Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria

Kalina, Karl A.; Gebhart, Philipp; Brummund, Jörg; Linden, Lennart; Sun, WaiChing; Kästner, Markus

doi:10.1016/j.cma.2023.116739

Cited by 11 publications

(3 citation statements)

References 105 publications

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“…Hence, an optimizer with fast convergence is favorable. The optimizer Sequential Least Squares Programming (SLSQP) has shown to perform well for this application [17,20,26,72] and is therefore used in the numerical examples in Sect. 5.…”

Section: Integrationmentioning

confidence: 99%

“…The integration training method yields highly accurate results for the ideal data set and outperforms the other methods in terms of accuracy. However, it should be noted that this method uses the SLSQP optimizer for computational reasons, which has been shown to provide better results for smaller networks than Adam [72]. Since no additional network is required for this method, SLSQP can be used in a computationally efficient manner with fewer function evaluations compared to Adam.…”

Section: Integrationmentioning

confidence: 99%

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Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables

Rosenkranz,

Kalina,

Brummund

et al. 2024

Comput Mech

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We present an approach for the data-driven modeling of nonlinear viscoelastic materials at small strains which is based on physics-augmented neural networks (NNs) and requires only stress and strain paths for training. The model is built on the concept of generalized standard materials and is therefore thermodynamically consistent by construction. It consists of a free energy and a dissipation potential, which can be either expressed by the components of their tensor arguments or by a suitable set of invariants. The two potentials are described by fully/partially input convex neural networks. For training of the NN model by paths of stress and strain, an efficient and flexible training method based on a long short-term memory cell is developed to automatically generate the internal variable(s) during the training process. The proposed method is benchmarked and thoroughly compared with existing approaches. Different databases with either ideal or noisy stress data are generated for training by using a conventional nonlinear viscoelastic reference model. The coordinate-based and the invariant-based formulation are compared and the advantages of the latter are demonstrated. Afterwards, the invariant-based model is calibrated by applying the three training methods using ideal or noisy stress data. All methods yield good results, but differ in computation time and usability for large data sets. The presented training method based on a recurrent cell turns out to be particularly robust and widely applicable. We show that the presented model together with the recurrent cell for training yield complete and accurate 3D constitutive models even for sparse bi- or uniaxial training data.

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Section: Integrationmentioning

confidence: 99%

Section: Integrationmentioning

confidence: 99%

Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables

Rosenkranz,

Kalina,

Brummund

et al. 2024

Comput Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…Magneto-active polymers (e.g., magnetostrictive) are a class of composite materials that consist of a polymer embedded with magnetisable particles, driven by a straininduced mechanism called magnetic polarisation owing to the dipolar displacement occurring in magnetic and piezomagnetic (magnetostrictive) materials under magnetic field exposure [1][2][3][4][5][6][7] serving deformation in soft robotics and actuations [8]. Magnetostriction occurs in almost all ferromagnetic materials such as iron, cobalt, nickel and their corresponding alloys [9].…”

Section: Introductionmentioning

confidence: 99%

Low Magnetic Field Induced Extrinsic Strains in Multifunctional Particulate Composites: An Interrupted Mechanical Strengthening in 3D-Printed Nanocomposites

Mucolli,

Midmer,

Manolesos

et al. 2024

J. Compos. Sci.

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The current paper reports on the quantification of the effect of magnetic fields on the mechanical performance of ferromagnetic nanocomposites in situ during basic standard tensile testing. The research investigates altering the basic mechanical properties (modulus and strength) via the application of a contact-less magnetic field as a primary attempt for a future composites strengthening mechanism. The nanocomposite specimens were fabricated using filament-based 3D printing and were comprised of ferromagnetic nanoparticle-embedded thermoplastic polymers. The nanoparticles were iron particles dispersed at 21 wt.% (10.2 Vol.%) inside a polylactic acid (PLA) polymer, characterised utilising optical microscopy and 3D X-ray computed tomography. The magnetic field was stationary and produced using permanent neodymium round-shaped magnets available at two field strengths below 1 Tesla. The 3D printing was a MakerBot Replicator machine operating based upon a fused deposition method, which utilised 1.75 mm-diameter filaments made of iron particle-based PLA composites. The magnetic field-equipped tensile tests were accompanied by a real-time digital image correlation technique for localized strain measurements across the specimens at a 10-micron pixel resolution. It was observed that the lateral magnetic field induces a slight Poisson effect on the development of extrinsic strain across the length of the tensile specimens. However, the effect reasonably interferes with the evolution of strain fields via the introduction of localised compressive strains attributed to accumulated magnetic polarisation at the magnetic particles on an extrinsic scale. The theory overestimated the moduli by a factor of approximately 3.1. To enhance the accuracy of its solutions for 3D-printed specimens, it is necessary to incorporate pore considerations into the theoretical derivations. Additionally, a modest 10% increase in ultimate tensile strength was observed during tensile loading. This finding suggests that field-assisted strengthening can be effective for as-received 3D-printed magnetic composites in their solidified state, provided that the material and field are optimally designed and implemented. This approach could propose a viable method for remote field tailoring to strengthen the material by mitigating defects induced during the 3D printing process.

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On some energy‐based variational principles in non‐dissipative magneto‐mechanics using a vector potential approach

Gebhart,

Wallmersperger

2024

Numerical Meth Engineering

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This contribution covers the variational‐based modeling of non‐dissipative magneto‐mechanical systems using a vector potential approach and the thorough analysis and discussion of corresponding conforming finite element methods. Since the construction of divergence‐free finite element spaces explicitly enforcing the Coulomb gauge poses some major challenges, we propose some primal and mixed variational principles that ensure well posedness of the problem and allow to seek the vector potential in unconstrained function spaces. The performance of these methods is assessed in two comparative benchmark studies. The focus of both studies lies on the accurate approximation of field quantities in systems with material discontinuities and re‐entrant corners.

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Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria

Cited by 11 publications

References 105 publications

Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables

Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables

Low Magnetic Field Induced Extrinsic Strains in Multifunctional Particulate Composites: An Interrupted Mechanical Strengthening in 3D-Printed Nanocomposites

On some energy‐based variational principles in non‐dissipative magneto‐mechanics using a vector potential approach

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