Identifying the coefficients of thermal expansion of an electronic device composed of various materials using the virtual fields method

Abstract

A method for inverse determination of the coefficients of thermal expansion of an electronic device that is composed of multiple materials, i.e. dissimilar materials, is proposed. The virtual fields method is applied for obtaining the coefficients of thermal expansion. Appropriate virtual displacement fields have been automatically obtained instead of using any arbitrary virtual displacement. This leads to an accurate and effective determination of the coefficient of thermal expansion. Full-field displacement distributions measured by digital image correlation are used as input for the inverse analysis. The validity of the proposed method has been demonstrated by measuring samples made of various materials. Furthermore, the proposed method is applied to samples simulating electronic devices with and without constraints on the boundary. Results show that the coefficients of thermal expansion of an object composed of dissimilar materials are obtained properly. The proposed method is expected to be used for determining the coefficients of thermal expansion of actual electronic devices.