The concept of the asymptotic behaviour of particulate materials is described,including its enhancement considering asymptotic states in extension.A 3D discrete element model with permanent elastic spherical particles is set up.The numerical sample is stretched from different initial states,and the influence of the strain rate direction on the final state is studied.Asymptotic behaviour is clearly observed.The asymptotic stress ratio (including critical state friction angle) is observed not to be constant,but it is a variable depending on the stress level.Existence of extension asymptotic states is observed,and the notion of normal extension line is introduced.
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