Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation
Long-range interactions occurring in heterogeneous materials are responsible for the dispersive character of wave propagation. To capture these experimental phenomena without resorting to molecular and/or atomistic models, generalized continuum theories can be conveniently used. In this framework, t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-11-01
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| Series: | Journal of the Mechanical Behavior of Materials |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmbm-2018-2002 |
| _version_ | 1818394709708505088 |
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| author | De Domenico Dario Askes Harm Aifantis Elias C. |
| author_facet | De Domenico Dario Askes Harm Aifantis Elias C. |
| author_sort | De Domenico Dario |
| collection | DOAJ |
| description | Long-range interactions occurring in heterogeneous materials are responsible for the dispersive character of wave propagation. To capture these experimental phenomena without resorting to molecular and/or atomistic models, generalized continuum theories can be conveniently used. In this framework, this paper presents a three-length-scale gradient elasticity formulation whereby the standard equations of elasticity are enhanced with one additional strain gradient and two additional inertia gradients to describe wave dispersion in microstructured materials. It is well known that continualization of lattice systems with distributed microstructure leads to gradient models. Building on these insights, the proposed gradient formulation is derived by continualization of the response of a non-local lattice model with two-neighbor interactions. A similar model was previously proposed in the literature for a two-length-scale gradient formulation, but it did not include all the terms of the expansions that contributed to the response at the same order. By correcting these inconsistencies, the three-length-scale parameters can be linked to geometrical and mechanical properties of the material microstructure. Finally, the ability of the gradient formulation to simulate wave dispersion in a broad range of materials (aluminum, bismuth, nickel, concrete, mortar) is scrutinized against experimental observations. |
| first_indexed | 2024-12-14T06:05:31Z |
| format | Article |
| id | doaj.art-39a7f8887fb74782ac8e73206eb38b8f |
| institution | Directory Open Access Journal |
| issn | 0334-8938 2191-0243 |
| language | English |
| last_indexed | 2024-12-14T06:05:31Z |
| publishDate | 2018-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of the Mechanical Behavior of Materials |
| spelling | doaj.art-39a7f8887fb74782ac8e73206eb38b8f2022-12-21T23:14:18ZengDe GruyterJournal of the Mechanical Behavior of Materials0334-89382191-02432018-11-01275-680580810.1515/jmbm-2018-2002Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulationDe Domenico Dario0Askes Harm1Aifantis Elias C.2Department of Engineering, University of Messina, Contrada Di Dio, 98166 Sant’Agata, Messina, ItalyDepartment of Civil and Structural Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UKLaboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54006, GreeceLong-range interactions occurring in heterogeneous materials are responsible for the dispersive character of wave propagation. To capture these experimental phenomena without resorting to molecular and/or atomistic models, generalized continuum theories can be conveniently used. In this framework, this paper presents a three-length-scale gradient elasticity formulation whereby the standard equations of elasticity are enhanced with one additional strain gradient and two additional inertia gradients to describe wave dispersion in microstructured materials. It is well known that continualization of lattice systems with distributed microstructure leads to gradient models. Building on these insights, the proposed gradient formulation is derived by continualization of the response of a non-local lattice model with two-neighbor interactions. A similar model was previously proposed in the literature for a two-length-scale gradient formulation, but it did not include all the terms of the expansions that contributed to the response at the same order. By correcting these inconsistencies, the three-length-scale parameters can be linked to geometrical and mechanical properties of the material microstructure. Finally, the ability of the gradient formulation to simulate wave dispersion in a broad range of materials (aluminum, bismuth, nickel, concrete, mortar) is scrutinized against experimental observations.https://doi.org/10.1515/jmbm-2018-2002enriched continuagradient elasticityinternal length scalelattice modelsmaterial microstructurewave dispersion |
| spellingShingle | De Domenico Dario Askes Harm Aifantis Elias C. Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation Journal of the Mechanical Behavior of Materials enriched continua gradient elasticity internal length scale lattice models material microstructure wave dispersion |
| title | Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation |
| title_full | Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation |
| title_fullStr | Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation |
| title_full_unstemmed | Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation |
| title_short | Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation |
| title_sort | capturing wave dispersion in heterogeneous and microstructured materials through a three length scale gradient elasticity formulation |
| topic | enriched continua gradient elasticity internal length scale lattice models material microstructure wave dispersion |
| url | https://doi.org/10.1515/jmbm-2018-2002 |
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