Development of special multi-material elements

A procedure for developing multi-material elements, which are able to eliminate the weakness of the conventional ®nite elements in determining the stress distributions along the interfaces of di€erent materials, has been proposed. The results obtained by this multi-material element type are in good agreement with those obtained by a modi®ed ®nite element approach, which employs the least square ®tting method to improve the calculation of interfacial stresses. Moreover, these two solutions are superior to the conventional ®nite element solution. The improvements made by these two modi®ed solutions are entirely due to the imposition of the necessary and sucient equilibrium and compatibility conditions at the interfaces. It is worth noting that while the two modi®ed ®nite element approaches provide comparable accuracy, the proposed approach using new multi-material elements is much easier to implemen