A Hyper-Surface for the Combined Rate and Size Effects on the Material Properties

The recent interests in developing multiscale model-based simulation procedures have brought about the challenging tasks of bridging different spatial and temporal scales within a unified framework. However, the research focus has been on the scale effect in the spatial domain with the loading rate being assumed to be quasi-static. Although material properties are rate-dependent in nature, little has been done in understanding combined loading rate and specimen size effects on the material properties at different scales. In addition, the length and time scales that can be probed by the molecular level simulations are still fairly limited due to the limitation of computational capability. Based on the experimental and computational capabilities available, therefore, an attempt is made here to formulate a hyper-surface in both spatial and temporal domains to predict combined size and rate effects on the mechanical properties of materials.