A unified determinant-preserving formulation for compressible/incompressible finite viscoelasticity
This paper presents a formulation alongside a numerical solution algorithm to describe the mechanical response of bodies made of a large class of viscoelastic materials undergoing arbitrary quasistatic finite deformations. With the objective of having a unified formulation that applies to a wide ran...
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| Vydáno v: | Journal of the mechanics and physics of solids Ročník 177; s. 105312 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
England
Elsevier Ltd
01.08.2023
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| Témata: | |
| ISSN: | 0022-5096 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | This paper presents a formulation alongside a numerical solution algorithm to describe the mechanical response of bodies made of a large class of viscoelastic materials undergoing arbitrary quasistatic finite deformations. With the objective of having a unified formulation that applies to a wide range of highly compressible, nearly incompressible, and fully incompressible soft organic materials in a numerically tractable manner, the viscoelasticity is described within a Lagrangian setting by a two-potential mixed formulation. In this formulation, the deformation field, a pressure field that ensues from a Legendre transform, and an internal variable of state Fv that describes the viscous part of the deformation are the independent fields. Consistent with the experimental evidence that viscous deformation is a volume-preserving process, the internal variable Fv is required to satisfy the constraint detFv=1. To solve the resulting initial–boundary-value problem, a numerical solution algorithm is proposed that is based on a finite-element (FE) discretization of space and a finite-difference discretization of time. Specifically, a Variational Multiscale FE method is employed that allows for an arbitrary combination of shape functions for the deformation and pressure fields. To deal with the challenging non-convex constraint detFv=1, a new time integration scheme is introduced that allows to convert any explicit or implicit scheme of choice into a stable scheme that preserves the constraint detFv=1 identically. A series of test cases is presented that showcase the capabilities of the proposed formulation. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 All authors declare that they do not have any financial or personal relationships that may be perceived as influencing their work. Author Statement |
| ISSN: | 0022-5096 |
| DOI: | 10.1016/j.jmps.2023.105312 |