Conceptual difficulties of multiscale analysis

Multiscale phenomena can be observed in many current engineering applications that students learn in typical undergraduate and graduate engineering education programs. For example, in determining the strength of a material, the presence of micro-scale cracks, dislocations, and voids can dramatically alter the reliability of the material. However, current modeling restrictions such as limited computational time and capabilities can inhibit the study of these behaviors. To deal with this challenge, multiscale analysis techniques are being devised to conserve computational time without sacrificing results. These techniques are being taught to engineering undergraduate and graduate students across the country with mixed results. We have examined why this topic is difficult for students to understand using both qualitative and quantitative methods, and have identified some of these key difficulties. In addition, we have examined how these conceptual hurdles are overcome by both students and researchers at varying levels (pre-college students, undergraduate students, graduate students, post-doctoral fellows, and professors), and have developed different approaches to incorporate into the classroom. A better understanding of these common conceptual hurdles allows for better teaching strategies to be developed that addresses these issues directly and more concisely to preempt or correct difficulties in understanding earlier. In this paper we will present results from interviews with several students, faculty, and post-doctoral researchers. These interviews enabled us to capture in-depth perspectives, from different educational stages, on teaching and conceptual understanding of multiscale analysis. This data provides essential insights into the topic, and serves as the foundation for developing curricular materials in this area.