Glass Structures & Engineering

, Volume 3, Issue 1, pp 55–74 | Cite as

Adhesive connections in glass structures—part II: material parameter identification on thin structural silicone

  • Michael DrassEmail author
  • Gregor Schwind
  • Jens Schneider
  • Stefan Kolling
Research Paper


The present paper proposes two methodologies of identifying hyperelastic material parameters of thin structural silicones based on so-called direct and inverse methods. Based on part I of this paper, analytical investigations were performed to conduct homogeneous experiments with structural silicones. To obtain more insight wether or not an experiment provides a homogeneous stress state, the so-called triaxiality was introduced, which allows one to illustrate differences between homogeneous and inhomogeneous experiments. With the help of this scalar, it was possible to design experimental test setups, which ensure a homogeneous stress and strain distribution within the tested rubber-like material. Furthermore an engineering approach to determine the testing speed of arbitrary experiments dependent on one reference testing speed and experiment was presented. This approach ensured equivalent strain energies between arbitrary and reference test specimens during testing, by which expensive strain rate controlled experiments can be relinquished. Based on these analytical studies, experimental data could be provided for the material parameter identification, which exhibits firstly a nearly homogeneous stress state in accordance to the desired stress and strain field of the applied mathematical model and secondly providing nearly equivalent strain energies within different experimental test set-ups and geometries of test specimens. Returning to the present paper, the first methodology identifies simultaneously hyperelastic material parameters based on a set of conventional and homogeneous experimental tests, like uniaxial tension and uniaxial compression, biaxial tension as well as shear-pancake tests. The second methodology determines inversely hyperelastic material parameters utilizing the inverse Finite Element Method based on one single unconventional and inhomogeneous experimental test, here a microindentation test. The main idea is to obtain reliable hyperelastic material parameters based on a single, inhomogeneous experiment to avoid many, time-consuming homogeneous experiments. To validate the inversely determined hyperelastic material parameters, simultaneous multi-experiment data fits are performed to relate the obtained material parameters to those of the microindentation tests. Considering the set of homogeneous experiments, two classical hyperelastic constitutive equations (Neo-Hooke and Mooney–Rivlin) were utilized to determine constitutive parameters. Due to the simplicity of the classical material laws, a more sophisticated, novel phenomenological hyperelastic material law will be proposed and compared with the results of the classical models respectively the results obtained by a modern hyperelastic material model after Kaliske & Heinrich, which generally delivers outstanding results for the material parameter identification.


Thin structural silicone adhesive Material parameter identification Inverse finite element method Incompressible hyperelasticity 

List of symbols


Uniaxial tension test


Uniaxial compression test


Biaxial tension test


Shear pancake test


Microindentation test


Material parameter identification


Inverse finite element method


Finite element model updating


Trust region method


Least absolute residuals


Meta model of optimal prognosis


Root mean squared error

\({\left( \bullet \right) _{\mathrm{{iso}}}}\)


tr\(\left( \bullet \right) \)

Trace of argument

Grad\(\left( \bullet \right) \)

Gradient of argument


Deformation gradient


Relative volume


Right Cauchy-Green tensor


Left Cauchy-Green tensor


Isochoric left Cauchy-Green tensor

\(\lambda _i\)

Principal stretches

\(\varepsilon _i^{\mathrm{{eng}}}\)

Engineering strain

\({I_{\mathbf{{ b}}}}\)

First principal strain invariant of \(\mathbf b \)

\({II_{\mathbf{{ b}}}}\)

Second principal strain invariant of \(\mathbf b \)

\({III_{\mathbf{{ b}}}}\)

Third principal strain invariant of \(\mathbf b \)


Principal engineering stress

\(\sigma _i\)

Principal Cauchy stress


Hydrostatic stress

\(\varPsi ( \bullet )\)

Helmholtz free energy

\(\mathcal {S}\)

Objective function

\(\varPhi _{{k}}\)

Trigger function


Vector of material parameters



We would like to thank Dow Corning Inc. and Interpane Glas Industrie AG gratefully for their support during our studies by providing us testing material.

Supplementary material

40940_2017_48_MOESM1_ESM.xlsx (93 kb)
Supplementary material 1 (xlsx 92 KB)


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Copyright information

© Springer International Publishing AG 2017
corrected publication November 2017

Authors and Affiliations

  1. 1.Institute of Structural Mechanics and DesignTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institute of Mechanics and MaterialsTechnische Hochschule MittelhessenGiessenGermany

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