I found some articles related to molecular dynamics (MD) simulations in the journal "International Journal of Non-Linear Mechanics", we all know that the nonlinear failure criterions are more adaptable used to describe the characteristic of rock mass, such as nonlinear failure characteristic of rock strength, structural characteristic and the effect of the stress to the strength of rock mass. so MD belongs to non-linear mechanics method? I mean it's possible for me to simulate the nonlinear failure of rocks using molecular dynamics (MD) simulations?
Besides, what's the difference between nonlinear mechanics and nonlinear dynamics?
You are referring to two different things. Nonlinear mechanics usually refers to either nonlinear relationship between stress and strain in a material, or nonlinear terms in strain-displacement expressions. The former is usually called material nonlinearity, while the latter is referred to as geometric nonlinearity.
In the realm of dynamical systems, nonlinearity refers to nonlinear ODE's describing the time evolution of the system. So, for usual case of forces depending on positions of particles, Newtonian mechanics result in nonlinear ODE's.
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