The strain rate contribution in the generalized flame surface density (FSD) [GRAPHICS] transport equation remains a leading order unclosed source term, which plays a pivotal role in the modeling of [GRAPHICS] transport for all filter widths [GRAPHICS] in the context of large eddy simulations (LES). To date, most FSD-based closures have been proposed for flames without differential diffusion effects of heat and mass, characterized by a global Lewis number equal to unity (i.e., [GRAPHICS] ). The effects of differential diffusion arising due to non-unity Lewis number on the FSD transport have rarely been analyzed in existing literature. In the present analysis, the statistical behaviors of the strain rate term of the FSD transport equation have been analyzed using a DNS database of freely propagating statistically planar turbulent premixed flames with a global Lewis number ranging from 0.34 to 1.2 (i.e., [GRAPHICS] = 0.34-1.2). The FSD strain rate term has been split into components originating from the gradients of Favre-filtered velocity components (i.e., [GRAPHICS] ), strain rate contribution due to chemical heat release (i.e., [GRAPHICS] ) and sub-grid processes (i.e., [GRAPHICS] ). The contributions of [GRAPHICS] and [GRAPHICS] assume positive values throughout the flame brush for all values of [GRAPHICS] . The performances of the existing models for [GRAPHICS] and [GRAPHICS] have been assessed for flames with different values of global Lewis number [GRAPHICS] . The contribution of [GRAPHICS] remains positive throughout the flame brush for the [GRAPHICS] = 0.6, 0.8, 1.0, and 1.2 flames but the variation of [GRAPHICS] towards the burned gas side of the flame brush for the [GRAPHICS] flame remains qualitatively different in comparison to the other cases considered here. The effects of [GRAPHICS] on the local alignment of reaction progress variable gradient with principal strain rates are responsible for the observed influences of Lewis number on the sub-grid strain rate term [GRAPHICS] . The existing models have been found to be inadequate for the purpose of capturing the qualitative behaviors of the sub-grid strain rate term [GRAPHICS] for [GRAPHICS] flames. Here a new model has been proposed based on a-priori analysis of explicitly filtered DNS data, which has been demonstrated to capture both the qualitative and quantitative behaviors of [GRAPHICS] for all values of [GRAPHICS] for flames with [GRAPHICS] ranging from 0.34 to 1.2.