The continuum sensitivity method for the computational design of three-dimensional deformation processes

Acharjee, Swagato; Zabaras, Nicholas

doi:10.1016/j.cma.2004.05.033

Cited by 22 publications

(18 citation statements)

References 17 publications

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“…It aims to determine the optimal shape of a workpiece, whereby the forming process and the desired final shape is known. Contributions regarding this challenge are commonly categorized into sheet metal forming -see for example the inverse approach in [23], the rollback method in [24] or the strategy with trimming spline functions in [25], respectively -and into bulk metal forming, see e. g. the continuum sensitivity approach for contact problems in [26] and the iterative strategy with an inverse mechanical formulation in [27].…”

Section: Shape Optimizationmentioning

confidence: 99%

On gradient‐based optimization strategies for inverse problems in metal forming

Landkamer¹,

Söhngen²,

Steinmann³

et al. 2017

GAMM-Mitteilungen

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In the context of metal forming, optimization issues typically lead to inverse problems with a least-squares minimization as the objective. Due to the nonlinearities in forming simulations, iterative optimization approaches have to be considered. Gradient-based solution strategies for two inverse problems are proposed and compared to each other. Firstly, the identification of elasto-plastic material parameters is regarded. Secondly, a recently developed approach for the determination of an optimal workpiece design is investigated. As a special feature, both approaches can be coupled in a non-invasive fashion to arbitrary external finite element software via subroutines.

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Section: Shape Optimizationmentioning

confidence: 99%

On gradient‐based optimization strategies for inverse problems in metal forming

Landkamer¹,

Söhngen²,

Steinmann³

et al. 2017

GAMM-Mitteilungen

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“…Development of continuum sensitivity analysis technique for design of complex three dimensional deformation processes [7].…”

Section: Status Of Effortmentioning

confidence: 99%

“…The design differentiation of for every ij, a kinematically admissible sensitivity deformation field expressed over the reference configuration B0. Details on the methodologies to obtain sensitivities for three-dimensional die and preform design problems, and to model sensitivities of die-workpiece contact through design-differentiation of a regularized contact problem can be found in our work in [7]. Once the final sensitivities of the texture to process variables is found at the end of simulation of a deformation process, a variety of gradient optimization algorithms can be invoked to minimize the objective function defined in Eq.…”

mentioning

confidence: 99%

Robust Multi-Length Scale Deformation Process Design for the Control of Microstructure-Sensitive Material Properties

Zabaras¹

2007

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information , 1215 Jefferson Davis Highway, Suite 1204. Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)2 SUPPLEMENTARY NOTES14. ABSTRACT The objective of this work was to develop a robust design methodology for optimizing microstructure-sensitive properties in aircraft components manufactured using metal forming processes. The multi-scale forming design simulator developed provides means to select the sequence of deformation processes, design the dies and preforms for each process stage as well as the process conditions such that a product is obtained with desired shape and microstructure. Modeling of uncertainty propagation in such multi-scale models of deformation is extremely complex considering the nonlinear coupled phenomena that need to be accounted for. The work addresses key mathematical and computational issues related to robust multi-scale design of deformation processes. Our research accomplishments include development of new mathematical models based on spectral polynomial chaos, support space, and entropy maximization techniques for modeling sources of uncertainties in material deformation processes. These models, in conjunction with multi-scale homogenization models, allow simulations of the effect of microstructural variability on the reliability of macro-scale systems. We have developed the first stochastic variational multi-scale simulator with an explicit sub-grid model, a robust deformation process simulator using spectral and collocation methods for simulating uncertainties in metal forming processes. Finally, recent developments including an information theoretic framework for modeling microstructural uncertainties is summarized. EXECUTIVE SUMMARYThe objective of this work is to develop a robust design methodology for optimizing microstructuresensitive properties in aircraft components manufactured using metal forming processes. The multi-scale forming design simulator developed as a part of this project provides means to select the sequence of deformation processes, design the dies and preforms for each process stage as well as the process conditions such that a product is obtained with desired shape and microstructure. Modeling of uncertainty propagation in such multi-scale models of deformation is ex...

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“…Michaleris and Tortorelli [10] for example provided a general framework for the calculation of elasto-plastic tangent operators or Archajee and Zabaras [11] already presented a sensitivity approach for three-dimensional contact problems. However, in most cases it is cumbersome to compute the required sensitivity derivations of the system responses.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Case study on the influence of kinematic hardening within a parameter-free and non-invasive form finding approach

Landkammer

Steinmann

2016

MATEC Web Conf.

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Abstract. Inverse form finding -as a type of shape optimization -aims in determining the optimal preform design of a workpiece for a specific forming process, whereby the desired target geometry is known. Recently, a novel parameter-free and heuristic approach was developed to tackle this nonlinear optimization problem. Benchmark tests already delivered promising results. As a particular note-worthy feature of the approach, a coupling to an arbitrary finite element software is feasible in a non-invasive fashion. The aim of this contribution is to investigate the effect of kinematic hardening and cyclic loading on the convergence behavior of the algorithm.

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The continuum sensitivity method for the computational design of three-dimensional deformation processes

Cited by 22 publications

References 17 publications

On gradient‐based optimization strategies for inverse problems in metal forming

On gradient‐based optimization strategies for inverse problems in metal forming

Robust Multi-Length Scale Deformation Process Design for the Control of Microstructure-Sensitive Material Properties

Case study on the influence of kinematic hardening within a parameter-free and non-invasive form finding approach

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