This paper presents a discontinuous Galerkin weak form for bond-based peridynamic models to predict the damage of fiber-reinforced composite laminates. To represent the anisotropy of a laminate in a peridynamic model, a lamina is simplified as a transversely isotropic medium under a plane stress condition. The laminated structure is modeled by stacking the surface mesh layers along the thickness direction according to the laminate sequence. To avoid a mesh dependence on either the fiber orientation or the discretization, the spherical harmonic expansion theory is employed to construct a function for the micro-elastic modulus in terms of the bond-fiber angle. The laminate material is decomposed into an isotropic matrix material part and a transversely isotropic material part. The bond stiffness can be evaluated using the engineering material constants, based on the equivalence between the elastic energy density in the peridynamic theory and the elastic energy density in the classic continuum mechanics theory. Benchmark tests are conducted to verify the proposed model. Numerical results illustrate that the convergence of simulations with different horizon sizes and meshes can be achieved. In terms of damage analysis, the proposed model can capture the dynamic process of the complex coupling of the inner-layer and delamination damage modes.
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This work was sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. The authors would also like to thank Dr. John O. Hallquist from Livermore Software Technology Corporation for his support to this research. Helpful discussions with Dr. Stewart Silling from Sandia National Laboratories, New Mexico, as well as with Dr. Mazdak Ghajari from Imperial College are gratefully acknowledged.
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Ren, B., Wu, C.T., Seleson, P. et al. A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations. Int J Fract 214, 49–68 (2018). https://doi.org/10.1007/s10704-018-0317-4
- Peridynamic theory
- Finite element method
- Failure analysis
- Discontinuous Galerkin method
- Fiber-reinforced composites