This article presents a multi-scale progressive micro-mechanical fatigue model. The model employs fundamental equation of the kinetic theory of fracture to calculate damage parameters of both fiber and matrix during cyclic loading. In order to adapt the equation, required material coefficients of the constituents can be achieved from fatigue test results of longitudinal and transverse unidirectional composites, only. Sharing stress capacities of fiber and matrix are determined using a modified progressive micro-mechanical bridging model in the presence of damage. The damage parameters in the constituents are calculated employing two different equivalent scalars. However, during sinusoidal load application, these damage parameters are also updated using a first kind Bessel function of amplitude stresses in the constituents as well as their material coefficients. The enhanced formulation is then implemented into the commercial finite element software of ABAQUS via a developed user material (UMAT) subroutine utilizing a suitable failure criteria and an own solution algorithm. Advantages of the proposed model are assessed and comparisons with available solutions are presented.
This work aims to calculate interlaminar stress distribution through the thickness of multilayered composite shell structures by employing a novel nonlinear layer-wise shell finite element formulation. Adapting the Mindlin-Reissner theory in each layer, the shear-deformable layer-wise shell element presents the interlaminar shear stress distributions by increasing the number of layers. The interlaminar normal stress distribution is then determined by the finite difference solution of the general form of equilibrium equation in the non-orthogonal curvilinear grid along the Gaussian points. Two boundary conditions at the bottom and the top surfaces are satisfied by adopting the linear Lagrange interpolation function. The developed formulation is assessed through some illustrative problems solved using a proprietary finite element computer program. The results compare very well with those available in the literature and those obtained by simulations with the commercial finite element software Ansys.
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