Nonproportional loading effects on elastic-plastic behavior based on stress resultants for thin plates of strain hardening materials (Q1338391)

A rate form of the stress resultant constitutive law is derived for power-law materials with the associated flow rule. A limited number of uniaxial combined bending and membrane force cases are examined for the plane stress and plane strain conditions. The results for through-the- thickness integration method (incorporating the finite deformations) are also presented and employed as benchmarks to assess the suitability of the stress resultant theory. The modifications required in the hardening rule for the case of finite deformations are indicated. The results from the stress resultant theory are compared with those from through-the- thickness integration method for both the small deformation and large deformation cases. The finite deformation results are useful in sheet forming operations. The stress resultant theory is indicated to be computationally more efficient for the finite element simulations of the metal forming problems.