ArticleProceedings. Mathematical, physical, and engineering sciences2018
A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 5 papers.
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5 citing papers in PubMed.
- Quasi-Static Deformations of Fiber-Reinforced Materials Based on Hyperelasticity.Materials (Basel, Switzerland) · 2026Article
- Mechanical characterization of human umbilical and chorionic plate arteries affected by fetal growth restriction.PNAS nexus · 2026Article
- Characterization of mechanical damage and viscoelasticity on aortas from guinea pigs subjected to hypoxia.Scientific reports · 2025Article
- Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics.Frontiers in cell and developmental biology · 2021Review
- Soft metamaterials with dynamic viscoelastic functionality tuned by pre-deformation.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2019Article
Corrections and comments
- Erratum issued
Authors and funding
3 authors.
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Abstract
The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean
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