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摘要
This paper presents a new micromechanical based approach for the modeling of the highly anisotropic and non-linear stiffening response of fibrous materials with random network microstructure at finite strains. The first key aspect of the proposed approach arises from the experimentally justified need to model the elastic microscopic response of the constituent fibers, which are one-dimensional elements, as linear elastic. This linear elastic behavior is modified in the lower strain regime to account for the inherent fiber undulations and the associated fiber unfolding phenomena. Another key aspect is the reorientation of these fibers which is identified as one primary mechanism for the overall macroscopic stiffening. The one-dimensional elements are statistically distributed as unit vectors in a non-uniform manner over an affine referential network space of orientations represented by a unit circle in the two-dimensional case of interest here. A physically motivated reorientation of these unit vectors is achieved by a bijective map which asymptotically aligns them with the maximum loading direction in the referential orientation space. A rate-independent evolution law for this map is sought by a physically motivated assumption to maintain the overall elastic framework of the proposed formulation. A closed form solution to the new evolution law is also presented which allows faster computation of updating orientations without resorting to numerical integration or storing history variables. The unit vectors upon reorientation in the referential orientation space are then mapped to the spatial orientation space by the macrodeformation gradient to compute the macroscopic Kirchhoff stress and the associated spatial elasticity modulus. Reorientation of these unit vectors results in the evolution of the associated probability density function which is also computed in closed form depending on the initial probability density. However, it is shown that for a bijective reorientation map, the homogenization of micro-variables over the referential orientation space is independent of the evolving probability density function. Homogeneous deformation tests are performed to highlight the elastic framework of the proposed formulation. A direct comparison of the numerical results with the experimental results from the literature is made which demonstrates the predictive capabilities of the proposed formulation.
- 出版日期2014-4
