Based on Euler backward integral method

an integration algorithm of constitutive equation is suggested for adaptive sub-stepping schemes. And the consistent tangent matrices are derived. According to the projection vector of trial stress beyond the yielding surface

the pseudo yielding function and plastic potential function is introduced for apex area of yielding surface. So

integration algorithms adopted of two projection vectors make trial stress in apex area to return to apex point of yielding surface. The consistent tangent matrices for two vectors are also derived. Zero stress point in the yielding surface is replaced by minimum value. An ABAQUS-UMAT subroutine using D-P criterion for linear elastic-perfectly plastic model is programmed; and two examples are analyzed to validate these methods.