Elastic instabilities of soft laminates with stiffening behavior Article Swipe
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.apm.2024.03.011
This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications.
Related Topics
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.apm.2024.03.011
- OA Status
- hybrid
- Cited By
- 6
- References
- 101
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4392977156
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4392977156Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1016/j.apm.2024.03.011Digital Object Identifier
- Title
-
Elastic instabilities of soft laminates with stiffening behaviorWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-03-20Full publication date if available
- Authors
-
Qi Yao, Nitesh Arora, Dean Chen, Yuhai Xiang, Stephan RudykhList of authors in order
- Landing page
-
https://doi.org/10.1016/j.apm.2024.03.011Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1016/j.apm.2024.03.011Direct OA link when available
- Concepts
-
Stiffening, Materials science, Composite material, Composite laminates, Structural engineering, Engineering, Composite numberTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
6Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 5, 2024: 1Per-year citation counts (last 5 years)
- References (count)
-
101Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4392977156 |
|---|---|
| doi | https://doi.org/10.1016/j.apm.2024.03.011 |
| ids.doi | https://doi.org/10.1016/j.apm.2024.03.011 |
| ids.openalex | https://openalex.org/W4392977156 |
| fwci | 2.44991961 |
| type | article |
| title | Elastic instabilities of soft laminates with stiffening behavior |
| awards[0].id | https://openalex.org/G7924722522 |
| awards[0].funder_id | https://openalex.org/F4320338335 |
| awards[0].display_name | |
| awards[0].funder_award_id | 852281-MAGIC |
| awards[0].funder_display_name | H2020 European Research Council |
| biblio.issue | |
| biblio.volume | 130 |
| biblio.last_page | 675 |
| biblio.first_page | 658 |
| topics[0].id | https://openalex.org/T12897 |
| topics[0].field.id | https://openalex.org/fields/22 |
| topics[0].field.display_name | Engineering |
| topics[0].score | 0.9986000061035156 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2210 |
| topics[0].subfield.display_name | Mechanical Engineering |
| topics[0].display_name | Structural Analysis of Composite Materials |
| topics[1].id | https://openalex.org/T11870 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9984999895095825 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2205 |
| topics[1].subfield.display_name | Civil and Structural Engineering |
| topics[1].display_name | Structural Analysis and Optimization |
| topics[2].id | https://openalex.org/T10221 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.9977999925613403 |
| 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 | Composite Structure Analysis and Optimization |
| funders[0].id | https://openalex.org/F4320334678 |
| funders[0].ror | https://ror.org/0472cxd90 |
| funders[0].display_name | European Research Council |
| funders[1].id | https://openalex.org/F4320338335 |
| funders[1].ror | https://ror.org/0472cxd90 |
| funders[1].display_name | H2020 European Research Council |
| is_xpac | False |
| apc_list.value | 3480 |
| apc_list.currency | USD |
| apc_list.value_usd | 3480 |
| apc_paid.value | 3480 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 3480 |
| concepts[0].id | https://openalex.org/C108729823 |
| concepts[0].level | 2 |
| concepts[0].score | 0.9375638961791992 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q3716064 |
| concepts[0].display_name | Stiffening |
| concepts[1].id | https://openalex.org/C192562407 |
| concepts[1].level | 0 |
| concepts[1].score | 0.702488362789154 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[1].display_name | Materials science |
| concepts[2].id | https://openalex.org/C159985019 |
| concepts[2].level | 1 |
| concepts[2].score | 0.5906161665916443 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q181790 |
| concepts[2].display_name | Composite material |
| concepts[3].id | https://openalex.org/C145922259 |
| concepts[3].level | 3 |
| concepts[3].score | 0.5374266505241394 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q5156763 |
| concepts[3].display_name | Composite laminates |
| concepts[4].id | https://openalex.org/C66938386 |
| concepts[4].level | 1 |
| concepts[4].score | 0.42969322204589844 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q633538 |
| concepts[4].display_name | Structural engineering |
| concepts[5].id | https://openalex.org/C127413603 |
| concepts[5].level | 0 |
| concepts[5].score | 0.1379108428955078 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q11023 |
| concepts[5].display_name | Engineering |
| concepts[6].id | https://openalex.org/C104779481 |
| concepts[6].level | 2 |
| concepts[6].score | 0.08270558714866638 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q50707 |
| concepts[6].display_name | Composite number |
| keywords[0].id | https://openalex.org/keywords/stiffening |
| keywords[0].score | 0.9375638961791992 |
| keywords[0].display_name | Stiffening |
| keywords[1].id | https://openalex.org/keywords/materials-science |
| keywords[1].score | 0.702488362789154 |
| keywords[1].display_name | Materials science |
| keywords[2].id | https://openalex.org/keywords/composite-material |
| keywords[2].score | 0.5906161665916443 |
| keywords[2].display_name | Composite material |
| keywords[3].id | https://openalex.org/keywords/composite-laminates |
| keywords[3].score | 0.5374266505241394 |
| keywords[3].display_name | Composite laminates |
| keywords[4].id | https://openalex.org/keywords/structural-engineering |
| keywords[4].score | 0.42969322204589844 |
| keywords[4].display_name | Structural engineering |
| keywords[5].id | https://openalex.org/keywords/engineering |
| keywords[5].score | 0.1379108428955078 |
| keywords[5].display_name | Engineering |
| keywords[6].id | https://openalex.org/keywords/composite-number |
| keywords[6].score | 0.08270558714866638 |
| keywords[6].display_name | Composite number |
| language | en |
| locations[0].id | doi:10.1016/j.apm.2024.03.011 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S153281200 |
| locations[0].source.issn | 0307-904X, 1872-8480 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0307-904X |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Applied Mathematical Modelling |
| locations[0].source.host_organization | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_name | Elsevier BV |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_lineage_names | Elsevier BV |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| 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 | Applied Mathematical Modelling |
| locations[0].landing_page_url | https://doi.org/10.1016/j.apm.2024.03.011 |
| locations[1].id | pmh:oai:https://researchrepository.universityofgalway.ie:10379/18968 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400871 |
| 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 | Spectrum Research Repository (Concordia University) |
| locations[1].source.host_organization | https://openalex.org/I60158472 |
| locations[1].source.host_organization_name | Concordia University |
| locations[1].source.host_organization_lineage | https://openalex.org/I60158472 |
| locations[1].license | cc-by |
| locations[1].pdf_url | https://researchrepository.universityofgalway.ie/bitstreams/68155e4b-d7bd-4da1-a743-a25c88605dee/download |
| locations[1].version | submittedVersion |
| locations[1].raw_type | journal 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://hdl.handle.net/10379/18968 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5101853644 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-9817-0515 |
| authorships[0].author.display_name | Qi Yao |
| authorships[0].countries | US |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I135310074 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States |
| authorships[0].institutions[0].id | https://openalex.org/I135310074 |
| authorships[0].institutions[0].ror | https://ror.org/01y2jtd41 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I135310074 |
| authorships[0].institutions[0].country_code | US |
| authorships[0].institutions[0].display_name | University of Wisconsin–Madison |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Qi Yao |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States |
| authorships[1].author.id | https://openalex.org/A5029407982 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-2301-4264 |
| authorships[1].author.display_name | Nitesh Arora |
| authorships[1].countries | US |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I130701444 |
| authorships[1].affiliations[0].raw_affiliation_string | School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, 30332, Georgia, United States |
| authorships[1].affiliations[1].institution_ids | https://openalex.org/I135310074 |
| authorships[1].affiliations[1].raw_affiliation_string | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States |
| authorships[1].institutions[0].id | https://openalex.org/I130701444 |
| authorships[1].institutions[0].ror | https://ror.org/01zkghx44 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I130701444 |
| authorships[1].institutions[0].country_code | US |
| authorships[1].institutions[0].display_name | Georgia Institute of Technology |
| authorships[1].institutions[1].id | https://openalex.org/I135310074 |
| authorships[1].institutions[1].ror | https://ror.org/01y2jtd41 |
| authorships[1].institutions[1].type | education |
| authorships[1].institutions[1].lineage | https://openalex.org/I135310074 |
| authorships[1].institutions[1].country_code | US |
| authorships[1].institutions[1].display_name | University of Wisconsin–Madison |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Nitesh Arora |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States, School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, 30332, Georgia, United States |
| authorships[2].author.id | https://openalex.org/A5037498536 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-9527-7720 |
| authorships[2].author.display_name | Dean Chen |
| authorships[2].countries | US |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I135310074 |
| authorships[2].affiliations[0].raw_affiliation_string | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States |
| authorships[2].affiliations[1].institution_ids | https://openalex.org/I161318765 |
| authorships[2].affiliations[1].raw_affiliation_string | Departments of Mechanical and Aerospace Engineering, University of California, Los Angeles, USA |
| authorships[2].institutions[0].id | https://openalex.org/I161318765 |
| authorships[2].institutions[0].ror | https://ror.org/046rm7j60 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I161318765 |
| authorships[2].institutions[0].country_code | US |
| authorships[2].institutions[0].display_name | University of California, Los Angeles |
| authorships[2].institutions[1].id | https://openalex.org/I135310074 |
| authorships[2].institutions[1].ror | https://ror.org/01y2jtd41 |
| authorships[2].institutions[1].type | education |
| authorships[2].institutions[1].lineage | https://openalex.org/I135310074 |
| authorships[2].institutions[1].country_code | US |
| authorships[2].institutions[1].display_name | University of Wisconsin–Madison |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Dean Chen |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States, Departments of Mechanical and Aerospace Engineering, University of California, Los Angeles, USA |
| authorships[3].author.id | https://openalex.org/A5101542910 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-1530-8345 |
| authorships[3].author.display_name | Yuhai Xiang |
| authorships[3].countries | US |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I130238516 |
| authorships[3].affiliations[0].raw_affiliation_string | Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, 55455, Minnesota, United States |
| authorships[3].institutions[0].id | https://openalex.org/I130238516 |
| authorships[3].institutions[0].ror | https://ror.org/017zqws13 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I130238516 |
| authorships[3].institutions[0].country_code | US |
| authorships[3].institutions[0].display_name | University of Minnesota |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Yuhai Xiang |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, 55455, Minnesota, United States |
| authorships[4].author.id | https://openalex.org/A5034796771 |
| authorships[4].author.orcid | https://orcid.org/0000-0002-4568-8326 |
| authorships[4].author.display_name | Stephan Rudykh |
| authorships[4].countries | IE, US |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I188760350 |
| authorships[4].affiliations[0].raw_affiliation_string | School of Mathematical and Statistical Sciences, University of Galway, University Road, Galway, Ireland |
| authorships[4].affiliations[1].institution_ids | https://openalex.org/I135310074 |
| authorships[4].affiliations[1].raw_affiliation_string | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States |
| authorships[4].institutions[0].id | https://openalex.org/I188760350 |
| authorships[4].institutions[0].ror | https://ror.org/03bea9k73 |
| authorships[4].institutions[0].type | education |
| authorships[4].institutions[0].lineage | https://openalex.org/I188760350 |
| authorships[4].institutions[0].country_code | IE |
| authorships[4].institutions[0].display_name | Ollscoil na Gaillimhe – University of Galway |
| authorships[4].institutions[1].id | https://openalex.org/I135310074 |
| authorships[4].institutions[1].ror | https://ror.org/01y2jtd41 |
| authorships[4].institutions[1].type | education |
| authorships[4].institutions[1].lineage | https://openalex.org/I135310074 |
| authorships[4].institutions[1].country_code | US |
| authorships[4].institutions[1].display_name | University of Wisconsin–Madison |
| authorships[4].author_position | last |
| authorships[4].raw_author_name | Stephan Rudykh |
| authorships[4].is_corresponding | True |
| authorships[4].raw_affiliation_strings | Department of Mechanical Engineering, University of Wisconsin, Madison, WI, 53706, United States, School of Mathematical and Statistical Sciences, University of Galway, University Road, Galway, Ireland |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.1016/j.apm.2024.03.011 |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Elastic instabilities of soft laminates with stiffening behavior |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T12897 |
| primary_topic.field.id | https://openalex.org/fields/22 |
| primary_topic.field.display_name | Engineering |
| primary_topic.score | 0.9986000061035156 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2210 |
| primary_topic.subfield.display_name | Mechanical Engineering |
| primary_topic.display_name | Structural Analysis of Composite Materials |
| related_works | https://openalex.org/W2121188127, https://openalex.org/W2911174503, https://openalex.org/W2220185659, https://openalex.org/W2992422696, https://openalex.org/W2050096417, https://openalex.org/W2349979379, https://openalex.org/W2093231562, https://openalex.org/W2348470493, https://openalex.org/W2019400865, https://openalex.org/W2113519976 |
| cited_by_count | 6 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 5 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 1 |
| locations_count | 2 |
| best_oa_location.id | doi:10.1016/j.apm.2024.03.011 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S153281200 |
| best_oa_location.source.issn | 0307-904X, 1872-8480 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 0307-904X |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Applied Mathematical Modelling |
| best_oa_location.source.host_organization | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_name | Elsevier BV |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_lineage_names | Elsevier BV |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| 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 | Applied Mathematical Modelling |
| best_oa_location.landing_page_url | https://doi.org/10.1016/j.apm.2024.03.011 |
| primary_location.id | doi:10.1016/j.apm.2024.03.011 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S153281200 |
| primary_location.source.issn | 0307-904X, 1872-8480 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0307-904X |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Applied Mathematical Modelling |
| primary_location.source.host_organization | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_name | Elsevier BV |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_lineage_names | Elsevier BV |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| 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 | Applied Mathematical Modelling |
| primary_location.landing_page_url | https://doi.org/10.1016/j.apm.2024.03.011 |
| publication_date | 2024-03-20 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W2759141497, https://openalex.org/W3125930444, https://openalex.org/W2089555797, https://openalex.org/W2158673433, https://openalex.org/W2166038325, https://openalex.org/W4318294048, https://openalex.org/W2884600537, https://openalex.org/W6804832465, https://openalex.org/W2884987420, https://openalex.org/W6684397947, https://openalex.org/W2316372476, https://openalex.org/W2774594948, https://openalex.org/W3155826666, https://openalex.org/W2099006292, https://openalex.org/W2058364550, https://openalex.org/W1966016720, https://openalex.org/W2149567066, https://openalex.org/W2411092182, https://openalex.org/W2859477549, https://openalex.org/W2944280895, https://openalex.org/W2617407647, https://openalex.org/W6794077455, https://openalex.org/W2056369486, https://openalex.org/W2783157787, https://openalex.org/W2170421299, https://openalex.org/W4360838280, https://openalex.org/W2040753209, https://openalex.org/W4313887874, https://openalex.org/W6793499462, https://openalex.org/W2037662277, https://openalex.org/W3217692680, https://openalex.org/W2075625830, https://openalex.org/W6634403331, https://openalex.org/W1978176680, https://openalex.org/W2156545742, https://openalex.org/W2082787456, https://openalex.org/W1539058908, https://openalex.org/W1564743156, https://openalex.org/W2338656, https://openalex.org/W2537356261, https://openalex.org/W3040731110, https://openalex.org/W1981228624, https://openalex.org/W2021965384, https://openalex.org/W2547134710, https://openalex.org/W2806429576, https://openalex.org/W2801920829, https://openalex.org/W4280596827, https://openalex.org/W2138611107, https://openalex.org/W2919970731, https://openalex.org/W4225264454, https://openalex.org/W6846078560, https://openalex.org/W4383532777, https://openalex.org/W4206957721, https://openalex.org/W1979505409, https://openalex.org/W3041771560, https://openalex.org/W2802161750, https://openalex.org/W571598163, https://openalex.org/W6782384539, https://openalex.org/W2082488954, https://openalex.org/W2005910730, https://openalex.org/W2015035786, https://openalex.org/W2126573907, https://openalex.org/W2047439171, https://openalex.org/W2205846399, https://openalex.org/W1978225787, https://openalex.org/W2181330169, https://openalex.org/W2051628199, https://openalex.org/W2529889965, https://openalex.org/W2019395644, https://openalex.org/W2564763816, https://openalex.org/W2729033936, https://openalex.org/W3036329997, https://openalex.org/W4288914097, https://openalex.org/W3205891791, https://openalex.org/W3157881381, https://openalex.org/W2587397448, https://openalex.org/W2760856402, https://openalex.org/W2890518931, https://openalex.org/W3178455289, https://openalex.org/W2961344315, https://openalex.org/W2913860281, https://openalex.org/W4221080768, https://openalex.org/W4381433932, https://openalex.org/W2326535753, https://openalex.org/W2770491308, https://openalex.org/W2114061345, https://openalex.org/W2611499284, https://openalex.org/W2059639188, https://openalex.org/W3016456333, https://openalex.org/W4312084748, https://openalex.org/W2088990151, https://openalex.org/W2791363855, https://openalex.org/W2965395385, https://openalex.org/W2167541649, https://openalex.org/W4304811527, https://openalex.org/W3158171242, https://openalex.org/W3082012931, https://openalex.org/W2884400302, https://openalex.org/W3155053814, https://openalex.org/W1572186356, https://openalex.org/W4200192668 |
| referenced_works_count | 101 |
| abstract_inverted_index.a | 16, 33, 84, 99 |
| abstract_inverted_index.We | 97 |
| abstract_inverted_index.an | 64, 139 |
| abstract_inverted_index.as | 78, 186 |
| abstract_inverted_index.be | 194 |
| abstract_inverted_index.by | 125, 196 |
| abstract_inverted_index.in | 7, 153, 163, 216 |
| abstract_inverted_index.is | 88 |
| abstract_inverted_index.of | 41, 57, 70, 80, 102, 112, 123, 183, 199, 209 |
| abstract_inverted_index.on | 18, 90 |
| abstract_inverted_index.to | 12, 116 |
| abstract_inverted_index.(or | 72 |
| abstract_inverted_index.The | 180 |
| abstract_inverted_index.and | 21, 75, 105, 155, 160, 190, 202 |
| abstract_inverted_index.can | 137, 193 |
| abstract_inverted_index.for | 67, 212 |
| abstract_inverted_index.the | 3, 25, 29, 39, 49, 54, 68, 92, 108, 113, 117, 121, 127, 134, 151, 156, 197, 207 |
| abstract_inverted_index.Gent | 30, 165 |
| abstract_inverted_index.This | 0, 44, 61, 146 |
| abstract_inverted_index.also | 148 |
| abstract_inverted_index.both | 19 |
| abstract_inverted_index.find | 106 |
| abstract_inverted_index.from | 53 |
| abstract_inverted_index.high | 34 |
| abstract_inverted_index.show | 168 |
| abstract_inverted_index.soft | 8, 210 |
| abstract_inverted_index.such | 185 |
| abstract_inverted_index.than | 171 |
| abstract_inverted_index.that | 107 |
| abstract_inverted_index.wide | 100 |
| abstract_inverted_index.with | 15, 32, 175 |
| abstract_inverted_index.focus | 17 |
| abstract_inverted_index.fully | 164, 172 |
| abstract_inverted_index.layer | 119 |
| abstract_inverted_index.macro | 159 |
| abstract_inverted_index.micro | 161 |
| abstract_inverted_index.model | 31, 47 |
| abstract_inverted_index.onset | 69 |
| abstract_inverted_index.other | 203 |
| abstract_inverted_index.paper | 1, 62, 147 |
| abstract_inverted_index.phase | 27, 103 |
| abstract_inverted_index.range | 101 |
| abstract_inverted_index.rapid | 110 |
| abstract_inverted_index.ratio | 37 |
| abstract_inverted_index.stiff | 118 |
| abstract_inverted_index.under | 95 |
| abstract_inverted_index.which | 167 |
| abstract_inverted_index.choice | 198 |
| abstract_inverted_index.finite | 13 |
| abstract_inverted_index.higher | 169 |
| abstract_inverted_index.larger | 176 |
| abstract_inverted_index.matrix | 114 |
| abstract_inverted_index.ratio. | 130 |
| abstract_inverted_index.ratios | 189 |
| abstract_inverted_index.region | 142 |
| abstract_inverted_index.stable | 141 |
| abstract_inverted_index.tuning | 208 |
| abstract_inverted_index.between | 158 |
| abstract_inverted_index.chains. | 60 |
| abstract_inverted_index.changes | 152 |
| abstract_inverted_index.derives | 63 |
| abstract_inverted_index.desired | 213 |
| abstract_inverted_index.elastic | 4 |
| abstract_inverted_index.imposed | 89 |
| abstract_inverted_index.limited | 55 |
| abstract_inverted_index.modulus | 36 |
| abstract_inverted_index.phases. | 43 |
| abstract_inverted_index.produce | 138 |
| abstract_inverted_index.ratios. | 179 |
| abstract_inverted_index.results | 52 |
| abstract_inverted_index.stretch | 129, 178, 188 |
| abstract_inverted_index.without | 143 |
| abstract_inverted_index.analysis | 87 |
| abstract_inverted_index.behavior | 6, 40, 94 |
| abstract_inverted_index.buckling | 214 |
| abstract_inverted_index.captures | 48 |
| abstract_inverted_index.compared | 115 |
| abstract_inverted_index.consider | 98 |
| abstract_inverted_index.critical | 128, 177, 181, 187, 191 |
| abstract_inverted_index.material | 81, 204 |
| abstract_inverted_index.observed | 144 |
| abstract_inverted_index.patterns | 215 |
| abstract_inverted_index.periodic | 9 |
| abstract_inverted_index.properly | 132 |
| abstract_inverted_index.strains, | 14 |
| abstract_inverted_index.Moreover, | 83 |
| abstract_inverted_index.describes | 38 |
| abstract_inverted_index.enlarging | 206 |
| abstract_inverted_index.functions | 79 |
| abstract_inverted_index.increases | 120 |
| abstract_inverted_index.laminates | 10, 124, 174, 211 |
| abstract_inverted_index.longwave) | 73 |
| abstract_inverted_index.molecular | 59 |
| abstract_inverted_index.numerical | 85 |
| abstract_inverted_index.polymeric | 58 |
| abstract_inverted_index.practical | 217 |
| abstract_inverted_index.stability | 122, 170 |
| abstract_inverted_index.subjected | 11 |
| abstract_inverted_index.absolutely | 140 |
| abstract_inverted_index.analytical | 65 |
| abstract_inverted_index.controlled | 195 |
| abstract_inverted_index.decreasing | 126 |
| abstract_inverted_index.laminates, | 166 |
| abstract_inverted_index.non-linear | 50 |
| abstract_inverted_index.parameters | 136, 201 |
| abstract_inverted_index.prediction | 66 |
| abstract_inverted_index.relatively | 109 |
| abstract_inverted_index.stiffening | 111, 135, 200 |
| abstract_inverted_index.transition | 157 |
| abstract_inverted_index.Considering | 24 |
| abstract_inverted_index.identifying | 91 |
| abstract_inverted_index.illustrates | 150 |
| abstract_inverted_index.instability | 5, 74, 77, 93, 154, 162 |
| abstract_inverted_index.macroscopic | 20, 71 |
| abstract_inverted_index.microscopic | 22, 76 |
| abstract_inverted_index.neo-Hookean | 173 |
| abstract_inverted_index.parameters. | 82 |
| abstract_inverted_index.properties, | 205 |
| abstract_inverted_index.stiffening, | 28 |
| abstract_inverted_index.Essentially, | 131 |
| abstract_inverted_index.combinations | 104 |
| abstract_inverted_index.compression. | 96 |
| abstract_inverted_index.constitutive | 51 |
| abstract_inverted_index.instability. | 145 |
| abstract_inverted_index.investigates | 2 |
| abstract_inverted_index.manipulating | 133 |
| abstract_inverted_index.non-Gaussian | 45 |
| abstract_inverted_index.wavenumbers, | 192 |
| abstract_inverted_index.Bloch-Floquet | 86 |
| abstract_inverted_index.applications. | 218 |
| abstract_inverted_index.bulk-to-shear | 35 |
| abstract_inverted_index.extensibility | 56 |
| abstract_inverted_index.incompressible | 42 |
| abstract_inverted_index.instabilities, | 184 |
| abstract_inverted_index.instabilities. | 23 |
| abstract_inverted_index.systematically | 149 |
| abstract_inverted_index.characteristics | 182 |
| abstract_inverted_index.statistics-based | 46 |
| abstract_inverted_index.deformation-induced | 26 |
| cited_by_percentile_year.max | 98 |
| cited_by_percentile_year.min | 90 |
| corresponding_author_ids | https://openalex.org/A5034796771 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 5 |
| corresponding_institution_ids | https://openalex.org/I135310074, https://openalex.org/I188760350 |
| citation_normalized_percentile.value | 0.8188661 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |