A comparison of projection-based model reduction concepts in the context of nonlinear biomechanics

Radermacher, Annika; Reese, Stefanie

doi:10.1007/s00419-013-0742-9

Cited by 25 publications

(20 citation statements)

References 68 publications

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“…In the case of nonlinear mechanical RVE problems, it is still necessary to evaluate all local quantities (stress and material tangent) in each evaluation point of the RVE (see for a more detailed derivation of the presently used POD method in the nonlinear context [42,43]). In order to reduce the computational effort further, extended projection-based reduction methods have been developed (e.g.…”

Section: Solution Of Reduced Rve Boundary Value Problemmentioning

confidence: 99%

Displacement-based multiscale modeling of fiber-reinforced composites by means of proper orthogonal decomposition

Radermacher¹,

Bednarcyk

Stier³

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

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Many applications are based on the use of materials with heterogeneous microstructure. Prominent examples are fiber-reinforced composites, multi-phase steels or soft tissue to name only a few. The modeling of structures composed of such materials is suitably carried out at different scales. At the micro scale, the detailed microstructure is taken into account, whereas the modeling at the macro scale serves to include sophisticated structural geometries with complex boundary conditions. The procedure is crucially based on an intelligent bridging between the scales. One of the methods derived for this purpose is the meanwhile well established FE 2 method which, however, leads to a very high computational effort. Unfortunately, this impedes the use of the FE 2 method and similar methodologies for practically relevant problems as they occur e.g. in production or medical technology. The goal of the present paper is to significantly improve computational efficiency by using model reduction. The suggested procedure is very generally applicable. It holds for large deformations as well as for all relevant types of inelasticity. An important merit of the work is the computation of the consistent tangent operator based on the reduced stiffness matrix of the microstructure. In this way a very fast (in most cases quadratic) convergence within the Newton iteration at macro level is achieved.

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Section: Solution Of Reduced Rve Boundary Value Problemmentioning

confidence: 99%

Displacement-based multiscale modeling of fiber-reinforced composites by means of proper orthogonal decomposition

Radermacher¹,

Bednarcyk

Stier³

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the solution of typically large systems of equations resulting from nonlinear engineering problems, efficient numerical procedures are desired. One possibility to reduce the computational effort and simulation time is the use of model reduction methods, e. g. the proper orthogonal decomposition (POD), which is a projection-based reduction method with applications in both linear and nonlinear solid mechanics [4]. For applying the POD, a reasonable number of snapshots is necessary.…”

Section: Introductionmentioning

confidence: 99%

“…For this investigation, the POD is applied to the modeling of the z-pin pullout. However, the POD can also be applied to other phenomena such as plastic deformation of structures due to seismic loads [1] or in nonlinear biomechanics [4].…”

Section: Introductionmentioning

confidence: 99%

Ideas regarding a physically motivated selection of snapshots for POD calculations – a potential application to z‐pin pullout?

Weber

Fangye

Zastrau

et al. 2017

Proc Appl Math and Mech

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In order to keep the computational effort manageable, which arises from the modeling of micro-heterogeneous materials, methods of model reduction are more and more used in computational mechanics. In this contribution, the proper orthogonal decomposition is analyzed. Applying this method to the pullout of metallic fibers, conclusions are drawn which relate the proper orthogonal modes to the mode shapes related to this physical phenomenon.

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“…In the recent decades a lot of work is done to extend existent model reduction methods or to develop new model reduction methods for non-linear problems. The proper orthogonal decomposition (POD) method is successfully applied in the context of non-linear solid mechanics with hyperelastic material laws [4,5]. But there are still problems of the efficiency of POD for highly non-linear behavior which are observed in forming processes.…”

Section: Introductionmentioning

confidence: 99%

Selective proper orthogonal decomposition model reduction for forming simulations

Radermacher

Reese

Hadoush

2013

Proc Appl Math and Mech

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Robot-based incremental sheet metal forming is a cost-effective and flexible method for prototype and low batch size production. The simulation of such processes is very challenging and elaborate from the computational point of view. To reduce the computational effort model reduction techniques such as proper orthogonal decomposition (POD) can be applied. But the reduction of highly non-linear models in solid mechanics for example forming simulation still leads to problems of efficiency and accuracy. Therefore, the aim of this paper is to present an alternative way to use POD for forming processes. The presented selective POD (SPOD) method is used to split the model into two domains depending on the degree of plastic strain. Only the domain with approximately linear elastic behavior will be reduced by using POD. Utilizing the SPOD method for the example of forming a horizontal flute reduces the computational time up to around 30 per cent. High accuracy with approximation errors smaller than one per mill is achieved.

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A comparison of projection-based model reduction concepts in the context of nonlinear biomechanics

Cited by 25 publications

References 68 publications

Displacement-based multiscale modeling of fiber-reinforced composites by means of proper orthogonal decomposition

Displacement-based multiscale modeling of fiber-reinforced composites by means of proper orthogonal decomposition

Ideas regarding a physically motivated selection of snapshots for POD calculations – a potential application to z‐pin pullout?

Selective proper orthogonal decomposition model reduction for forming simulations

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