LCE: Computational Methods for Mechanism-Based Higher-Order Continuum Theories

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Computational Methods for Mechanism-Based Higher-Order Continuum TheoriesH. Gao, Division of Mechanics and Computation, Stanford University, Palo Alto, CA 94305Y. Huang, Dept. of Mechanical and Industrial Engr., University of Illinois, Urbana, CA 61801The objective is to develop novel computational methods for the recently proposed virtual internal bond (VIB) method. The VIB method extends the application range of classical continuum mechanics to modeling cohesive elasticity at much smaller length scales (e.g., lattice spacing in elastic deformation). A major obstacle to the application of such theory is the lack of efficient numerical methods for higher order or nonlocal continuum theories involving multiple distinct materials length scales. Here we plan to develop a robust and reliable numerical method to analyze multiscale phenomena that cannot be addressed by classical continuum theories. Our effort will include the development of efficient and scalable numerical methods for multiscale computation. We will compare the numerical results with experiments to validate the theory, and use the numerical method to investigate several fundamental problems that cannot be addressed by classical continuum theories.