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Consistent tangent operators for rate-independent elastoplasticity. (English) Zbl 0535.73025
It is shown that for problems involving rate constitutive equations, such as rate-independent elastoplasticity, the notion of consistency between the tangent (stiffness) operator and the integration algorithm employed in the solution of the incremental problem, plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon Newton’s method. Within the framework of closest-point-projection algorithms, a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed. To wit, associative \(J_ 2\) flow rules with general nonlinear kinematic and isotropic hardening rules, as well as a simple class of non-associative flow rule are considered. The resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of Newton’s method, whereas use of the so-called elasto-plastic tangent in conjunction with a radial return integration algorithm, a procedure often employed, results in Newton type of algorithms with suboptimal rate of convergence. Application is made to a set of numerical examples which include saturation hardening laws of exponential type.

74S30 Other numerical methods in solid mechanics (MSC2010)
74S99 Numerical and other methods in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
49M15 Newton-type methods
Full Text: DOI
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