A comparison between a recursive method based on an inverse mechanical formulation and shape optimization for solving inverse form finding problems in isotropic elastoplasticity - Germain, Sandrine; Landkammer, Philipp; Steinmann, Paul (PAMM 2014, 2014)
UnivIS-Import:2015-07-08:Pub.2014.tech.FT.FT-TM.acompa_4

A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in logarithmic strain space - Germain, Sandrine; Steinmann, Paul (Proceedings of Applied Mathematics and Mechanics (PAMM), 2011)
In this paper an inverse mechanical formulation and a Limited-Broyden-Flechter-Goldfarb-Shanno method for shape optimization are compared. Both methods deal with the determination of the undeformed shape of an hyperelastic part knowing its deformed configuration and the applied loads. We consider anisotropic hyperelastic materials that are formulated in the logarithmic strain space. Beside the theoretical aspects, we present a numerical example. We established that no difference could be found between the node coordinates on the undeformed sheets computed with both methods. However the convergence to the solution is faster for the inverse mechanical formulation compared to the L-BFGS algorithm.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.acompa_8

Material model identification for DC04 based on the numerical modelling of the polycrystalline microstructure and experimental data - Lehmann, Eva; Schmaltz, Stefan; Germain, Sandrine; Fassmann, Dennis; Weber, Christoph; Loehnert, Stefan; Schaper, Mirko; Bach, Friedrich-Wilhelm; Steinmann, Paul; Willner, Kai; Wriggers, Peter (15th ESAFORM Conference Proceeding, 2012)
Sheet-bulk-metal forming processes require an accurate material model which is derived in this contribution. The microscopic model is based on a simulation of a real microstructure. A validation on the macroscopical scale is performed through the reproduction of the experimentally calculated yield surface based on the homogenised structural response of a corresponding deformed representative volume element (RVE). The microstructural material model is also compared with a macroscopical phenomenological model based on logarithmic strains. The homogenised microscopic model and the phenomenological macroscopic model are in good agreement with the evolution of the stresses and strains obtained during the experiments.© (2012) Trans Tech Publications.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.materi
Keywords: Anisotropic finite elastoplasticity; Homogenisation; Material modelling; Sheet-bulk-metal forming

On a recursive algorithm for avoiding mesh distortion in inverse form finding - Germain, Sandrine; Steinmann, Paul (Journal of the Serbian Society for Computational Mechanics, 2012)
A challenge in the design of functional parts is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. A shape optimization formulation might be used to determine the initial shape in the sense of an inverse problem via successive iterations of a direct mechanical problem. In this paper, we present a shape optimization formulation for elastoplastic materials with a constitutive model for anisotropic additive elastoplasticity in the logarithmic strain space. A discrete sensitivity analysis is performed and gives the analytical gradient of the objective function needed in the optimization algorithm. We found that the use of the coordinates of the functional component as design variables led to mesh distortions. Without a split of the total force applied on the component and an update of the undeformed configuration between two steps the optimization algorithm is not able to find an appropriate minimum. Three numerical examples in isotropic and anisotropic elastoplasticity illustrate the structure of such a recursive algorithm for avoiding mesh distortions.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.onarec
Keywords: Anisotropy; Elastoplasticity; Inverse form finding; Large strain; Shape optimization

On a recursive formulation for solving inverse form finding problems in isotropic elastoplasticity - Germain, Sandrine; Landkammer, Philipp; Steinmann, Paul (Advanced Modeling and Simulation in Engineering Sciences, 2014)
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.onarec

On Inverse Form Finding for Anisotropic Elastoplastic Materials - Germain, Sandrine; Steinmann, Paul (AIP Conference Proceedings, 2011)
The goal of this contribution is to present an extension of the work of Germain et al. [1] on inverse form finding for anisotropic hyperelastic materials to the case of anisotropic elastoplastic materials formulated in the logarithmic strain space. A short review of the theoretical aspects is presented. Based on some numerical examples we show that our method for inverse form finding in elastoplasticity can be used if the plastic strains are previously given as it is the case when a desired hardening state is prescribed. © 2011 American Institute of Physics.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.oninve_3
Keywords: Anisotropy; Elastoplasticity; Inverse Form Finding; Large Strain; Logarithmic Strain

On inverse form finding for orthotropic plasticity - Landkammer, Philipp; Germain, Sandrine; Steinmann, Paul (Computer Assisted Mechanics and Engineering Sciences, 2014)
Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired spatial configuration that is obtained after a forming process, the boundary conditions and the applied loads are known. Inputting the optimal material configuration, a subsequent FEM computation then has to result exactly in the nodal coordinates of the desired deformed workpiece. Germain et al. [1] recently presented a new form finding strategy for isotropic elastoplasticity. Switching between the direct and the inverse mechanical formulation, while fixing the internal plastic variables in the inverse step, uniquely detects the undeformed configuration iteratively. In this contribution, the developed recursive algorithm is extended to anisotropic plasticity. In particular the orthotropic Hill yield function is considered. A load and a displacement-controlled example demonstrate that this new strategy requires only a few iterations to determine the optimal initial design whereby an almost linear convergence rate is obtained. Copyright © 2013 by Institute of Fundamental Technological Research, Polish Academy of Sciences.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.oninve
Keywords: Inverse FEM; Inverse form finding; Logarithmic strain space; Optimum blank design; Orthotropic Hill's yield criterion

On two different inverse form finding methods for hyperelastic and elastoplastic materials - Germain, Sandrine; Steinmann, Paul (PAMM, 2012)
This contribution focuses on two different developments of mechanical- computational methods for the optimal determination of the initial shape of formed functional components knowing the deformed configuration, the applied loads and the boundary conditions. The first method uses an inverse mechanical formulation and can be applied to materials with hyperelastic behaviors. For materials with elastoplastic properties this method is not advocated, without knowing the final plastic strains, due to the non uniqueness of the solution. The second method uses a shape optimization formulation in the sense of an inverse problem via successive iterations of the direct problem. For hyperelastic materials the inverse mechanical formulation is preferred for its velocity and the non exhibition of possible mesh distortions. In the shape optimization formulation mesh distortions can be avoided by an update of the reference configuration of the functional part. Both methods are using a formulation in the logarithmic strain space. A numerical example for materials with isotropic elastoplastic behaviors illustrates the shape  optimization formulation.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.ontwod

Optimum blank design by using the inverse FEM in orthotropic elastoplasticity - Landkammer, Philipp; Germain, Sandrine; Steinmann, Paul (PAMM, 2014)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.optimu_1

Shape Optimization for Anisotropic Elastoplasticity in Logarithmic Strain Space - Germain, Sandrine; Steinmann, Paul (COMPLAS XI Proceeding (CD), 2011)
This paper deals with shape optimization for anisotropic elastoplasticity in logarithmic strain space. We aim to find an appropriate undeformed configuration of a workpiece knowing in advance its deformed configuration, the boundary conditions and the applied loads. The node coordinates of the finite element (FE) domain are chosen as design variables. A discrete sensitivity analysis is presented and analytical gradients are performed. A numerical example illustrates the theoretical aspects.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.shapeo
Keywords: Anisotropy; Elastoplasticity; Shape optimization

Towards inverse form finding methods for a deep drawing steel DC04 - Germain, Sandrine; Steinmann, Paul (15th ESAFORM Conference Proceeding, 2012)
A challenge in the design of functional parts in metal forming processes is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. An inverse mechanical or a shape optimization formulation might be used to solve this problem, which is inverse to the standard kinematic analysis in which the undeformed shape is known and the deformed shape unknown. The objective of the inverse mechanical formulation aims in the inverse deformation map that determines the (undeformed) material configuration, where the spatial (deformed) configuration and the mechanical loads are given. The shape optimization formulation predicts the initial shape in the sense of an inverse problem via successive iterations of the direct problem. In this paper, both methods are presented using a formulation in the logarithmic strain space. An update of the reference configuration of the sheet of metal during the optimization process is proposed in order to avoid mesh distortions. A first example showed the results obtained with both methods in isotropic hyperelasticity. A second example illustrated a simplified deep drawing computed with the shape optimization formulation in isotropic elastoplasticity. From the undeformed shapes obtained with both methods the deformed shapes are acquired with the direct mechanical formulation. Compared to the target deformed shape a minor difference in node coordinates is found. The computation time is lower with the inverse mechanical formulation in hyperelasticity. The update of the reference configuration in the shape optimization formulation allowed to avoid mesh distortions but increased the computational costs. © (2012) Trans Tech Publications.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.toward
Keywords: Inverse form finding; Large strain; Metal forming; Shape optimization