Chapter 7 - A further Introduction of Concurrent Multiscale Methods

The main focus of this chapter is an introduction of the various versions of concurrent multiscale methods as well as the difficulties in developing multiscale simulation schemes. Specifically, three direct connection (DC) methods including MAAD, CADD, bridge domain methods are further introduced. They belong to, respectively, multiscale methods of energy-based, force-based, and energy-based but with blended region. In addition, the embedded statistical coupling method (ESCM) are also introduced. The difficulties in a seamless transition between the atomistic and continuum scales caused by the DC methods due to the incompatibility of stiffness and constitutive laws between materials at two sides of the interface are introduced through 1D analysis. Benchmark tests are introduced for different DC methods to understand the accuracy of different methods.

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