Modeling Viscoelastic Behavior in Transient Analyses

Blelloch, Paul; Austin, Eric M.

doi:10.1007/978-3-030-47709-7_8

Cited by 1 publication

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“…A close examination of recently published articles reveals many interested in the modeling of transient behavior in viscoelastic finite elements. Many employ these common constitutive relations and often use a step-wise integration scheme, such as the Newmark-Beta method [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A generalized time-domain constitutive finite element approach for viscoelastic materials

Abercrombie,

Gregory McDaniel,

Walsh

2024

Modelling Simul. Mater. Sci. Eng.

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Despite the existence of time domain finite element formulations forviscoelastic materials, there are still substantial ways to improve the analysis. Tothe authors’ knowledge, the formulation of the problem is always done with respectto a single constitutive relation and so limits the implementer to a single scheme withwhich to model relaxation. Furthermore, all current constitutive relations involvethe finding of fitting parameters for an analytical function, which is a sufficientlypainful process to warrant the study of best fitting procedures to this day. Incontrast, this effort is the first full derivation of the two dimensional problem fromfundamental principles. It is also the first generalization of the problem, which freesusers to select constitutive relations without re-derivation or re-expression of theproblem. This approach is also the first approach to the problem that could leadto the elimination of constitutive relations for representing relaxation in viscoelasticmaterials. Following, the full derivation, several common constitutive relations areoutlined with analysis of how they may best be implemented in the generalized form.Several expressions for viscoelastic terms are also provided given linear, quadratic, andexponential interpolation assumptions.

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