Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T13:17:52.723855Z
Paper Citation Record · LEDGER
As of 15 August 2026, this Paper Citation Record lists 92 of 92 outbound references and 1 inbound Pith citation observation for arXiv:2412.13370.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T13:17:52.723855Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:11:55.521745Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T21:11:56.081015Z
92 of 92 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 3f8b46c2-e897-497e-9b30-ad625f80d5e4 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites
Reference 1
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Observation 0849ed9b-01ea-46b0-9b3d-a0d04405e7ea · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical properties of anisotropic fiber-reinforced composites
Reference 2
Source-reported events for the cited work
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Observation beb55f4e-7a62-44cf-9aa4-c70f2cf06a20 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites
Reference 3
Source-reported events for the cited work
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Observation 8b9aa9c0-0b30-408f-98ef-f67e4f4a8223 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks The anisotropic hooke’s law for cancellous bone and wood
Reference 4
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Observation e603e585-44e7-4a03-aaff-0dc8a37d841c · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Computational modeling of mechanical anisotropy in the cornea and sclera
Reference 5
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Observation 6d16e072-a199-4b37-af8d-8f3fe6190746 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Anisotropy properties of tissues: a basis for fabrication of biomimetic anisotropic scaffolds for tissue engineering
Reference 6
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Observation dcfe6615-8a8d-4dce-9f82-575952fbaca5 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical behavior of materials
Reference 7
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Observation 406a1aac-3c3a-42bb-9774-a9eec53bd0f8 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Aspects of computational homogenization at finite deformations: a unifying review from reuss’ to voigt’s bound
Reference 8
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Observation f100282f-cee2-4d5e-97ba-9ab292cbb0b8 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Bickel, Jan Rys, Steve Marschner, Chiara Daraio, and Markus H
Reference 9
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Observation 6945aa36-71ab-4a9d-a65e-9948f5db8625 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical metamaterials and their engineering applications
Reference 10
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Observation d9996b32-301b-4166-9ced-2d9de24aa24d · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Anisotropy and heterogeneity of microstructure and mechanical properties in metal additive manufacturing: A critical review
Reference 11
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Observation 39d03daa-bf5d-4ebf-9d2e-b7eee058615d · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Properties of materials: anisotropy, symmetry, structure
Reference 12
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Observation b073f265-c8ab-462f-9172-9b13585b4370 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Microstructural image analysis applied to fibre composite materials: a review
Reference 13
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Observation 2483ffce-f0c6-4b30-a3c5-f5051f618056 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Microstructural imaging techniques: a comparison between light and scanning electron microscopy
Reference 14
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Observation 303dd65c-c551-4909-97f1-80d032c61c9e · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Multiscale modeling: a review
Reference 15
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Observation 6391376b-669b-4714-accb-c114eab8a7cd · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Principles of multiscale modeling
Reference 16
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Observation c3948827-307e-4ddc-b717-f420ecc86320 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks A numerical two-scale homogenization scheme: the fe2-method
Reference 17
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Observation 49221b8c-e73c-485d-9295-8fc16bb40ea0 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work
Reference 18
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Observation 0aff51b3-cd31-42bf-8ee7-bb95917742ba · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work
Reference 19
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Observation 7e0245f6-1e31-44c0-bc04-f324465c9d39 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work
Reference 20
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Observation 0c6fb025-96b4-431b-8d4a-0e257a2ad165 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work
Reference 21
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Observation 95a47ac6-4f48-49a6-afa7-5ff9e23a7461 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks A variational approach to the theory of the elastic behaviour of multiphase materials
Reference 22
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Observation d6c017be-4364-4b59-9fe6-b046c642d70d · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Variational bounds on the effective moduli of anisotropic composites
Reference 23
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Observation 52a118af-420a-490e-ba4a-f3094d6466f5 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Homogenization approach in engineering
Reference 24
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Observation 995ceabc-4eb6-4fec-a1ed-095e17bfdc84 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks The determination of the elastic field of an ellipsoidal inclusion, and related problems
Reference 25
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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work
Reference 26
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Observation f207d4cd-c1fb-4df4-8b2a-3d9ac5edbf89 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Average stress in matrix and average elastic energy of materials with misfitting inclusions
Reference 27
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Observation 13d5f3cc-1785-4702-9849-dafb15dac9a8 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Luo and G.J
Reference 28
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Observation eecd129f-aa3c-4348-990b-90c77e3898db · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks On the elastic moduli of some heterogeneous materials
Reference 29
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Observation d7810d77-73ed-4134-946f-8773eb1c4941 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work
Reference 30
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Observation 11eb9af5-c8c7-4d7d-a7a3-edcf46310dd5 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks On constitutive macro-variables for heterogeneous solids at finite strain
Reference 31
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Observation fe31333a-ede5-45ea-8cd9-2673b284d935 · outbound
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Reference 32
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Observation 8f1eac77-0813-4409-b20e-30f2f91e05a9 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Geers, V .G
Reference 33
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Observation b9a67eeb-4795-49b9-b93c-325927274b87 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work
Reference 34
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Observation 52162f5c-d916-40c7-9993-a7dbc7af36d1 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and voronoi cell finite element model
Reference 35
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Observation 03fff8f8-cc8e-467d-9692-27d7dfdf03cd · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Multiscale modeling of microstructure–property relations
Reference 36
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Observation cbb1c0cc-c60c-4313-8baf-a1cc90f68d4d · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Multiscale fe2 elastoviscoplastic analysis of composite structures
Reference 37
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Observation 2519e217-d5d2-4daa-bf81-3c39d92ad613 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks A review of the fe 2 method for composites
Reference 38
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Observation 161b2365-7a9f-4da6-a3a7-552a7dfcf16c · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Local approximate gaussian process regression for data- driven constitutive models: development and comparison with neural networks
Reference 39
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Observation 4226b042-cc89-4111-80d0-c87efd4eecb7 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks A review on data-driven constitutive laws for solids
Reference 40
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Observation ff08e3a4-7faf-4a9c-898a-dfc10cad1513 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Representations for isotropic and anisotropic non-polynomial tensor functions
Reference 41
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Observation 551dbcb5-3840-4a36-a589-d5776eafb893 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function
Reference 42
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Observation 45a661f7-45a8-43ef-a1e9-e94b9531ba10 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Multilayer feedforward networks are universal approx- imators
Reference 43
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Observation a0234aff-bdd4-4968-a253-0269a2b523df · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Tensor basis gaussian process models of hyperelastic materials
Reference 44
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Observation c677de18-a0c5-4032-91b5-e59dd6f06bbd · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks On physics-informed data-driven isotropic and anisotropic constitutive mod- els through probabilistic machine learning and space-filling sampling
Reference 45
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Observation 5e476b27-9795-4157-82e4-e3e293a72ce0 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Neural networks meet hyperelasticity: A guide to enforcing physics
Reference 46
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Observation 38d5d9dc-5656-4ecc-a5a9-d0f8fd9a5045 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Polyconvex anisotropic hyperelasticity with neural networks
Reference 47
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Inverse design of anisotropic microstructures using physics-augmented neural networks Learning hyperelastic anisotropy from data via a tensor basis neural network
Reference 48
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Observation 62b068dd-4155-4d6d-8226-4e520c6d1606 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks A new family of constitutive artificial neural networks towards automated model discovery
Reference 49
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Observation 75787a14-917a-4f3a-8589-bc91b7f3ed50 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Klein, Fabian J
Reference 50
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Inverse design of anisotropic microstructures using physics-augmented neural networks Non-linear elastic deformations
Reference 51
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Inverse design of anisotropic microstructures using physics-augmented neural networks Structural tensors for anisotropic solids
Reference 52
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Observation 26c6335a-2193-453a-986b-f22a5c89bb8c · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks On the representation of constitutive relations using structure tensors
Reference 53
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Inverse design of anisotropic microstructures using physics-augmented neural networks Kalina, J ¨org Brummund, WaiChing Sun, and Markus K¨astner
Reference 54
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Observation fd6b28f4-af77-470b-9afb-a5381dba6fe4 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks An introduction to continuum mechanics , volume 158
Reference 55
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Reference 56
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Inverse design of anisotropic microstructures using physics-augmented neural networks Convexity conditions and existence theorems in nonlinear elasticity.Archive for rational mechanics and Analysis, 63(4):337–403, 1976
Reference 57
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Reference 58
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Reference 59
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Inverse design of anisotropic microstructures using physics-augmented neural networks Boyd and Lieven Vandenberghe
Reference 60
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Inverse design of anisotropic microstructures using physics-augmented neural networks Input convex neural networks
Reference 61
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Inverse design of anisotropic microstructures using physics-augmented neural networks Mathematical methods in continuum mechanics of solids
Reference 62
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Inverse design of anisotropic microstructures using physics-augmented neural networks Nonlinear solid mechanics: a continuum approach for engineering science
Reference 63
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Reference 64
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Reference 65
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Inverse design of anisotropic microstructures using physics-augmented neural networks Pytorch: An imperative style, high-performance deep learning library
Reference 66
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Inverse design of anisotropic microstructures using physics-augmented neural networks Adam: A Method for Stochastic Optimization
Reference 67
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Inverse design of anisotropic microstructures using physics-augmented neural networks A simplex method for function minimization
Reference 68
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Inverse design of anisotropic microstructures using physics-augmented neural networks Implementing the nelder-mead simplex algorithm with adaptive parameters
Reference 69
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Reference 70
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Inverse design of anisotropic microstructures using physics-augmented neural networks The CMA Evolution Strategy: A Tutorial
Reference 71
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Reference 72
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Observation 4a7c1ebf-3e69-42b3-8906-d0f223fb60c8 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Mathematical elasticity: Three-dimensional elasticity
Reference 73
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Inverse design of anisotropic microstructures using physics-augmented neural networks A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations
Reference 74
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Inverse design of anisotropic microstructures using physics-augmented neural networks A new constitutive framework for arterial wall mechanics and a comparative study of material models
Reference 75
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Observation 4433db73-b560-45eb-9405-b2f71f3ac6a5 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Model- data-driven constitutive responses: application to a multiscale computational framework
Reference 76
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Observation c365bb22-d86d-4a4d-ae94-679d6bf625cc · outbound
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Reference 77
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Observation f52c2b83-b054-47ed-83ed-427bcb24dfd8 · outbound
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Reference 78
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Observation 6823ab87-60c9-4dfa-86d5-4364e0bd7527 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Ranganathan and Martin Ostoja-Starzewski
Reference 79
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Observation 6aa88ae0-0a41-4561-bfd0-f2fe0d10b40e · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects
Reference 80
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Observation cfced910-c418-4851-be0a-c5ba0e834b28 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Vlassis, Puhan Zhao, Ran Ma, Tommy Sewell, and WaiChing Sun
Reference 81
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Observation 55993317-c47c-4297-a376-54347848bebd · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Hyperelastic behaviors of closed-cell porous materials at a wide porosity range
Reference 82
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Observation 2b7111b2-b3d2-46ec-bc5e-b77369c584ed · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical analysis of heterogeneous materials with higher-order parameters
Reference 83
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Observation c2c09d58-85bf-4a84-880b-f950fef073dc · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Fe ann: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining
Reference 84
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Observation 22cfccc0-4f25-44b8-a5b4-8e8e89042f57 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Loss of polyconvexity by homogenization: a new example
Reference 85
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Observation a3715512-1664-43e9-8000-e43bb371e475 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Loss of polyconvexity by homogenization
Reference 86
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Observation 47fd40a3-d0e4-46e5-a29e-57d1965b419a · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations
Reference 87
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Observation 4fb2a1ea-0d01-4102-84db-cea5b27195ed · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Identification of material parameters for constitutive equations
Reference 88
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Observation a50b0a3f-7079-4e31-84c3-43f22efa8466 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal vari- ables
Reference 89
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Observation e372aca2-319f-4788-b816-ed23c7aef222 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Automated model discovery of finite strain elastoplasticity from uniaxial experiments
Reference 90
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Observation c0a31151-c780-4795-b671-f4ce8021b0a3 · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Fuhg, Asghar Jadoon, Oliver Weeger, D
Reference 91
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Observation 27ff4b21-133c-40c7-b37d-dcd11b82bd8d · outbound
Inverse design of anisotropic microstructures using physics-augmented neural networks Russ, Glaucio H
Reference 92
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Observation 83e9d771-4d69-48e5-887a-82af60630c98 · inbound
Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials Inverse design of anisotropic microstructures using physics-augmented neural networks
Reference 52
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