Multidimensional rank-one convexification of incremental damage models at finite strains Article Swipe
Daniel Balzani
,
Maximilian Köhler
,
Timo Neumeier
,
Malte A. Peter
,
Daniel Peterseim
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1007/s00466-023-02354-3
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1007/s00466-023-02354-3
This paper presents computationally feasible rank-one relaxation algorithms for the efficient simulation of a time-incremental damage model with nonconvex incremental stress potentials in multiple spatial dimensions. While the standard model suffers from numerical issues due to the lack of convexity, our experiments showed that the relaxation by rank-one convexification delivering an approximation to the quasiconvex envelope prevents mesh dependence of the solutions of finite element discretizations. By the combination, modification and parallelization of the underlying convexification algorithms, the novel approach becomes computationally feasible. A descent method and a Newton scheme enhanced by step-size control prevent stability issues related to local minima in the energy landscape and the computation of derivatives. Numerical techniques for the construction of continuous derivatives of the approximated rank-one convex envelope are discussed. A series of numerical experiments demonstrates the ability of the computationally relaxed model to capture softening effects and the mesh independence of the computed approximations. An interpretation in terms of microstructural damage evolution is given, based on the rank-one lamination process.
Related Topics
Concepts
Rank (graph theory)
Convexity
Applied mathematics
Computation
Finite element method
Mathematical optimization
Relaxation (psychology)
Mathematics
Maxima and minima
Series (stratigraphy)
Algorithm
Mathematical analysis
Structural engineering
Financial economics
Psychology
Combinatorics
Paleontology
Economics
Engineering
Biology
Social psychology
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s00466-023-02354-3
- https://link.springer.com/content/pdf/10.1007/s00466-023-02354-3.pdf
- OA Status
- hybrid
- Cited By
- 3
- References
- 50
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4381085642
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4381085642Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1007/s00466-023-02354-3Digital Object Identifier
- Title
-
Multidimensional rank-one convexification of incremental damage models at finite strainsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-06-17Full publication date if available
- Authors
-
Daniel Balzani, Maximilian Köhler, Timo Neumeier, Malte A. Peter, Daniel PeterseimList of authors in order
- Landing page
-
https://doi.org/10.1007/s00466-023-02354-3Publisher landing page
- PDF URL
-
https://link.springer.com/content/pdf/10.1007/s00466-023-02354-3.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://link.springer.com/content/pdf/10.1007/s00466-023-02354-3.pdfDirect OA link when available
- Concepts
-
Rank (graph theory), Convexity, Applied mathematics, Computation, Finite element method, Mathematical optimization, Relaxation (psychology), Mathematics, Maxima and minima, Series (stratigraphy), Algorithm, Mathematical analysis, Structural engineering, Financial economics, Psychology, Combinatorics, Paleontology, Economics, Engineering, Biology, Social psychologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
3Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2024: 2Per-year citation counts (last 5 years)
- References (count)
-
50Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4381085642 |
|---|---|
| doi | https://doi.org/10.1007/s00466-023-02354-3 |
| ids.doi | https://doi.org/10.1007/s00466-023-02354-3 |
| ids.openalex | https://openalex.org/W4381085642 |
| fwci | 0.47663415 |
| type | article |
| title | Multidimensional rank-one convexification of incremental damage models at finite strains |
| awards[0].id | https://openalex.org/G1669571322 |
| awards[0].funder_id | https://openalex.org/F4320320879 |
| awards[0].display_name | |
| awards[0].funder_award_id | BA2823/17-1 PE1464/7-1 PE2143/5-1 |
| awards[0].funder_display_name | Deutsche Forschungsgemeinschaft |
| biblio.issue | 1 |
| biblio.volume | 73 |
| biblio.last_page | 47 |
| biblio.first_page | 27 |
| topics[0].id | https://openalex.org/T11366 |
| topics[0].field.id | https://openalex.org/fields/22 |
| topics[0].field.display_name | Engineering |
| topics[0].score | 1.0 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2204 |
| topics[0].subfield.display_name | Biomedical Engineering |
| topics[0].display_name | Elasticity and Material Modeling |
| topics[1].id | https://openalex.org/T11558 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9994000196456909 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2211 |
| topics[1].subfield.display_name | Mechanics of Materials |
| topics[1].display_name | Composite Material Mechanics |
| topics[2].id | https://openalex.org/T10514 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.9968000054359436 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2211 |
| topics[2].subfield.display_name | Mechanics of Materials |
| topics[2].display_name | Numerical methods in engineering |
| funders[0].id | https://openalex.org/F4320320879 |
| funders[0].ror | https://ror.org/018mejw64 |
| funders[0].display_name | Deutsche Forschungsgemeinschaft |
| is_xpac | False |
| apc_list.value | 2790 |
| apc_list.currency | EUR |
| apc_list.value_usd | 3590 |
| apc_paid.value | 2790 |
| apc_paid.currency | EUR |
| apc_paid.value_usd | 3590 |
| concepts[0].id | https://openalex.org/C164226766 |
| concepts[0].level | 2 |
| concepts[0].score | 0.5548607707023621 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q7293202 |
| concepts[0].display_name | Rank (graph theory) |
| concepts[1].id | https://openalex.org/C72134830 |
| concepts[1].level | 2 |
| concepts[1].score | 0.5331199765205383 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q5166524 |
| concepts[1].display_name | Convexity |
| concepts[2].id | https://openalex.org/C28826006 |
| concepts[2].level | 1 |
| concepts[2].score | 0.5263256430625916 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[2].display_name | Applied mathematics |
| concepts[3].id | https://openalex.org/C45374587 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5160155296325684 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q12525525 |
| concepts[3].display_name | Computation |
| concepts[4].id | https://openalex.org/C135628077 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5115038156509399 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q220184 |
| concepts[4].display_name | Finite element method |
| concepts[5].id | https://openalex.org/C126255220 |
| concepts[5].level | 1 |
| concepts[5].score | 0.48829007148742676 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[5].display_name | Mathematical optimization |
| concepts[6].id | https://openalex.org/C2776029896 |
| concepts[6].level | 2 |
| concepts[6].score | 0.48507729172706604 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q3935810 |
| concepts[6].display_name | Relaxation (psychology) |
| concepts[7].id | https://openalex.org/C33923547 |
| concepts[7].level | 0 |
| concepts[7].score | 0.47897815704345703 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[7].display_name | Mathematics |
| concepts[8].id | https://openalex.org/C186633575 |
| concepts[8].level | 2 |
| concepts[8].score | 0.4623182415962219 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q845060 |
| concepts[8].display_name | Maxima and minima |
| concepts[9].id | https://openalex.org/C143724316 |
| concepts[9].level | 2 |
| concepts[9].score | 0.42142370343208313 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q312468 |
| concepts[9].display_name | Series (stratigraphy) |
| concepts[10].id | https://openalex.org/C11413529 |
| concepts[10].level | 1 |
| concepts[10].score | 0.35371267795562744 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[10].display_name | Algorithm |
| concepts[11].id | https://openalex.org/C134306372 |
| concepts[11].level | 1 |
| concepts[11].score | 0.1669989824295044 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[11].display_name | Mathematical analysis |
| concepts[12].id | https://openalex.org/C66938386 |
| concepts[12].level | 1 |
| concepts[12].score | 0.09764271974563599 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q633538 |
| concepts[12].display_name | Structural engineering |
| concepts[13].id | https://openalex.org/C106159729 |
| concepts[13].level | 1 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q2294553 |
| concepts[13].display_name | Financial economics |
| concepts[14].id | https://openalex.org/C15744967 |
| concepts[14].level | 0 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q9418 |
| concepts[14].display_name | Psychology |
| concepts[15].id | https://openalex.org/C114614502 |
| concepts[15].level | 1 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[15].display_name | Combinatorics |
| concepts[16].id | https://openalex.org/C151730666 |
| concepts[16].level | 1 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q7205 |
| concepts[16].display_name | Paleontology |
| concepts[17].id | https://openalex.org/C162324750 |
| concepts[17].level | 0 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q8134 |
| concepts[17].display_name | Economics |
| concepts[18].id | https://openalex.org/C127413603 |
| concepts[18].level | 0 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q11023 |
| concepts[18].display_name | Engineering |
| concepts[19].id | https://openalex.org/C86803240 |
| concepts[19].level | 0 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[19].display_name | Biology |
| concepts[20].id | https://openalex.org/C77805123 |
| concepts[20].level | 1 |
| concepts[20].score | 0.0 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q161272 |
| concepts[20].display_name | Social psychology |
| keywords[0].id | https://openalex.org/keywords/rank |
| keywords[0].score | 0.5548607707023621 |
| keywords[0].display_name | Rank (graph theory) |
| keywords[1].id | https://openalex.org/keywords/convexity |
| keywords[1].score | 0.5331199765205383 |
| keywords[1].display_name | Convexity |
| keywords[2].id | https://openalex.org/keywords/applied-mathematics |
| keywords[2].score | 0.5263256430625916 |
| keywords[2].display_name | Applied mathematics |
| keywords[3].id | https://openalex.org/keywords/computation |
| keywords[3].score | 0.5160155296325684 |
| keywords[3].display_name | Computation |
| keywords[4].id | https://openalex.org/keywords/finite-element-method |
| keywords[4].score | 0.5115038156509399 |
| keywords[4].display_name | Finite element method |
| keywords[5].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[5].score | 0.48829007148742676 |
| keywords[5].display_name | Mathematical optimization |
| keywords[6].id | https://openalex.org/keywords/relaxation |
| keywords[6].score | 0.48507729172706604 |
| keywords[6].display_name | Relaxation (psychology) |
| keywords[7].id | https://openalex.org/keywords/mathematics |
| keywords[7].score | 0.47897815704345703 |
| keywords[7].display_name | Mathematics |
| keywords[8].id | https://openalex.org/keywords/maxima-and-minima |
| keywords[8].score | 0.4623182415962219 |
| keywords[8].display_name | Maxima and minima |
| keywords[9].id | https://openalex.org/keywords/series |
| keywords[9].score | 0.42142370343208313 |
| keywords[9].display_name | Series (stratigraphy) |
| keywords[10].id | https://openalex.org/keywords/algorithm |
| keywords[10].score | 0.35371267795562744 |
| keywords[10].display_name | Algorithm |
| keywords[11].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[11].score | 0.1669989824295044 |
| keywords[11].display_name | Mathematical analysis |
| keywords[12].id | https://openalex.org/keywords/structural-engineering |
| keywords[12].score | 0.09764271974563599 |
| keywords[12].display_name | Structural engineering |
| language | en |
| locations[0].id | doi:10.1007/s00466-023-02354-3 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S147854436 |
| locations[0].source.issn | 0178-7675, 1432-0924 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0178-7675 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Computational Mechanics |
| locations[0].source.host_organization | https://openalex.org/P4310319900 |
| locations[0].source.host_organization_name | Springer Science+Business Media |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310319900, https://openalex.org/P4310319965 |
| locations[0].source.host_organization_lineage_names | Springer Science+Business Media, Springer Nature |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://link.springer.com/content/pdf/10.1007/s00466-023-02354-3.pdf |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Computational Mechanics |
| locations[0].landing_page_url | https://doi.org/10.1007/s00466-023-02354-3 |
| locations[1].id | pmh:oai:uni-augsburg.opus-bayern.de:99667 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400930 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | OPUS (Augsburg University) |
| locations[1].source.host_organization | https://openalex.org/I119916105 |
| locations[1].source.host_organization_name | Augsburg University |
| locations[1].source.host_organization_lineage | https://openalex.org/I119916105 |
| locations[1].license | cc-by |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | doc-type:article |
| locations[1].license_id | https://openalex.org/licenses/cc-by |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/99667 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5067096341 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-1422-4262 |
| authorships[0].author.display_name | Daniel Balzani |
| authorships[0].countries | DE |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I904495901 |
| authorships[0].affiliations[0].raw_affiliation_string | Continuum Mechanics, Ruhr-Universität Bochum, Universitätsstr. 150, 44801, Bochum, Germany |
| authorships[0].institutions[0].id | https://openalex.org/I904495901 |
| authorships[0].institutions[0].ror | https://ror.org/04tsk2644 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I904495901 |
| authorships[0].institutions[0].country_code | DE |
| authorships[0].institutions[0].display_name | Ruhr University Bochum |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | D. Balzani |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Continuum Mechanics, Ruhr-Universität Bochum, Universitätsstr. 150, 44801, Bochum, Germany |
| authorships[1].author.id | https://openalex.org/A5040315958 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-0981-8215 |
| authorships[1].author.display_name | Maximilian Köhler |
| authorships[1].countries | DE |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I904495901 |
| authorships[1].affiliations[0].raw_affiliation_string | Continuum Mechanics, Ruhr-Universität Bochum, Universitätsstr. 150, 44801, Bochum, Germany |
| authorships[1].institutions[0].id | https://openalex.org/I904495901 |
| authorships[1].institutions[0].ror | https://ror.org/04tsk2644 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I904495901 |
| authorships[1].institutions[0].country_code | DE |
| authorships[1].institutions[0].display_name | Ruhr University Bochum |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | M. Köhler |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Continuum Mechanics, Ruhr-Universität Bochum, Universitätsstr. 150, 44801, Bochum, Germany |
| authorships[2].author.id | https://openalex.org/A5065770358 |
| authorships[2].author.orcid | https://orcid.org/0009-0001-2363-0203 |
| authorships[2].author.display_name | Timo Neumeier |
| authorships[2].countries | DE |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I179225836 |
| authorships[2].affiliations[0].raw_affiliation_string | Institute of Mathematics, University of Augsburg, Universitätsstr. 12a, 86159, Augsburg, Germany |
| authorships[2].institutions[0].id | https://openalex.org/I179225836 |
| authorships[2].institutions[0].ror | https://ror.org/03p14d497 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I179225836 |
| authorships[2].institutions[0].country_code | DE |
| authorships[2].institutions[0].display_name | University of Augsburg |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | T. Neumeier |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Institute of Mathematics, University of Augsburg, Universitätsstr. 12a, 86159, Augsburg, Germany |
| authorships[3].author.id | https://openalex.org/A5052979989 |
| authorships[3].author.orcid | https://orcid.org/0000-0001-6107-9806 |
| authorships[3].author.display_name | Malte A. Peter |
| authorships[3].countries | DE |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I179225836 |
| authorships[3].affiliations[0].raw_affiliation_string | Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universitätsstr. 12a, 86159, Augsburg, Germany |
| authorships[3].institutions[0].id | https://openalex.org/I179225836 |
| authorships[3].institutions[0].ror | https://ror.org/03p14d497 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I179225836 |
| authorships[3].institutions[0].country_code | DE |
| authorships[3].institutions[0].display_name | University of Augsburg |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | M. A. Peter |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universitätsstr. 12a, 86159, Augsburg, Germany |
| authorships[4].author.id | https://openalex.org/A5014228488 |
| authorships[4].author.orcid | https://orcid.org/0000-0001-7213-556X |
| authorships[4].author.display_name | Daniel Peterseim |
| authorships[4].countries | DE |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I179225836 |
| authorships[4].affiliations[0].raw_affiliation_string | Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universitätsstr. 12a, 86159, Augsburg, Germany |
| authorships[4].institutions[0].id | https://openalex.org/I179225836 |
| authorships[4].institutions[0].ror | https://ror.org/03p14d497 |
| authorships[4].institutions[0].type | education |
| authorships[4].institutions[0].lineage | https://openalex.org/I179225836 |
| authorships[4].institutions[0].country_code | DE |
| authorships[4].institutions[0].display_name | University of Augsburg |
| authorships[4].author_position | last |
| authorships[4].raw_author_name | D. Peterseim |
| authorships[4].is_corresponding | False |
| authorships[4].raw_affiliation_strings | Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universitätsstr. 12a, 86159, Augsburg, Germany |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://link.springer.com/content/pdf/10.1007/s00466-023-02354-3.pdf |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Multidimensional rank-one convexification of incremental damage models at finite strains |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11366 |
| primary_topic.field.id | https://openalex.org/fields/22 |
| primary_topic.field.display_name | Engineering |
| primary_topic.score | 1.0 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2204 |
| primary_topic.subfield.display_name | Biomedical Engineering |
| primary_topic.display_name | Elasticity and Material Modeling |
| related_works | https://openalex.org/W2375684291, https://openalex.org/W2354676191, https://openalex.org/W3188646203, https://openalex.org/W136674370, https://openalex.org/W2909957174, https://openalex.org/W2105527480, https://openalex.org/W4320035781, https://openalex.org/W1986257383, https://openalex.org/W4230882308, https://openalex.org/W1997957156 |
| cited_by_count | 3 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 1 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 2 |
| locations_count | 2 |
| best_oa_location.id | doi:10.1007/s00466-023-02354-3 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S147854436 |
| best_oa_location.source.issn | 0178-7675, 1432-0924 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 0178-7675 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Computational Mechanics |
| best_oa_location.source.host_organization | https://openalex.org/P4310319900 |
| best_oa_location.source.host_organization_name | Springer Science+Business Media |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310319900, https://openalex.org/P4310319965 |
| best_oa_location.source.host_organization_lineage_names | Springer Science+Business Media, Springer Nature |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://link.springer.com/content/pdf/10.1007/s00466-023-02354-3.pdf |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Computational Mechanics |
| best_oa_location.landing_page_url | https://doi.org/10.1007/s00466-023-02354-3 |
| primary_location.id | doi:10.1007/s00466-023-02354-3 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S147854436 |
| primary_location.source.issn | 0178-7675, 1432-0924 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0178-7675 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Computational Mechanics |
| primary_location.source.host_organization | https://openalex.org/P4310319900 |
| primary_location.source.host_organization_name | Springer Science+Business Media |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319900, https://openalex.org/P4310319965 |
| primary_location.source.host_organization_lineage_names | Springer Science+Business Media, Springer Nature |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://link.springer.com/content/pdf/10.1007/s00466-023-02354-3.pdf |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Computational Mechanics |
| primary_location.landing_page_url | https://doi.org/10.1007/s00466-023-02354-3 |
| publication_date | 2023-06-17 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W2020413485, https://openalex.org/W2142463173, https://openalex.org/W418503264, https://openalex.org/W2132995814, https://openalex.org/W2045970486, https://openalex.org/W1933579735, https://openalex.org/W2126799873, https://openalex.org/W2792905325, https://openalex.org/W779518458, https://openalex.org/W2922542198, https://openalex.org/W2100025012, https://openalex.org/W2093403201, https://openalex.org/W2054535420, https://openalex.org/W2007016988, https://openalex.org/W1977302783, https://openalex.org/W2051433469, https://openalex.org/W1990237558, https://openalex.org/W2084759830, https://openalex.org/W2134886919, https://openalex.org/W2065841032, https://openalex.org/W1988813075, https://openalex.org/W2025299767, https://openalex.org/W2083637560, https://openalex.org/W3214552298, https://openalex.org/W4316127176, https://openalex.org/W4295359836, https://openalex.org/W4230752651, https://openalex.org/W2992001690, https://openalex.org/W2570295260, https://openalex.org/W1975747602, https://openalex.org/W2801069317, https://openalex.org/W4294686020, https://openalex.org/W2036832737, https://openalex.org/W2096165789, https://openalex.org/W2505515853, https://openalex.org/W6601231545, https://openalex.org/W2065721961, https://openalex.org/W1691973880, https://openalex.org/W1963612623, https://openalex.org/W2147280642, https://openalex.org/W2052196552, https://openalex.org/W2097537106, https://openalex.org/W4362524263, https://openalex.org/W1125369971, https://openalex.org/W2142862873, https://openalex.org/W3045351184, https://openalex.org/W1594119316, https://openalex.org/W2509141630, https://openalex.org/W4205961268, https://openalex.org/W608535524 |
| referenced_works_count | 50 |
| abstract_inverted_index.A | 84, 127 |
| abstract_inverted_index.a | 14, 88 |
| abstract_inverted_index.An | 152 |
| abstract_inverted_index.By | 67 |
| abstract_inverted_index.an | 51 |
| abstract_inverted_index.by | 47, 92 |
| abstract_inverted_index.in | 23, 102, 154 |
| abstract_inverted_index.is | 160 |
| abstract_inverted_index.of | 13, 39, 60, 63, 73, 109, 116, 119, 129, 135, 148, 156 |
| abstract_inverted_index.on | 163 |
| abstract_inverted_index.to | 36, 53, 99, 140 |
| abstract_inverted_index.and | 71, 87, 106, 144 |
| abstract_inverted_index.are | 125 |
| abstract_inverted_index.due | 35 |
| abstract_inverted_index.for | 9, 113 |
| abstract_inverted_index.our | 41 |
| abstract_inverted_index.the | 10, 28, 37, 45, 54, 61, 68, 74, 78, 103, 107, 114, 120, 133, 136, 145, 149, 164 |
| abstract_inverted_index.This | 1 |
| abstract_inverted_index.from | 32 |
| abstract_inverted_index.lack | 38 |
| abstract_inverted_index.mesh | 58, 146 |
| abstract_inverted_index.that | 44 |
| abstract_inverted_index.with | 18 |
| abstract_inverted_index.While | 27 |
| abstract_inverted_index.based | 162 |
| abstract_inverted_index.local | 100 |
| abstract_inverted_index.model | 17, 30, 139 |
| abstract_inverted_index.novel | 79 |
| abstract_inverted_index.paper | 2 |
| abstract_inverted_index.terms | 155 |
| abstract_inverted_index.Newton | 89 |
| abstract_inverted_index.convex | 123 |
| abstract_inverted_index.damage | 16, 158 |
| abstract_inverted_index.energy | 104 |
| abstract_inverted_index.finite | 64 |
| abstract_inverted_index.given, | 161 |
| abstract_inverted_index.issues | 34, 97 |
| abstract_inverted_index.method | 86 |
| abstract_inverted_index.minima | 101 |
| abstract_inverted_index.scheme | 90 |
| abstract_inverted_index.series | 128 |
| abstract_inverted_index.showed | 43 |
| abstract_inverted_index.stress | 21 |
| abstract_inverted_index.ability | 134 |
| abstract_inverted_index.becomes | 81 |
| abstract_inverted_index.capture | 141 |
| abstract_inverted_index.control | 94 |
| abstract_inverted_index.descent | 85 |
| abstract_inverted_index.effects | 143 |
| abstract_inverted_index.element | 65 |
| abstract_inverted_index.prevent | 95 |
| abstract_inverted_index.related | 98 |
| abstract_inverted_index.relaxed | 138 |
| abstract_inverted_index.spatial | 25 |
| abstract_inverted_index.suffers | 31 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.approach | 80 |
| abstract_inverted_index.computed | 150 |
| abstract_inverted_index.enhanced | 91 |
| abstract_inverted_index.envelope | 56, 124 |
| abstract_inverted_index.feasible | 5 |
| abstract_inverted_index.multiple | 24 |
| abstract_inverted_index.presents | 3 |
| abstract_inverted_index.prevents | 57 |
| abstract_inverted_index.process. | 167 |
| abstract_inverted_index.rank-one | 6, 48, 122, 165 |
| abstract_inverted_index.standard | 29 |
| abstract_inverted_index.Numerical | 111 |
| abstract_inverted_index.efficient | 11 |
| abstract_inverted_index.evolution | 159 |
| abstract_inverted_index.feasible. | 83 |
| abstract_inverted_index.landscape | 105 |
| abstract_inverted_index.nonconvex | 19 |
| abstract_inverted_index.numerical | 33, 130 |
| abstract_inverted_index.softening | 142 |
| abstract_inverted_index.solutions | 62 |
| abstract_inverted_index.stability | 96 |
| abstract_inverted_index.step-size | 93 |
| abstract_inverted_index.algorithms | 8 |
| abstract_inverted_index.continuous | 117 |
| abstract_inverted_index.convexity, | 40 |
| abstract_inverted_index.delivering | 50 |
| abstract_inverted_index.dependence | 59 |
| abstract_inverted_index.discussed. | 126 |
| abstract_inverted_index.lamination | 166 |
| abstract_inverted_index.potentials | 22 |
| abstract_inverted_index.relaxation | 7, 46 |
| abstract_inverted_index.simulation | 12 |
| abstract_inverted_index.techniques | 112 |
| abstract_inverted_index.underlying | 75 |
| abstract_inverted_index.algorithms, | 77 |
| abstract_inverted_index.computation | 108 |
| abstract_inverted_index.derivatives | 118 |
| abstract_inverted_index.dimensions. | 26 |
| abstract_inverted_index.experiments | 42, 131 |
| abstract_inverted_index.incremental | 20 |
| abstract_inverted_index.quasiconvex | 55 |
| abstract_inverted_index.approximated | 121 |
| abstract_inverted_index.combination, | 69 |
| abstract_inverted_index.construction | 115 |
| abstract_inverted_index.demonstrates | 132 |
| abstract_inverted_index.derivatives. | 110 |
| abstract_inverted_index.independence | 147 |
| abstract_inverted_index.modification | 70 |
| abstract_inverted_index.approximation | 52 |
| abstract_inverted_index.interpretation | 153 |
| abstract_inverted_index.approximations. | 151 |
| abstract_inverted_index.computationally | 4, 82, 137 |
| abstract_inverted_index.convexification | 49, 76 |
| abstract_inverted_index.microstructural | 157 |
| abstract_inverted_index.parallelization | 72 |
| abstract_inverted_index.discretizations. | 66 |
| abstract_inverted_index.time-incremental | 15 |
| cited_by_percentile_year.max | 96 |
| cited_by_percentile_year.min | 91 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 5 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.7900000214576721 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile.value | 0.56045138 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |