Application of gradient plastic theory based on FEPG platform

Based on the FEPG platform, the finite element program using gradient plastic theory is developed to solve mesh dependence after strain softening. A u-λ algorithm with damp factor is proposed, which can solve the equation of displacement and yield surface simultaneously. The algorithm can not only get displacement and plastic multiplier together, but also avoid the stress haul back calculation in stress return algorithm widely used in finite element solution procedures. The softening modulus and the internal character length are introduced into D-P yield function, and the constitutive model can consider strain softening and gradient effect. The damp Newton algorithm is used to calculate softening problems. The results of a case study show that the u-λ algorithm with damp factor can be used to solve softening problems, the gradient plastic theory described by finite element weak form has no requirement of continuity, and appropriate outcome can be obtained by the first-order element, thus the mesh dependence of simulation is basically solved.