Open Access
ARTICLE
A Novel Constitutive Equation for Inverse Analysis Method and its Application in Sheet Metal Forming
Xiaoyang Lu1, Bingtao Tang1, Xiaoli Lu2
1 Institute of Engineering Mechanics, Shandong Jianzhu University, Jinan 250101, China
2 College of Electrical Information Engineering, Zhengzhou University of Light Industry,
Zhengzhou 450002, China
Structural Longevity 2010, 4(1), 11-20. https://doi.org/10.3970/sl.2010.004.011
Abstract
The Traditional Inverse Analysis Method (TIAM) of sheet metal stamping has the shortcomings of neglecting the effects of deformation history on stress
prediction. An Updated Inverse Analysis Method (UIAM) is proposed based on
the final workpiece in Euler coordinate system. The UIAM uses the constitutive
equation based on flow theory of plasticity to consider the loading history. In order
to avoid numerous iterations to ensure the numerical stability in Newton-Raphson
scheme to obtain plastic multiplier ∆λ, the equation in unknown stress vectors is
transformed into a scalar equation using the notion of the equivalent stress. Thus a
scalar equation of two orders and only one unknown factor ∆λ is obtained. A simple transformation matrix is introduced to reverse this matrix, so that the multiplier
∆λ can be solved explicitly. Results obtained with the TIAM based on deformation theory of plasticity and the updated one based on flow theory of plasticity are
compared with those of the incremental forward finite element solver LS-DYNA.
The comparisons of blank configurations and the effective strain distribution show
that the proposed plasticity integration algrithm is effective and reliable.
Keywords
Cite This Article
Lu, X., Tang, B., Lu, X. (2010). A Novel Constitutive Equation for Inverse Analysis Method and its Application in Sheet Metal Forming.
Structural Longevity, 4(1), 11–20. https://doi.org/10.3970/sl.2010.004.011