Mechkit: A continuum mechanics toolkit in
Python

Bauer, Julian Karl; L., Kinon, Philipp; Hund, Jonas; Latussek, Lisa; Meyer, Nils; Böhlke, Thomas

doi:10.21105/joss.04389

JOSS

2022

DOI: 10.21105/joss.04389

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Mechkit: A continuum mechanics toolkit in Python

Julian Karl Bauer¹,

Kinon, Philipp L.²,

Jonas Hund³

et al.

Abstract: The Python package mechkit is a toolkit for researchers in the field of continuum mechanics and material modeling. mechkit contains methods and operators for elementary tasks concerning tensor algebra and tensor notation, e.g., linear mapping, base transformations and active as well as passive transformations of tensors.

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Cited by 2 publications

References 16 publications

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On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains

Krauß,

Bauer,

Mitsch

et al. 2024

J Elast

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Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The design process of components made of such fiber-reinforced composites is usually accompanied by a virtual process chain. In this virtual process chain, process-induced FOT are computed in a flow simulation and transferred to the structural simulation. Within the structural simulation, effective macroscopic properties are identified based on the averaged information contained in the FOT. Solving the field equations in flow simulations as well as homogenization of effective stiffnesses necessitates the application of a closure scheme, computing higher-order statistical moments based on assumptions. Additionally, non-congruent spatial discretizations require an intermediate mapping operation. This mapping operation is required, if the discretization, i.e., mesh, of the flow simulation differs from the discretization of the structural simulation. The main objective of this work is to give an answer to the question: Does the sequence of closure and mapping influence the achieved results? It will turn out, that the order influences the result, raising the consecutive question: Which order is beneficial? Both questions are addressed by deriving a quantification of the closure-related uncertainty. The two possible sequences, mapping followed by closure and closure followed by mapping, yield strongly different results, with the magnitude of the deviation even exceeding the magnitude of a reference result. Graphical consideration reveals that for both transversely isotropic and planar FOT-input, invalid results occur if the mapping takes place prior to closure. This issue is retrieved by orientation averaging stiffness tensors. As a by-product, we explicitly define for the first time the admissible parameter space of orthotropic fourth-order fiber orientation tensors and define a distance measure in this parameter space.

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On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains

Krauß,

Bauer,

Mitsch

et al. 2024

J Elast

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A Python package for homogenization procedures in fiber reinforced polymers

Christ¹,

Scheuring²,

Montesano³

et al. 2023

JOSS

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Mechkit: A continuum mechanics toolkit in Python

Cited by 2 publications

References 16 publications

On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains

On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains

A Python package for homogenization procedures in fiber reinforced polymers

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