An asymptotic strategy to couple homogenized elastic structures

Abstract

A two-scale methodology to calculate the local stress-strain state (SSS) in structures composed of connected elements is proposed. The methodology is based on the assumption that the connecting unit has a size small in comparison to the objects being connected. It is demonstrated that the problem of connection allows asymptotic decomposition. At the macroscopic level (the zero order approximation), an interface problem, with appropriate interface conditions, is revealed. At this order, the individual properties of the joint are neglected. These properties manifest themselves at the next asymptotic order, which takes into account all individual joint properties using the solution of the macroscopic problem. The local SSS in the vicinity of joint consists of the SSS in the connecting unit, together with rapidly decaying boundary layers in the connected elements. A detail elucidation of the local SSS in the connecting unit is an important distinction of this work from previous studies of connected structures. Motivated by the asymptotic analysis, a numerical method for simultaneously calculating the SSS in both the connected structures and the connecting unit is developed. An illustrative example, involving computation of the SSS in the vicinity of an explosion welding seam, is presented.