Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
This paper proposes an exact analytical formula for the topological sensitivity of the macroscopic response of elastic microstructures to the insertion of circular inclusions. The macroscopic response is assumed to be predicted by a well-established multi-scale constitutive theory where the macrosco...
| Authors: | ; ; |
|---|---|
| Format: | Article |
| Status: | Published version |
| Publication date: | 2010 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/131349 |
| Online Access: | http://hdl.handle.net/11336/131349 |
| Access Level: | Open access |
| Keyword: | MULTI-SCALE MODELLING SENSITIVITY ANALYSIS SYNTHESIS OF MICROSTRUCTURES TOPOLOGICAL DERIVATIVE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/2.5 https://purl.org/becyt/ford/2 https://purl.org/becyt/ford/2.3 |
| _version_ | 1878403068911943680 |
|---|---|
| author | Giusti, Sebastian Miguel |
| author2 | Novotny, Antonio A. De Souza Neto, Eduardo Alberto |
| author2_role | author author |
| author_browse | De Souza Neto, Eduardo Alberto Giusti, Sebastian Miguel Novotny, Antonio A. |
| author_facet | Giusti, Sebastian Miguel Novotny, Antonio A. De Souza Neto, Eduardo Alberto |
| author_role | author |
| collection | CONICET Digital (CONICET) |
| description | This paper proposes an exact analytical formula for the topological sensitivity of the macroscopic response of elastic microstructures to the insertion of circular inclusions. The macroscopic response is assumed to be predicted by a well-established multi-scale constitutive theory where the macroscopic strain and stress tensors are defined as volume averages of their microscopic counterpart fields over a representative volume element (RVE) of material. The proposed formula-a symmetric fourth-order tensor field over the RVE domain-is a topological derivative which measures how the macroscopic elasticity tensor changes when an infinitesimal circular elastic inclusion is introduced within the RVE. In the limits, when the inclusion/matrix phase contrast ratio tends to zero and infinity, the sensitivities to the insertion of a hole and a rigid inclusion, respectively, are rigorously obtained. The derivation relies on the topological asymptotic analysis of the predicted macroscopic elasticity and is presented in detail. The derived fundamental formula is of interest to many areas of applied and computational mechanics. To illustrate its potential applicability, a simple finite element-based example is presented where the topological derivative information is used to automatically generate a bi-material microstructure to meet pre-specified macroscopic properties. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | AR_376363835ff00a6bf997a7ed12c3d03e |
| identifier_str_mv | Giusti, Sebastian Miguel; Novotny, Antonio A.; De Souza Neto, Eduardo Alberto; Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions; The Royal Society; Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences; 466; 2118; 8-6-2010; 1703-1723 1364-5021 1471-2946 CONICET Digital CONICET |
| institution | Consejo Nacional de Investigaciones Científicas y Técnicas |
| instname_str | Consejo Nacional de Investigaciones Científicas y Técnicas |
| language | eng |
| network_acronym_str | AR |
| network_name_str | Argentina |
| oai_identifier_str | oai:ri.conicet.gov.ar:11336/131349 |
| publishDate | 2010 |
| publishDateSort | 2010 |
| publisher | The Royal Society |
| publisherStr | The Royal Society |
| reponame_str | CONICET Digital (CONICET) |
| spelling | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions Giusti, Sebastian Miguel Novotny, Antonio A. De Souza Neto, Eduardo Alberto MULTI-SCALE MODELLING SENSITIVITY ANALYSIS SYNTHESIS OF MICROSTRUCTURES TOPOLOGICAL DERIVATIVE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/2.5 https://purl.org/becyt/ford/2 https://purl.org/becyt/ford/2.3 This paper proposes an exact analytical formula for the topological sensitivity of the macroscopic response of elastic microstructures to the insertion of circular inclusions. The macroscopic response is assumed to be predicted by a well-established multi-scale constitutive theory where the macroscopic strain and stress tensors are defined as volume averages of their microscopic counterpart fields over a representative volume element (RVE) of material. The proposed formula-a symmetric fourth-order tensor field over the RVE domain-is a topological derivative which measures how the macroscopic elasticity tensor changes when an infinitesimal circular elastic inclusion is introduced within the RVE. In the limits, when the inclusion/matrix phase contrast ratio tends to zero and infinity, the sensitivities to the insertion of a hole and a rigid inclusion, respectively, are rigorously obtained. The derivation relies on the topological asymptotic analysis of the predicted macroscopic elasticity and is presented in detail. The derived fundamental formula is of interest to many areas of applied and computational mechanics. To illustrate its potential applicability, a simple finite element-based example is presented where the topological derivative information is used to automatically generate a bi-material microstructure to meet pre-specified macroscopic properties. Fil: Giusti, Sebastian Miguel. Laboratorio Nacional de Computación Científica; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina Fil: Novotny, Antonio A.. Laboratorio Nacional de Computación Científica; Brasil Fil: De Souza Neto, Eduardo Alberto. Swansea University; Reino Unido The Royal Society http://hdl.handle.net/11336/131349 Giusti, Sebastian Miguel; Novotny, Antonio A.; De Souza Neto, Eduardo Alberto; Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions; The Royal Society; Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences; 466; 2118; 8-6-2010; 1703-1723 1364-5021 1471-2946 CONICET Digital CONICET |
| spellingShingle | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions Giusti, Sebastian Miguel MULTI-SCALE MODELLING SENSITIVITY ANALYSIS SYNTHESIS OF MICROSTRUCTURES TOPOLOGICAL DERIVATIVE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/2.5 https://purl.org/becyt/ford/2 https://purl.org/becyt/ford/2.3 |
| status_str | publishedVersion |
| title | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions |
| title_full | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions |
| title_fullStr | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions |
| title_full_unstemmed | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions |
| title_short | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions |
| title_sort | Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions |
| topic | MULTI-SCALE MODELLING SENSITIVITY ANALYSIS SYNTHESIS OF MICROSTRUCTURES TOPOLOGICAL DERIVATIVE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/2.5 https://purl.org/becyt/ford/2 https://purl.org/becyt/ford/2.3 |
| topic_facet | MULTI-SCALE MODELLING SENSITIVITY ANALYSIS SYNTHESIS OF MICROSTRUCTURES TOPOLOGICAL DERIVATIVE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/2.5 https://purl.org/becyt/ford/2 https://purl.org/becyt/ford/2.3 |
| url | http://hdl.handle.net/11336/131349 |