Dr. Wenbin Yu gives a talk titled "Representative Structural Element: A New Paradigm for Multiscale Structural"

This talk presents a new paradigm for multiscale structural modeling using representative structural element (RSE). This paradigm can address two fundamental challenges of materials/structures modeling: rigorously capturing the interplay between different length scales and minimizing the use of ad hoc assumptions to avoid loss of accuracy.

RSE is extended from the well-known concept of representative volume element (RVE) in micromechanics. Two serious issues with RVE are that it isolates the micro- and macroscopic scales and neglects the interplay between micromechanics and structural mechanics. RSE remedies such deficiencies by directly connecting the microscopic (or atomic) world of matter with the macroscopic structural analysis. RSE provides a unified way to not only predict the corresponding material properties for the final macroscopic structural analysis, but also recover the localization within RSE based on the macroscopic structural behavior.

The variational asymptotic method (VAM) is adopted as the mathematical foundation to avoid ad hoc assumptions. VAM is based on the idea of dropping small terms, to carry out an asymptotic analysis of the functional governing the RSE, exploiting the smallness of small parameters inherent in the problem such as small structural dimensions and heterogeneity length scales. The solution of the original problem can be approximated asymptotically by solving a series of simpler variational statements. The loss of accuracy due to simplifications at different length scales in the modeling process is minimized by VAM.

The theories developed based on this approach are implemented using computational mechanics. Several examples will be used to demonstrate the clear benefits of this approach. The potential applications of this approach are briefly discussed.