Viscoelastic properties of fibre-network materials

International Journal of Engineering Science, 2014

Gradual fiber recruitment is one of the stiffening mechanisms observed in collagen reinforced biological tissues. Given the natural statistical distribution of the fiber orientation in biological materials, in agreement with experimental findings it is reasonable to assume a stochastic nature of the fiber recruitment mechanism. In the present study, we consider the presence of a stochastic recruitment mechanism in a hyperelastic fiber reinforced material model characterized by statistical distributions of the fiber orientation. The material model is based on a second order approximation of the strain energy density, considered as a function of the fourth pseudo-invariant I 4 , and on the multiplicative decomposition of the deformation gradient and, consequently, of the stretch. For a planar distribution of the fiber orientation, we choose an exponential analytical expression of the strain energy density and derive the stress and stiffness tensors. The mechanical behavior of the model is assessed, through uniaxial tests, by distinguishing the mean and the variance contributions of I 4 to the model is validated against experimental data.

Annals of Biomedical Engineering, 2012

While collagen is recognized as the predominant mechanical component of soft connective tissues, the role of the non-fibrillar matrix (NFM) is less well understood. Even model systems, such as the collagen-agarose co-gel, can exhibit complex behavior, making it difficult to identify relative contributions of specific tissue constituents. In the present study, we developed a two-component microscale model of collagen-agarose tissue analogs and used it to elucidate the interaction between collagen and NFM in uniaxial tension. Collagen fibers were represented with Voronoi networks, and the NFM was modeled as a neo-Hookean solid. Model predictions of total normal stress and Poisson's ratio matched experimental observations well (including high Poisson's values of~3), and the addition of NFM led to composition-dependent decreases in volume change and increases in fiber stretch. Because the NFM was more resistant to volume change than the fiber network, extension of the composite led to pressurization of the NFM. Within a specific range of parameter values (low shear modulus and moderate Poisson's ratio), the magnitude of the reaction force decreased relative to this pressurization component resulting in a negative (compressive) NFM stress in the loading direction, even though the composite tissue was in tension.

Biomaterials, 2015

In this paper, we present a general, fibril-based structural constitutive theory which accounts for three material aspects of crosslinked filamentous materials: the single fibrillar force response, the fibrillar network model, and the effects of alterations to the fibrillar network. In the case of the single fibrillar response, we develop a formula that covers the entropic and enthalpic deformation regions, and introduce the relaxation phase to explain the observed force decay after crosslink breakage. For the filamentous network model, we characterize the constituent element of the fibrillar network in terms its end-to-end distance vector and its contour length, then decompose the vector orientation into an isotropic random term and a specific alignment, paving the way for an expanded formalism from principal deformation to general 3D deformation; and, more important, we define a critical core quantity over which macroscale mechanical characteristics can be integrated: the ratio of...

Theoretical and Applied Fracture Mechanics, 1997

A nonlinear Zener model is developed to model the viscoelastic behavior of collagen fibers, a building block of the biological soft tissues in the skeletal system. The effects of the strain rate dependency, the loading history, rest, and recovery on the stress-strain relationship of collagen fibers were investigated using the Zener model. The following loading conditions were simulated: (1) the stress relaxation after cyclic loading, (2) the constant strain rate loading before and after cyclic loading (stabilization) and post recovery, and (3) the constant strain rate loading over a wide range of loading rates. In addition, we explored the critical values of stress and strain using different failure criteria at different strain rates. Four major findings were derived from these simulations. First of all, the stress relaxation is larger with a smaller number cycles of preloading. Second, the strain rate sensitivity diminishes after the stabilization and recovery from resting. Third, the stress-strain curve is dependent on the strain rate except for extreme loading conditions (very fast or slow rates of loading). Finally, the strain energy density (SED) criteria may be a more practical failure criterion than the ultimate stress or strain criterion for collagen fiber. These results provide the basis for interpretation of the viscoelastic and failure behaviors of complex structures such as spinal functional units with more economical CPU than full finite element modeling of the whole structure would have required.

Journal of the Mechanical Behavior of Biomedical Materials, 2014

The fibrous matrices are widely used as scaffolds for the regeneration of load-bearing tissues due to their structural and mechanical similarities with the fibrous components of the extracellular matrix. These scaffolds not only provide the appropriate microenvironment for the residing cells but also act as medium for the transmission of the mechanical stimuli, essential for the tissue regeneration, from macroscopic scale of the scaffolds to the microscopic scale of cells. The requirement of the mechanical loading for the tissue regeneration requires the fibrous scaffolds to be able to sustain the complex threedimensional mechanical loading conditions. In order to gain insight into the mechanical behavior of the fibrous matrices under large amount of elongation as well as shear, a statistical model has been formulated to study the macroscopic mechanical behavior of the electrospun fibrous matrix and the transmission of the mechanical stimuli from scaffolds to the cells via the constituting fibers. The study establishes the load-deformation relationships for the fibrous matrices for different structural parameters. It also quantifies the changes in the fiber arrangement and tension generated in the fibers with the deformation of the matrix. The model reveals that the tension generated in the fibers on matrix deformation is not homogeneous and hence the cells located in different regions of the fibrous scaffold might experience different mechanical stimuli. The mechanical response of fibrous matrices was also found to be dependent on the aspect ratio of the matrix. Therefore, the model establishes a structuremechanics interdependence of the fibrous matrices under large deformation, which can be utilized in identifying the appropriate structure and external mechanical loading conditions for the regeneration of load-bearing tissues.

Materials, 2015

Scaffold mechanical properties are essential in regulating the microenvironment of three-dimensional cell culture. A coupled fiber-matrix numerical model was developed in this work for predicting the mechanical response of collagen scaffolds subjected to various levels of non-enzymatic glycation and collagen concentrations. The scaffold was simulated by a Voronoi network embedded in a matrix. The computational model was validated using published experimental data. Results indicate that both non-enzymatic glycation-induced matrix stiffening and fiber network density, as regulated by collagen concentration, influence scaffold behavior. The heterogeneous stress patterns of the scaffold were induced by the interfacial mechanics between the collagen fiber network and the matrix. The knowledge obtained in this work could help to fine-tune the mechanical properties of collagen scaffolds for improved tissue regeneration applications.

Journal of Biomechanical Engineering, 2012

A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

In the present work, we demonstrate that the mesoscopic in-plane mechanical behavior of membrane elastomeric scaffolds can be simulated by replication of actual quantified fibrous geometries. Elastomeric electrospun polyurethane (ES-PEUU) scaffolds, with and without particulate inclusions, were utilized. Simulations were developed from experimentally-derived fiber network geometries, based on a range of scaffold isotropic and anisotropic behaviors. These were chosen to evaluate the effects on macro-mechanics based on measurable geometric parameters such as fiber intersections, connectivity, orientation, and diameter. Simulations were conducted with only the fiber material model parameters adjusted to match the macro-level mechanical test data. Fiber model validation was performed at the microscopic level by individual fiber mechanical tests using AFM. Results demonstrated very good agreement to the experimental data, and revealed the formation of extended preferential fiber orientations spanning the entire model space. We speculate that these emergent structures may be responsible for the tissue-like macroscale behaviors observed in electrospun scaffolds. To conclude, the modeling approach has implications for (1) gaining insight on the intricate relationship between fabrication variables, structure, and mechanics to manufacture more functional devices/materials, (2) elucidating the effects of cell or particulate inclusions on global construct mechanics, and (3) fabricating better performing tissue surrogates that could recapitulate native tissue mechanics.

The Huffington Post, 2015

We often hear it said that there are too many people on Earth, that ‘overpopulation’ is an existential threat, and that fewer people might consume proportionately less, resulting in some easy environmental gains such as less carbon output and fewer species extinctions. It’s a seductive logic, but is it true?

Agradecimientos racias, de corazón. Nunca es fácil escribir esta parte, y más cuando tanta gente ha contribuido de diferentes maneras a realizar este libro. Gracias a mis padres, mi hermano y mi maravillosa familia, pues siempre han sido mi motor y mi red de seguridad.