Closed form radial return algorithm for plane stress elastic-plastic analyses
article
Plane stress numerical simulations of elastic-plastic deformations are commonly based on in-plane projected equations, that is, direct inclusion of the plane stress constraints into the three-dimensional elastic predictor and plastic corrector algorithm. In case of a full three-dimensional formulation (without plane stress constraints) and a Von Mises yield criterion, a closed form return mapping can be obtained, resulting in a linear equation for the scalar plastic multiplier and subsequently an explicit constitutive function1(pg 223 eq. 7.101 and 7.103). An algorithm for plane stress using the full 3D constitutive formulation is introduced by de Borst,2 by enforcing plane stress at the structural level rather than in the constitutive integration algorithm. In this approach the plane stress constraint is satisfied only at converged equilibrium conditions. For an explicite code this approach is not appropriate as there is no equilibrium iteration. By applying the in-plane projected equations a nonlinear equation for the scalar plastic multiplier is obtained1(remark 9.8 pg 376). In this paper it is shown that yet a linear equation for the plastic multiplier and an explicit constitutive function that satisfies
the plane stress constraints can be obtained. Section 2.2 summarizes the plane stress formulation by De Souza Neto.1 Consequences of plane stress projected equations are presented in Section 2.3, and an explicit closed form radial return algorithm for plane stress in Section 2.4.
the plane stress constraints can be obtained. Section 2.2 summarizes the plane stress formulation by De Souza Neto.1 Consequences of plane stress projected equations are presented in Section 2.3, and an explicit closed form radial return algorithm for plane stress in Section 2.4.
TNO Identifier
985309
Source
International Journal for Numerical Methods in Engineering, 124, pp. 2122-2129.
Pages
2122-2129