Abstract
One of the main troubleshooting issues to deal with involves the material properties and definition of nonlinearity after the elastic behavior. In this chapter, details of large strain connected with the material law of behavior, especially, those used for hyperelasticity and rubber materials are given. The user will also find useful informations when the material definition is coupled with the User Material (UMAT) file to establish the correct settings or debugging protocol. The classic basis of a viscoelastic–plastic material behavior is still explained with a simple uniaxial stress versus strain curve, in order to prevent the reader from becoming overloaded by too many theory details, for instance, those available inside theoretical Abaqus documentation.
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Notes
- 1.
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.
- 2.
A complement of information about the usage of hyperelastic materials can be found in the Abaqus Analysis User’s Guide in Sect. 22.5 Hyperelasticity.
- 3.
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference [3]. The Jaumann rate of the Cauchy stress is a further specialization of the Lie derivative (Truesdell rate). For this rate, \(\omega \) is the spin tensor (the skew part in Eq. 4.3 of the velocity gradient) as follows:
$$\begin{aligned} \tilde{\sigma } = \dot{\sigma } + \sigma .\omega - \omega .\sigma \end{aligned}$$(5.14)Many constitutive equations are designed in the form of a relation between a stress rate and a strain rate (or the rate of deformation tensor). The mechanical response of a material should not depend on the frame of reference. In other words, material constitutive equations should be frame indifferent (objective). If the stress and strain measures are material quantities then objectivity is automatically satisfied. However, if the quantities are spatial, then the objectivity of the stress rate is not guaranteed even if the strain rate is objective.
- 4.
See Abaqus Theory Guide v6.14 in Sect. 4.6.2 Fitting of hyperelastic and hyperfoam constants.
- 5.
See Abaqus Theory Guide v6.14 in Sect. 4.6.3 Anisotropic hyperelastic material behavior.
- 6.
See Abaqus User Subroutines Reference Guide v6.14 Sect. 1.1.38 UHYPER User subroutine to define a hyperelastic material.
- 7.
See Abaqus User Subroutines Reference Guide v6.14 in Sect. 1.1.41 UMAT User subroutine to define a material’s mechanical behavior.
- 8.
See in Abaqus Theory Guide v6.14 in Sect. 3.2.2 Solid element formulation.
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Boulbes, R.J. (2020). Materials. In: Troubleshooting Finite-Element Modeling with Abaqus. Springer, Cham. https://doi.org/10.1007/978-3-030-26740-7_5
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DOI: https://doi.org/10.1007/978-3-030-26740-7_5
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