Because of the light weight and strong strength features, fiber-reinforced polymer (FRP) components are extensively used by structural engineers, especially in the automotive and aerospace industries. The heterogeneous nature and unique geometric structure of laminate components leads to complex damage modes. There are many numerical methods developed to simulate material failure such as the finite element method (FEM) with element-deletion, cohesive elements, meshfree methods, and the eXtended finite element method (XFEM). These methods are built based on the classical continuum mechanics theory, which has an intrinsic incompatibility between strong discontinuities of displacement fields occurring after failure and the continuum hypothesis of the theory.&nbsp;Peridynamics is a strongly nonlocal theory proposed by Silling. The peridynamic theory replaces the spatial differential operator in the governing equation of the classical continuum mechanics theory by a nonlocal integral operator, in which spatial differentiability assumptions are removed. As a consequence, strong discontinuities can be naturally represented by peridynamic models. In peridynamics, each material point interacts with a finite surrounding neighborhood via peridynamic bonds. Since the relative angle between a bond and the fiber orientation in a lamina can represent the anisotropic feature, the peridynamic theory has an inherent advantage in the modeling of FRP composites. The peridynamic theory uses a bond failure mechanism to represent material damage. This failure process is autonomously controlled by the nonlocal material response. Consequently, it has the capability to model the complex damage modes of FRP laminates.In this presentation, we will introduce an FEM-based peridyamic model to predict the mixed damage modes of unidirectional FRP laminates under dynamic loading. Based on its geometric structure and material composition, a long fiber lamina is considered as a transversely isotropic medium as a result of homogenization at the meso-scale. The laminated structure is modeled by stacking surface mesh layers along the thickness direction with arbitrary fiber angles. The peridynamic bonds between Gauss points are classified as inner-layer bonds and inter-layer bonds. To represent the anisotropy of a laminate, the micro-elastic modulus of the inner-layer and inter-layer bonds is calculated from the anisotropic engineering material constants separately. To capture complex failure behaviors of laminate structures, an empirical damage model is proposed under the tension, compression breakage of peridynamic bonds. This damage model can control the in-plane and delamination failure process. Benchmark tests are conducted to validate the elastic response of laminates under dynamic loading. In terms of damage analysis, the proposed model can capture the complex damage modes and resistive force of laminate structures.

An Fem-Based Peridynamic Model for Failure Analysis of Unidirectional Fiber-Reinforced Laminates

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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