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During each computational cycle, assuming the material is yielding, the strains will contain both elastic and plastic components, thus:

 

                                           

Only the elastic strain increments Δεegenerate stresses:

 

                                                     

These stress increments are added to stresses already existing from the previous load step and the updated stresses substituted into the failure criterion. If stress redistribution is necessary, yield criterion is violated (F>0), this is done by altering the load increment vector Fi in the global system of equations, corresponding to the load cycle i:

 

                                                                 

where K represents the elastic (initial) global stiffness matrix and Ui represents the global displacements increments. This vector holds two types of load, as given by:

 

                                                   

where Fa is the actual applied external load increment and Fbi is the body loads vector that varies from one iteration to the next and must be self-equilibrating so that the net loading on the system is not affected by it.

 

 

 

 

 

 

 

 

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