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Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts. (English) Zbl 1446.74024
Summary: For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in \({\mathbb {R}}^2\) . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery’s collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

74-10 Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids
74D10 Nonlinear constitutive equations for materials with memory
74A40 Random materials and composite materials
74Q05 Homogenization in equilibrium problems of solid mechanics
74S25 Spectral and related methods applied to problems in solid mechanics
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