Total deformation theory for non-proportional loading

摘要

This study presents a technique to apply a total deformation theory to non-proportional loading cases.A total deformation theory capable of analyzing a sequence of linear non-proportional load steps isproposed. Each linear loading path is defined with reference to its previous loading path, analogous toproportional loading. The application of the proposed formulation to tension-torsion loading of thintubes and pressure-torsion loading of thick-walled cylinders is carried out. It is shown that forsituations where stresses are known a priori, the proposed method gives the same plastic strain fieldas does incremental plasticity. For situations where stresses are not known a priori, a method toestimate the plastic strain for linear hardening materials is proposed. This method estimates thenecessary stress fields using conventional deformation plasticity. These stresses are then used in theproposed total deformation formulation to predict plastic strains. The plastic strain field resultingfrom this method is compared with finite element results obtained using incremental plasticity. Theresults are in very good agreement and the proposed method significantly reduces computation time.