The paper provides a deepened insight into the role of anisotropy in the analysis of residual stresses in arteries. Residual deformations are modelled following Holzapfel and Ogden (Holzapfel and Ogden 2010, J. R. Soc. Interface 7 , 787–799. ( doi:10.1098/rsif.2009.0357 )), which is based on extensive experimental data on human abdominal aortas (Holzapfel et al. 2007, Ann. Biomed. Eng. 35 , 530–545. ( doi:10.1007/s10439-006-9252-z )) and accounts for both circumferential and axial residual deformations of the individual layers of arteries—intima, media and adventitia. Each layer exhibits distinctive nonlinear and anisotropic mechanical behaviour originating from its unique microstructure; therefore, we use the most general form of strain-energy function (Holzapfel et al. 2015, J. R. Soc. Interface 12 , 20150188. ( doi:10.1098/rsif.2015.0188 )) to derive residual stresses for each layer individually. Finally, the systematic experimental data (Niestrawska et al. 2016, J. R. Soc. Interface 13 , 20160620. ( doi:10.1098/rsif.2016.0620 )) on both mechanical and structural properties of the different layers of the human abdominal aorta facilitate our discussion on (i) the importance of anisotropy in modelling residual stresses; (ii) the variability of residual stresses within the same class of tissue, the abdominal aorta; (iii) the limitations of conventional opening angle method to account for complex residual deformations; and (iv) the effect of residual stresses on the loaded configuration of the aorta mimicking in vivo conditions.

The equine distal limb wound healing model, characterized by delayed re-epithelialization and a fibroproliferative response to wounding similar to that observed in humans, is a valuable tool for the study of biomaterials poised for translation into both the veterinary and human medical markets. In the current study, we developed a novel method of biaxial biomechanical testing to assess the functional outcomes of healed wounds in a modified equine model and discovered significant functional and structural differences in both unwounded and injured skin at different locations on the distal limb that must be considered when using this model in future work. Namely, the medial skin was thicker and displayed earlier collagen engagement, medial wounds experienced a greater proportion of wound contraction during closure, and proximal wounds produced significantly more exuberant granulation tissue. Using this new knowledge of the equine model of aberrant wound healing, we then investigated the effect of a peptide-modified collagen–chitosan hydrogel on wound healing. Here, we found that a single treatment with the QHREDGS (glutamine–histidine–arginine–glutamic acid–aspartic acid–glycine–serine) peptide-modified hydrogel (Q-peptide hydrogel) resulted in a higher rate of wound closure and was able to modulate the biomechanical function toward a more compliant healed tissue without observable negative effects. Thus, we conclude that the use of a Q-peptide hydrogel provides a safe and effective means of improving the rate and quality of wound healing in a large animal model.

We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought beyond complete straightening to turn into eversion. We find that the suggested mathematical solution to these problems always exists and is unique when the solid is modelled as a homogeneous, isotropic, incompressible hyperelastic material with a strain-energy satisfying the strong ellipticity condition. We also provide explicit asymptotic solutions for thin sectors. When the deformations are severe enough, the compressed side of the elastic material may buckle and wrinkles could then develop. We analyse, in detail, the onset of this instability for the Mooney-Rivlin strain energy, which covers the cases of the neo-Hookean model in exact nonlinear elasticity and of third-order elastic materials in weakly nonlinear elasticity. In particular, the associated theoretical and numerical treatment allows us to predict the number and wavelength of the wrinkles. Guided by experimental observations, we finally look at the development of creases, which we simulate through advanced finite-element computations. In some cases, the linearized analysis allows us to predict correctly the number and the wavelength of the creases, which turn out to occur only a few per cent of strain earlier than the wrinkles.

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