### Chapter 5 - Concurrent multiscale Analysis by Generalized Particle Dynamics Methods

In this Chapter, a GP method, short for the generalized particle dynamics method, is used to
carry on concurrent multiscale analysis. The basic assumption of the GP method is that if the basic
material structure can be kept the same as the real material at all scales, the multiscale analysis
will be more accurate and more effective. Based on this assumption GP divides the simulation region
into areas containing particles of different scales, n; where n=1 is the atomistic scale and higher
values of n correspond to the continuum scale. Natural non-local boundary conditions via material
neighbor-link cells are used for a seamless transition between domains of different scales. An
inverse mapping method from the deformed particle domain
β_{n}
into the corresponding atomic domain
α_{n}
is proposed. All calculations of different scales can be conducted at the corresponding atomistic
α_{n}
domain by the same potential and same numerical algorithm as the atomistic scale of the model,
thus this method is also called extended molecular dynamics method. The comparison between
simulations of GP and MD for dislocation initiation and propagation is given. Based on the
introduction of the GP method, the state of art of concurrent multiscale analysis is introduced.