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  1. Abstract

    This work presents a stabilized formulation for phase‐field fracture of hyperelastic materials near the limit of incompressibility. At this limit, traditional mixed displacement and pressure formulations must satisfy the inf‐sup condition for solution stability. The mixed formulation coupled with the damage field can lead to an inhibition of crack opening as volumetric changes are severely penalized effectively creating a pressure‐bubble. To overcome this bottleneck, we utilize a mixed formulation with a perturbed Lagrangian formulation which enforces the incompressibility constraint in the undamaged material and reduces the pressure effect in the damaged material. A mesh‐dependent stabilization technique based on the residuals of the Euler–Lagrange equations multiplied with a differential operator acting on the weight space is used, allowing for linear interpolation of all field variables of the elastic subproblem. This formulation was validated with three examples at finite deformations: a plane‐stress pure‐shear test, a two‐dimensional geometry in plane‐stress, and a three‐dimensional notched sample. In the last example, we incorporate a hybrid formulation with an additive strain energy decomposition to account for different behaviors in tension and compression. The results show close agreement with analytical solutions for crack tip opening displacements and performs well at the limit of incompressibility.

  2. Free, publicly-accessible full text available January 9, 2024
  3. Free, publicly-accessible full text available October 26, 2023
  4. Efficiently manipulating and reproducing collagen (COL) alignment in vitro remains challenging because many of the fundamental mechanisms underlying and guiding the alignment process are not known. We reconcile experiments and coarse-grained molecular dynamics simulations to investigate the mechanical behaviors of a growing COL scaffold and assay how changes in fiber alignment and various cross-linking densities impact their alignment dynamics under shear flow. We find higher cross-link densities and alignment levels significantly enhance the apparent tensile/shear moduli and strength of a bulk COL system, suggesting potential measures to facilitate the design of stronger COL based materials. Since fibril alignment plays a key factor in scaffold mechanics, we next investigate the molecular mechanism behind fibril alignment with Couette flow by computationally investigating the effects of COL's structural properties such as chain lengths, number of chains, tethering conditions, and initial COL conformations on the COL's final alignment level. Our computations suggest that longer chain lengths, more chains, greater amounts of tethering, and initial anisotropic COL conformations benefit the final alignment, but the effect of chain lengths may be more dominant over other factors. These results provide important parameters for consideration in manufacturing COL-based scaffolds where alignment and cross-linking are necessary for regulating performance.
  5. The stiffnesses, β-structures, hydrogen bonds, and vibrational modes of wild-type collagen triple helices are compared with osteogenesis imperfecta-related mutants using integrative structural and dynamic analysis via molecular dynamics simulations and Markov state models. Differences in these characteristics are strongly related to the unwound structural states in the mutated regions that are specific to each mutation.