Multiscale Structural Mechanics
Learning Objective:On completing this course the student shall be able to:
- Identify distinct features of composites and challenges associated with modeling and simulation of composites.
- Critically evaluate major theories in the literature and explain their strengths and weaknesses.
- Exam and explain simulation results for composite structures.
- Apply mechanics of structure genome to derive models for composite structures.
- Design and analyze composite structures using SwiftComp and other commercial composite simulation software.
This course covers fundamentals of micromechanics, structural mechanics needed for design and analysis of composite structures capturing microstructural details including fiber/matrix and other constituent materials. This course assumes an introductory background in elasticity and finite element method, and aims to provide students a unified framework for multiscale structural mechanics. This course emphasizes concepts of mechanics through formulating and solving typical problems of anisotropic, heterogeneous structures, and helps foster an in-depth understanding of the subject. Students not only gain knowledge of the fundamental principles needed for multiscale simulation but also gain an integrated and consistent understanding of multiscale structural mechanics based on Continuum Mechanics.
Fall 2019 Syllabus
- Introduction: characteristics of composites, challenges of composites modelling, traditional approaches to composite models.
- Review of anisotropic elasticity and mechanics of composites.
- Variational methods: calculus of variations and Ritz method, variational asymptotic method.
- Fundamentals of micromechanics: RVE, Hill condition, boundary conditions, mean field theories, RVE analysis, method of cells and its variants, asymptotic homogenization theory.
- Fundamentals of structural mechanics: theory of beams and theory of plates.
- Failure of composite structures.
- Mechanics of structure genome.
- Use of SwiftComp for multiscale constitutive modeling of composite structures.