Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen Article Swipe

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Jan N. Fuhg , Nikolaos Bouklas , Reese E. Jones ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2308.11080

Data-driven constitutive modeling frameworks based on neural networks and classical representation theorems have recently gained considerable attention due to their ability to easily incorporate constitutive constraints and their excellent generalization performance. In these models, the stress prediction follows from a linear combination of invariant-dependent coefficient functions and known tensor basis generators. However, thus far the formulations have been limited to stress representations based on the classical Rivlin and Ericksen form, while the performance of alternative representations has yet to be investigated. In this work, we survey a variety of tensor basis neural network models for modeling hyperelastic materials in a finite deformation context, including a number of so far unexplored formulations which use theoretically equivalent invariants and generators to Finger-Rivlin-Ericksen. Furthermore, we compare potential-based and coefficient-based approaches, as well as different calibration techniques. Nine variants are tested against both noisy and noiseless datasets for three different materials. Theoretical and practical insights into the performance of each formulation are given.

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Artificial Intelligence

Finite Element Method

Mathematical Analysis

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Hyperelastic material Generalization Artificial neural network Tensor (intrinsic definition) Invariant (physics) Context (archaeology) Representation (politics) Computer science Basis (linear algebra) Cauchy elastic material Applied mathematics Algorithm Mathematics Constitutive equation Artificial intelligence Finite element method Mathematical analysis Pure mathematics Geometry Physics Paleontology Mathematical physics Politics Biology Thermodynamics Law Political science

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2308.11080
PDF: https://arxiv.org/pdf/2308.11080
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Cited By: 1
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2308.11080

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Title: Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen

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Publication year: 2023

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Publication date: 2023-08-21

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Authors: Jan N. Fuhg, Nikolaos Bouklas, Reese E. Jones

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Concepts: Hyperelastic material, Generalization, Artificial neural network, Tensor (intrinsic definition), Invariant (physics), Context (archaeology), Representation (politics), Computer science, Basis (linear algebra), Cauchy elastic material, Applied mathematics, Algorithm, Mathematics, Constitutive equation, Artificial intelligence, Finite element method, Mathematical analysis, Pure mathematics, Geometry, Physics, Paleontology, Mathematical physics, Politics, Biology, Thermodynamics, Law, Political science

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abstract_inverted_index.Ericksen	68
abstract_inverted_index.However,	51
abstract_inverted_index.context,	102
abstract_inverted_index.datasets	142
abstract_inverted_index.insights	150
abstract_inverted_index.modeling	2, 95
abstract_inverted_index.networks	7
abstract_inverted_index.recently	13
abstract_inverted_index.theorems	11
abstract_inverted_index.variants	134
abstract_inverted_index.attention	16
abstract_inverted_index.classical	9, 65
abstract_inverted_index.different	130, 145
abstract_inverted_index.excellent	28
abstract_inverted_index.functions	45
abstract_inverted_index.including	103
abstract_inverted_index.materials	97
abstract_inverted_index.noiseless	141
abstract_inverted_index.practical	149
abstract_inverted_index.equivalent	114
abstract_inverted_index.frameworks	3
abstract_inverted_index.generators	117
abstract_inverted_index.invariants	115
abstract_inverted_index.materials.	146
abstract_inverted_index.prediction	36
abstract_inverted_index.unexplored	109
abstract_inverted_index.Data-driven	0
abstract_inverted_index.Theoretical	147
abstract_inverted_index.alternative	74
abstract_inverted_index.approaches,	126
abstract_inverted_index.calibration	131
abstract_inverted_index.coefficient	44
abstract_inverted_index.combination	41
abstract_inverted_index.constraints	25
abstract_inverted_index.deformation	101
abstract_inverted_index.formulation	156
abstract_inverted_index.generators.	50
abstract_inverted_index.incorporate	23
abstract_inverted_index.performance	72, 153
abstract_inverted_index.techniques.	132
abstract_inverted_index.Furthermore,	120
abstract_inverted_index.considerable	15
abstract_inverted_index.constitutive	1, 24
abstract_inverted_index.formulations	55, 110
abstract_inverted_index.hyperelastic	96
abstract_inverted_index.performance.	30
abstract_inverted_index.investigated.	80
abstract_inverted_index.theoretically	113
abstract_inverted_index.generalization	29
abstract_inverted_index.representation	10
abstract_inverted_index.potential-based	123
abstract_inverted_index.representations	61, 75
abstract_inverted_index.coefficient-based	125
abstract_inverted_index.invariant-dependent	43
abstract_inverted_index.Finger-Rivlin-Ericksen.	119
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile