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    Biomechanics of Planar Collagenous Soft Tissues: Heterogeneities and Averaged Material Descriptions
    (University of Waterloo, 2026-11-03) Amiri, Arya
    The overarching goal of this thesis is to advance the understanding of biomechanical heterogeneities and averaged material description of planar collagenous soft biological tissues through experimental, constitutive, and computational approaches, while also refining and adapting existing methods to better suit the specific characteristics and complexities of soft tissues. Despite decades of research documenting the mechanical heterogeneity of soft tissues, existing frameworks have yet to be fully reconciled with the experimental evidence. As the first objective, reindeer back skin and velvet (antler skin) are mechanically tested using a biaxial tensile testing machine, providing a basis for demonstrating the significance of regional mechanical heterogeneity. Motivated to accurately represent each tissue region, the second objective evaluates the concept of averaged material descriptions, specifically ``response averaging" and ``parameter averaging", across various hyperelastic constitutive models, ranges of deformations, and test types, to accurately represent groups of specimens. These findings are further used in the third objective to study whether it is possible to accurately describe local spatial biomechanical heterogeneity with sufficient precision from only a few samples. Specifically, it is done by applying the averaging methods to both experimental stress-strain data and constitutive model outputs to accurately predict mechanically untested intermediate regions between adjacent mechanically characterized tissue regions. Having validated the predictive power of the averaged-material-description approach, the fourth objective of this thesis develops a framework for incorporating local spatial mechanical heterogeneity into finite element (FE) simulations of soft biological tissues. Specifically, motivated by functionally graded materials and using an averaging approach to describe local heterogeneity it proposes to model heterogeneous material constants expressed as continuous Fourier functions of spatial positions. Through case studies of aortic aneurysms and skin tissue, it is demonstrated that a continuous heterogeneous material definition leads to a different stress distribution compared with a homogeneous model and avoids stress concentrations associated with a segmental heterogeneous model. Hence, the integration of regional mechanical characterization and the proposed averaging techniques, combined with the developed method for implementing the mechanical heterogeneity into FEM simulations, explored across all objectives of this thesis, sets a new standard for studying soft tissue biomechanics.
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    Confinement effects on the miscibility of block copolymer blends
    (Springer Nature, 2016) Spencer, R. K. W.; Matsen, and M. W.
    Thin films of long and short symmetric AB diblock copolymers are examined using self-consistent field theory (SCFT). We focus on hard confining walls with a preference for the A component, such that the lamellar domains orient parallel to the film with an even number nu of monolayers. For neat melts, confinement causes the lamellar period, D, to deviate from its bulk value, D_b, in order to be commensurate with the film thickness, i.e., L=nu D/2. For blends, however, the melt also has the option of macrophase separating into nu^(l) large and nu^(s) small monolayers so as to provide a better fit, where L = nu^(l) D^(l)/2 + nu^(s) D^(s)/2. In addition to performing full SCFT calculations of the entire film, we develop a semi-analytical calculation for the coexistence of thick and thin monolayers that helps explain the complicated interplay between miscibility and commensurability.
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    Domain bridging in thermoplastic elastomers of star block copolymer
    (American Chemical Society, 2017) Spencer, Russell K. W.; Matsen, Mark W.
    The performance of thermoplastic elastomers composed of block copolymers is dependent upon the molecular bridges linking together the discrete minority domains. Here we devise a strategy for calculating the bridging statistics for complex block copolymer architectures, using self-consistent field theory. The method is demonstrated on (AB)_M stars with M identical diblock arms. The fraction of molecules forming bridges, nu_b, is found to increase rapidly with M to values well beyond that of conventional ABA triblock copolymers. Once M is of order 10, virtually all molecules form bridges and furthermore their arms tend to be distributed equally among neighboring minority domains. These high bridging fractions combined with the tendency of single molecules to bridge multiple domains makes diblock-arm stars an excellent candidate for improved thermoplastic elastomers.
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    Detection of surface enrichment driven by molecular weight disparity in virtually monodisperse polymers
    (American Chemical Society, 2018) Hill, Jacob A.; Endres, Kevin J.; Mahmoudi, Pendar; Matsen, Mark W.; Wesdemiotis, Chrys; Foster, Mark D.
    The preference for a shorter chain component at a polymer blend surface impacts surface properties key to application specific performance. While such segregation is known for blends containing low molecular weight additives or systems with large polydispersity, it has not been reported for anionically polymerized polymers that are viewed, in practice, as monodisperse. Observations with surface layer matrix-assisted laser desorption ionization time-of-flight mass spectrometry (SL-MALDI-ToF-MS), which distinguishes surface species without labelling, and provides the entire molecular weight distribution, demonstrate that entropically driven surface enrichment of shorter chains occurs even in low polydispersity materials. For 6 kDa polystyrene the number average molecular weight (Mn) at the surface is ca. 300 Da (5%) lower than that in the bulk and for 7 kDa poly(methyl methacryalate) the shift is ca. 500 Da. These observations are in qualitative agreement with results from a mean-field theory that considers a homopolymer melt with a molecular-weight distribution matched to the experiments.
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    Field-theoretic simulations of bottlebrush copolymers
    (American Institute of Physics (AIP), 2018) Spencer, Russell K. W.; Matsen, Mark W.
    Traditional particle-based simulations struggle with large bottlebrush copolymers, consisting of many side chains grafted to a backbone. Field-theoretical simulations (FTS) allow us to overcome the computational demands in order to calculate their equilibrium behavior. We consider bottlebrushes where all grafts are symmetric diblock copolymers, focusing on the order-disorder transition (ODT) and the size of ordered domains. Increasing the number of grafts and decreasing the spacing between them both raise the transition temperature. The ODT and lamellar period asymptotically approach constants as the number of grafts increases. As the spacing between grafts becomes large, the bottlebrushes behave like diblock copolymers, and as it becomes small, they behave like starblock copolymers. In between, the period increases, reaching a maximum when the spacing is approximately 0.35 times the length of the grafts. Comparison of FTS with mean-field calculations allows us to assess the effect of compositional fluctuations. Fluctuations suppress ordering, while having little effect on the period, as is the case for diblock copolymers.