Adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements

Widany, Kai‐Uwe; Mahnken, Rolf

doi:10.1016/j.cma.2012.06.017

Cited by 22 publications

(19 citation statements)

References 44 publications

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“…. , n s , in a precise manner; see, e.g., [Viertl 1996]. However, due to imprecision of measurements this is not realistic.…”

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

“…Such quantities of interest are characterized by functionals Q(u) of the solutions u to (6). Quantities of interest have been given much attention in adaptive strategies over the last several years; see, e.g., [Rüter 2004;Johansson et al 2007;Bangerth and Rannacher 2003;Widany and Mahnken 2012;Mahnken 2013] and, in the context of multiscale modeling, [Oden et al 2006]. Possible realizations of the quantity of interest may be (1) displacement at a certain point of the body P ∈ B with coordinates X P ∈ B at the end of loading with time…”

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

“…To this end, we introduce a so-called quantity of interest (or goal function) as an output quantity of the fuzzy analysis. Quantities of interest have been given much attention, e.g., in adaptive strategies over the last several years; see, e.g., [Rüter 2004;Johansson et al 2007;Bangerth and Rannacher 2003;Widany and Mahnken 2012;Mahnken 2013].…”

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

“…Equation (15b) introduces a second observation operator D : U → D, which maps the state variable u(s) ∈ U to points D(u(s)) in the data space D ∈ ‫ޒ‬ n d . Moreover, in order to point out the "design driven" data as a result of the state problem (6), (15b) introduces the reduced observation operator d : S → D to transform design variables s to the observation space [Vexler 2004]. In index notation (15b) can be written as d k (s) := D k (u(s)), k = 1, .…”

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

“…• They give the basis for adaptive refinement of the underlying FE discretization [Rüter 2004;Johansson et al 2007;Bangerth and Rannacher 2003;Widany and Mahnken 2012;Mahnken 2013].…”

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

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A variational formulation for fuzzy analysis in continuum mechanics

Mahnken¹

2017

Math. Mech. Compl. Sys.

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In order to improve the credibility of modern simulation tools, uncertainties of different kinds have to be considered. This work is focused on epistemic uncertainties in the framework of continuum mechanics, which are taken into account by fuzzy analysis. The underlying min-max optimization problem of the extension principle is approximated by α-discretization, resulting in a separation of minimum and maximum problems. To become more universal, socalled quantities of interest are employed, which allow a general formulation for the target problem of interest. In this way, the relation to parameter identification problems based on least-squares functions is highlighted. The solutions of the related optimization problems with simple constraints are obtained with a gradient-based scheme, which is derived from a sensitvity analysis for the target problem by means of a variational formulation. Two numerical examples for the fuzzy analysis of material parameters are concerned with a necking problem at large strain elastoplasticity and a perforated strip at large strain hyperelasticity to demonstrate the versatility of the proposed variational formulation.

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“…. , n s , in a precise manner; see, e.g., [Viertl 1996]. However, due to imprecision of measurements this is not realistic.…”

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

“…• They give the basis for adaptive refinement of the underlying FE discretization [Rüter 2004;Johansson et al 2007;Bangerth and Rannacher 2003;Widany and Mahnken 2012;Mahnken 2013].…”

Section: Variational Formulation For Fuzzy Analysis In Continuum Mechmentioning

confidence: 99%

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A variational formulation for fuzzy analysis in continuum mechanics

Mahnken¹

2017

Math. Mech. Compl. Sys.

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Identification of Material Parameters for Constitutive Equations

Mahnken

2017

Encyclopedia of Computational Mechanics Second Edition

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This contribution addresses various topics on parameter identification for constitutive equations on the basis of experimental data. Starting from the basic characteristics of inverse problems illustrated by simple examples, four different identification methods are introduced. Then, particular aspects of the least–squares approach are Outlined, such as direct and adjoint state differentiation methods, optimization, discretization error of FEM (finite element method), model error quantification of hierarchical modeling, consequences of instabilities, stochastic simulation, and statistical analysis. Uniform small strain problems as well as non‐uniform large strain problems are considered, where, for the latter, finite element results are incorporated into the optimization process. The examples are concerned with goal‐oriented adaptive refinement and statistical analysis for hierarchical modeling on the basis of an optical method for generation of experimental data in large strain elasticity.

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Sequential biaxial stretching of polycarbonate‐films for characterization of strain‐induced anisotropy

2018

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Amorphous polymers consist of polymer‐chains whose alignment is a well‐known microstructural evolution effect due to stretching of polymers. This so‐called morphology‐development is investigated in the literature, where for thin films simultaneous biaxial stretching is distinguished from sequential biaxial stretching. Both procedures have a strong influence on the macroscopic properties of an initially isotropic material, resulting in induced anisotropy. This work concentrates on sequential biaxial stretching of cold forming realized by tensile testing. To this end, thin polycarbonate films are examined in 2 loading phases: In the first preloading phase anisotropy is induced and in the consecutive second reloading phase, the material direction is varied. Optical measurements support the analysis of highly inhomogenous strain fields. As a main result two‐dimensional strain contours are obtained from test data which will set a basis for parameter identification of constitutive equations for strain‐induced anisotropy in the future.

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Adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements

Cited by 22 publications

References 44 publications

A variational formulation for fuzzy analysis in continuum mechanics

A variational formulation for fuzzy analysis in continuum mechanics

Identification of Material Parameters for Constitutive Equations

Sequential biaxial stretching of polycarbonate‐films for characterization of strain‐induced anisotropy

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