Deterministic Material-Based Averaging Theory Model of Collagen Gel Micromechanics

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Abstract
Mechanics of collagen gels, like that of many tissues, is governed by events occurring on a length scale much smaller than the functional scale of the material. To deal with the challenge of incorporating deterministic micromechanics into a continuous macroscopic model, we have developed an averaging-theory-based modeling framework for collagen gels. The averaging volume, which is constructed around each integration point in a macroscopic finite-element model, is assumed to experience boundary deformations homogeneous with the macroscopic deformation field, and a micromechanical problem is solved to determine the average stress at the integration point. A two-dimensional version was implemented with the microstructure modeled as a network of nonlinear springs, and 500 segments were found to be sufficient to achieve statistical homogeneity. The method was then used to simulate the experiments of Tower (Ann. Biomed. Eng., 30, pp. 1221–1233) who performed uniaxial extension of prealigned collagen gels. The simulation captured many qualitative features of the experiments, including a toe region and the realignment of the fibril network during extension. Finally, the method was applied to an idealized wound model based on the characterization measurements of Bowes (Wound Repair Regen., 7, pp. 179–186). The model consisted of a strongly aligned “wound” region surrounded by a less strongly aligned “healthy” region. The alignment of the fibrils in the wound region led to reduced axial strains, and the alignment of the fibrils in the healthy region, combined with the greater effective stiffness of the wound region, caused rotation of the wound region during uniaxial stretch. Although the microscopic model in this study was relatively crude, the multiscale framework is general and could be employed in conjunction with any microstructural model.