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Associated flow rule and Non associated flow rule

Can any one please explain me what is meant by associated and non-associated flow rule.


The plastic flow is mainly due to the rate of plastic strain increment vector

 and material flow at yield is governed by the gradient of the plastic potential flow. It is called associated plasticity, if the angle of dilation

 is equal to the angle of internal friction

. It means that the plastic flow develops along the normal to the yield surface. In general, however, the material plastic flow is non-associated in nature i.e., the vector of plastic strain rate is not normal to the yield surface and therefore, the dilation angle is not equal to the internal friction. The dilation angle is always taken smaller than the internal friction angle in numerical modelling, particularly for cohesive frictional materials.


  1. Pandey, A. K., and R. S. Bisht. "Numerical Modelling of Infilled Clay Brick Masonry Under Blast Loading."Advances in Structural Engineering 17.4 (2014): 591-606.
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