural traction,σ~∞ say on the remote boundary.It thus gives rise to the fol-lowing basic problems:(i)Can NLS be improved remarkably just by adjusting σ~∞?(it)What isthe relationship between the size of Ω and the,scale of inclusions?(iii)Which choice isbetter in calculating the effective properties,the whole domain Ω or an appropriatelyselected sub-domain of Ω? Targeting these problems,the equivalent loading,scheme(ELS)and equivalent matrix scheme(EMS)are proposed.It is theoretically analyzedthat both ELS and EMS can be used to precisely simulating the effective properties andlocal fields of matrix-inclusion composites,and both ELS and EMS are self-approved.As an application,ELS combined with a m-called pseudo-dislocations method is used toevaluate the effective properties and local fields of two-dimensional two-phase compos-ites with close-packed circular inclusions,or randomly distributed circular inclusions,or randomly distributed mierocracks.The results show that substituting the remote trac-tion σ~∞ with the effective stress field σ~E suggested by IDD scheme is a simple and effec-tive method,and the estimation of the effective properties and local fields is very closeto the accurate,solution.