A stabilised large-strain elasto-plastic Q1-P0 method

The mean dilatation method effectively involves bi-linear displacements and a constant pressure and is often known as the Q1-P0 formulation. Its non-l inear implementation was originally derived as a three-field formulation wh ich included the volume ratio via the Jacobian, J, of the deformation gradi ent as an additional separate variable. However, the latter term was not di rectly required in the numerical implementation once J was assumed constant along with the pressure. This formulation will here be termed the non-line ar Q1-P0 method. It is known to give good solutions for many practical larg e-strain elasto-plastic problems. However, for some problems, it has been s hown to be prone to severe 'hour-glassing'. With a view to remedying this s ituation, we here re-visit the three-field formulation and derive a modifie d form, which although variationally valid, is over-stiff in comparison to the original procedure (here simply called the Q1-P0 method). However, the concepts lead to a natural method for stabilising the Q1-P0 technique. The associated tangent stiffness matrix is symmetric. Copyright (C) 1999 John W iley & Sons, Ltd.