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A strain-energy function to model low and high strain non-linearities in highly filled elastomers
Published in Bertrand Huneau, Jean-Benoit Le Cam, Yann Marco, Erwan Verron, Constitutive Models for Rubber XI, 2019
T.W. Hohenberger, R.J. Windslow, Nicola Pugno, J.J.C. Busfield
Another option is to check the Drucker stability criterion which requires that any increment of positive stress results in a positive increment of strain. In essence, the stiffness along a true stress vs. strain curve must always be positive. This guarantees a positive-definite stretch tensor which ensures positive principal stretch ratios, a necessity by definition of stretch. Empirically confirming Drucker stability is straightforward in homogeneous modes of deformation, but even so, it may be violated during inhomogeneous deformations. For this work, Drucker stability was confirmed for UT, UC, PS, ET, and EC deformations. Stability during inhomogeneous deformation was empirically checked with FE implementation.
Multi-objective optimization of hyperelastic material constants
Published in Alexander Lion, Michael Johlitz, Constitutive Models for Rubber X, 2017
S. Connolly, D. Mackenzie, T. Comlekci
Prior to optimization, Abaqus’ evaluation tool was used for comparison to gain material constants for the selected hyperelastic model. This tool requires only the input of the experimental data sets and the selection of the material models to be evaluated. Abaqus then generates the ‘optimal’ hyperelastic constants using linear least squares method or a Levenberg-Marquardt algorithm for the Yeoh and Ogden curve fits respectively. The stability is then checked for uniaxial, planar and equibiaxial deformation in tension and compression within the nominal strain range: −0.9 ≤ ε ≤ 9.0, using the Drucker stability criterion. (Abaqus, 2016)
A constrained particle swarm optimization algorithm for hyperelastic and visco-hyperelastic characterization of soft biological tissues
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2020
Mohammadreza Ramzanpour, Mohammad Hosseini-Farid, Mariusz Ziejewski, Ghodrat Karami
Moreover, another constraint can be extracted from the Mooney-Rivlin model based on the Drucker stability criterion. Drucker stability criterion [59] states that irrespective of the material deformation, the internal energy must increase, formulated as the following for the uniaxial loading.