The embedded finite element technique provides a unique approach for modeling of fiber-reinforced composites. Meshing fibers as distinct bundles represented by truss elements embedded in a matrix material mesh allows for the assignment of more specific material properties for each component rather than homogenization of all of the properties. However, the implementations of the embedded element technique available in commercial software do not replace the material of the matrix elements with the material of the embedded elements. This causes a redundancy in the volume calculation of the overlapping meshes leading to artificially increased stiffness and mass. This paper investigates the consequences in the energy calculations of an explicit dynamic model due to this redundancy. A method for the correction of the redundancy within a finite element code is suggested which removes extra energy and is shown to be effective at correcting the energy calculations for large amounts of redundant volume.
In this research, the embedded element method is investigated as a method for creating a finite element model for fiber reinforced composites. Bundles of polyethylene fibers are represented by truss elements and embedded in a continuum element matrix material by tying the displacement of the two meshes together. This type of mesh can be created more quickly than layered models while still maintaining directional layers than can capture the indirect tension mechanism that is important to compression failure[1–4]. Here, we show that by varying the number of fibers represented by a single truss element, the size of the finite element model can be scaled up or down for macro or micro scale modeling without changing the material properties or modeling method being used.
The embedded finite element technique provides a unique approach for modeling of fiber-reinforced composites. Meshing fibers as distinct bundles represented by truss elements embedded in a matrix material mesh allows for the assignment of more specific material properties for each component rather than homogenization of all of the properties. However, the implementations of the embedded element technique available in commercial software do not replace the material of the matrix elements with the material of the embedded elements. This causes a redundancy in the volume calculation of the overlapping meshes leading to artificially increased stiffness and mass. This paper investigates the consequences in the energy calculations of an explicit dynamic model due to this redundancy. A method for the correction of the edundancy within a finite element code is suggested which removes extra energy and is shown to be effective at correcting the energy calculations for large amounts of redundant volume.
Kolsky Bar systems are subjected to inherent system error as all measurement devices are. This is especially true in that as the bar diameter decreases, the system becomes more sensitive to errors such as friction and misalignment. In this work we present a technique for identifying and quantifying the error of a Kolsky system. We also present a method of generating statistically significant bounds for Kolsky systems so that anomalous or improperly executed experiments can be quantitatively identified. This method does not rely on the intuition of the experimentalist to identify an anomalous experiment. After presenting our method for error identification, a series of tests are performed on 2024Aluminum alloy samples. A method is then presented where the system error, as well as some error contributed by a variance in sample dimension, are removed from the calculated error related to the stress on the samples. The result shows the effective variance of the sample response is quite high in the elastic loading period, but reduces when plasticity dominates. This is attributed to the presence of high frequency content in the travelling elastic waves which cannot be accurately measured currently, but is effectively damped out when plastic deformation dominates.
Typical Kolsky bars are 10–20mm in diameter with the lengths of each main bar being on the scale of meters. To push 104 and higher strain rates smaller diameter bars, accompanied by shorter lengths, are needed. As the diameters of the bars decreases the precision in the alignment of the system must increase to maintain the same relative tolerance as the larger experimental systems. Conversely, as the size of the bars decreases so does the magnitude of gravity based frictional forces due to the decreased mass of the system. Finite Element (FE) models are typically generated assuming a perfect experiment with exact alignment and no gravity. Additionally, these simulations tend to take advantage of the radial symmetry of an ideal experiment which removes any potential for modeling non-symmetric effects but has the added benefit of a reduced computational load. In this work, we discuss some of the results of these fast-running symmetry models to establish a baseline and demonstrate the first-order use case of such methods. We then take advantage of high-performance computing techniques to generate several three-dimensional, half symmetry simulations using Abaqus® allowing modeling of gravity and misalignment. The imperfection is initially modeled using the static general process followed by a dynamic explicit simulation in which the impact portion of the test is conducted. This multi-step simulation structure creates a system that can properly investigate the impact of these real-world, non-axis symmetric effects. These simulations fully explore the impacts of these experimental realities and are described in detail to allow other researchers to implement a similar FE modeling structure to aid in their experimentation and diagnostic efforts. Both a 12.7 mm and 3.16 mm diameter bar system are evaluated to quantify the degree that these various experimental imperfections have across two size scales of Kolsky bar systems.
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