Load step reduction for adjoint sensitivity analysis of finite strain elastoplasticity

In this paper, load step reduction techniques are investigated for adjoint sensitivity analysis of path-dependent nonlinear finite element systems. In particular, the focus is on finite strain elastoplasticity with typical hardening models. The aim is to reduce the computational cost in the adjoint sensitivity implementation. The adjoint sensitivity formulation is derived with the multiplicative decomposition of deformation gradient, which is applicable to finite strain elastoplasticity. Two properties of adjoint variables are investigated and theoretically proved under certain prerequisites. Based on these properties, load step reduction rules in the sensitivity analysis are discussed. The efficiency of the load step reduction and the applicability to isotropic hardening and kinematic hardening models are numerically demonstrated. Examples include a small-scale cantilever beam structure and a large-scale conrod structure under huge plastic deformations.

Analytical Prediction of Stretch-Bending Springback Based on the Proportional Kinematic Hardening Model

Pre-stretching and post-bending are the simplest loading methods for the profile stretch-bending technical process. The inner layers of the profile are stretched and then compressed during the loading process. Considering the Bauschinger effect of metal materials, a new material model called the proportional kinematic hardening model was proposed. The stretch-bending mechanical model was established under a pre-stretching and post-bending loading path. The stress and strain on the cross section of profiles were analyzed. The analytic expressions of curvature radius of the strain neutral layer and bending moment were derived after loading. The analytic method for determining the curvature radius of the geometric center layer after unloading and springback during stretch-bending was established. The rectangular section ST12 profile with symmetrical characteristics is adopted, the stretch-bending experimental results show that the new proportional kinematic hardening model is more accurate than the classical kinematic hardening model in predicting the stretch-bending springback.

On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

In this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Cyclic Behavior of Simple Models in Hypoplasticity and Plasticity with Nonlinear Kinematic Hardening

The paper gives insights into modeling and well-posedness analysis driven by cyclic behavior of particular rate-independent constitutive equations based on the framework of hypoplasticity and on the elastoplastic concept with nonlinear kinematic hardening. Compared to the classical concept of elastoplasticity, in hypoplasticity there is no need to decompose the deformation into elastic and plastic parts. The two different types of nonlinear approaches show some similarities in the structure of the constitutive relations, which are relevant for describing irreversible material properties. These models exhibit unlimited ratchetting under cyclic loading. In numerical simulation it will be demonstrated, how a shakedown behavior under cyclic loading can be achieved with a slightly enhanced simple hypoplastic equations proposed by Bauer

LASER SHOCK PEENING INDUCED BACK STRESS MITIGATION IN ROLLED STAINLESS STEEL

Laser shock peening (LSP) is investigated as a potential tool for reducing tensile back stress, shown here applied to rolled and annealed 304L austenitic steel. The back stress of treated and untreated dog-bone samples is extracted from hysteresis tensile testing. Electron back scatter diffraction (EBSD) and orientation imaging microscopy (OIM) analysis quantify the geometrically necessary dislocation (GND) density distribution of unstrained and strained as well as un-peened and peened conditions. Finite element analysis (FEA) simulation models back stress and residual stress development through tensile testing and LSP treatment using known LSP pressure models and Ziegler's non-linear kinematic hardening law. Non-linear regression fitting of tensile testing stress-strain in as-received specimens extracts the kinematic hardening parameters that are used in numerical study. This research shows LSP may be used to overcome manufacturing design challenges presented by yield asymmetry due to back stress in rolled steel.

Optimal Control of Plasticity with Inertia

The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic strain by controlling volume forces. The idea given in [10] is used to transform the state equation into an evolution variational inequality (EVI) involving a certain maximal monotone operator. Results from [27] are then used to analyze the EVI. A regularization is obtained via the Yosida approximation of the maximal monotone operator, this approximation is smoothed further to derive optimality conditions for the smoothed optimal control problem.

A Design Optimization Study for the Die Dimensioning Using the Locking Nut Folding Simulation

An inverse analysis based on optimization process is performed to determine die curvatures for a locking nut’s flange folding process which has highly nonlinear material behaviour. The nut material is AISI C1040 steel. The ring material is polyamide 6. The Chaboche’s nonlinear kinematic hardening rule is combined with bilinear isotropic hardening model as a hardening rule for the plasticity model combined with associated flow rule and von Mises yield criterion. The inverse analysis is applied to determine the curvatures by using genetic algorithm optimization method based on dimensional accuracy. The optimum mould curvatures are determined. So a comprehensive methodology is presented for determination of curvatures.