Continuum damage models with non-conventional finite element formulations
In recent years, some research effort has been devoted to the development of non-conventional finite element models for the analysis of concrete structures. These models use continuum damage mechanics to represent the physically non-linear behavior of this quasi-brittle material. Two alternative app...
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| Published in | International journal of non-linear mechanics Vol. 45; no. 2; pp. 83 - 99 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.03.2010
Elsevier |
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| Online Access | Get full text |
| ISSN | 0020-7462 1878-5638 1878-5638 |
| DOI | 10.1016/j.ijnonlinmec.2009.09.005 |
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| Abstract | In recent years, some research effort has been devoted to the development of non-conventional finite element models for the analysis of concrete structures. These models use continuum damage mechanics to represent the physically non-linear behavior of this quasi-brittle material. Two alternative approaches proved to be robust and computationally competitive when compared with the classical displacement finite element implementations. The first corresponds to the hybrid–mixed stress model where both the effective stress and the displacement fields are independently modeled in the domain of each finite element and the displacements are approximated along the static boundary, which is considered to include the inter-element edges. The second approach corresponds to a hybrid–displacement model. In this case, the displacements in the domain of each element and the tractions along the kinematic boundary are independently approximated. Since it is a displacement model, the inter-element boundaries are now included in the kinematic boundary. In both models, complete sets of orthonormal Legendre polynomials are used to define all approximations required, so very effective
p-refinement procedures can be implemented. This paper illustrates the numerical performance of these two alternative approaches and compares their efficiency and accuracy with the classical finite element models. For this purpose, a set of numerical tests is presented and discussed. |
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| AbstractList | In recent years, some research effort has been devoted to the development of nonconventional finite element models for the analysis of concrete structures. These models use continuum damage mechanics to represent the physically non-linear behavior of this quasi-brittle material. Two alternative approaches proved to be robust and computationally competitive when compared with the classical displacement finite element implementations. The first corresponds to the hybrid-mixed stress model where both the effective stress and the the displacement fields are independently modeled in the domain of each finite element and the displacements are approximated along the static boundary, which is considered to include the interelement edges. The second approach corresponds to a hybrid displacement model. In this case, the displacements in the domain of each element and the tractions along the kinematic boundary are independently approximated. Since it is a displacement model, the inter-element boundaries are now included in the kinematic boundary. In both models, complete sets of orthonormal Legendre polynomials are used to define all approximations required so very effective -refinement procedures can be implemented. This paper illustrates the numerical performance of these two alternative approaches and compares their efficiency and accuracy with the classical finite element models. For this purpose, a set of numerical tests is presented and discussed. In recent years, some research effort has been devoted to the development of non-conventional finite element models for the analysis of concrete structures. These models use continuum damage mechanics to represent the physically non-linear behavior of this quasi-brittle material. Two alternative approaches proved to be robust and computationally competitive when compared with the classical displacement finite element implementations. The first corresponds to the hybrid-mixed stress model where both the effective stress and the displacement fields are independently modeled in the domain of each finite element and the displacements are approximated along the static boundary, which is considered to include the inter-element edges. The second approach corresponds to a hybrid-displacement model. In this case, the displacements in the domain of each element and the tractions along the kinematic boundary are independently approximated. Since it is a displacement model, the inter-element boundaries are now included in the kinematic boundary. In both models, complete sets of orthonormal Legendre polynomials are used to define all approximations required, so very effective p-refinement procedures can be implemented. This paper illustrates the numerical performance of these two alternative approaches and compares their efficiency and accuracy with the classical finite element models. For this purpose, a set of numerical tests is presented and discussed. In recent years, some research effort has been devoted to the development of non-conventional finite element models for the analysis of concrete structures. These models use continuum damage mechanics to represent the physically non-linear behavior of this quasi-brittle material. Two alternative approaches proved to be robust and computationally competitive when compared with the classical displacement finite element implementations. The first corresponds to the hybrid–mixed stress model where both the effective stress and the displacement fields are independently modeled in the domain of each finite element and the displacements are approximated along the static boundary, which is considered to include the inter-element edges. The second approach corresponds to a hybrid–displacement model. In this case, the displacements in the domain of each element and the tractions along the kinematic boundary are independently approximated. Since it is a displacement model, the inter-element boundaries are now included in the kinematic boundary. In both models, complete sets of orthonormal Legendre polynomials are used to define all approximations required, so very effective p-refinement procedures can be implemented. This paper illustrates the numerical performance of these two alternative approaches and compares their efficiency and accuracy with the classical finite element models. For this purpose, a set of numerical tests is presented and discussed. |
| Author | Castro, L.M.S.S. Silva, C.M. |
| Author_xml | – sequence: 1 givenname: C.M. surname: Silva fullname: Silva, C.M. email: cmsilva@civil.ist.utl.pt – sequence: 2 givenname: L.M.S.S. surname: Castro fullname: Castro, L.M.S.S. email: luis@civil.ist.utl.pt |
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| CitedBy_id | crossref_primary_10_1080_15502287_2013_784380 crossref_primary_10_1016_j_compstruc_2015_05_022 crossref_primary_10_1016_j_engstruct_2014_09_017 crossref_primary_10_1007_s11029_017_9694_4 crossref_primary_10_1016_j_advengsoft_2012_02_009 crossref_primary_10_1016_j_compstruc_2013_04_017 crossref_primary_10_1016_j_advengsoft_2013_06_002 crossref_primary_10_1016_j_advengsoft_2020_102965 |
| Cites_doi | 10.1016/S0020-7683(01)00066-X 10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D 10.1002/cnm.837 10.1016/j.compstruc.2005.03.031 10.1016/j.cma.2003.07.013 10.1002/(SICI)1096-9845(199809)27:9<937::AID-EQE764>3.0.CO;2-5 10.1016/S0020-7683(01)00087-7 10.1007/s004660050428 10.1061/(ASCE)0733-9399(1987)113:10(1512) 10.1002/eqe.4290240905 10.1061/(ASCE)0733-9399(2002)128:11(1119) 10.1016/S0045-7949(98)00291-0 10.1016/0020-7683(95)00074-7 10.1061/(ASCE)0733-9399(1989)115:2(345) 10.1016/0020-7683(87)90083-7 10.1016/j.euromechsol.2004.03.006 10.1016/S0749-6419(01)00042-0 10.1016/j.compstruc.2006.08.093 10.1016/S0997-7538(00)01111-6 10.1061/(ASCE)0733-9399(1989)115:4(755) 10.1002/(SICI)1099-1484(199901)4:1<17::AID-CFM55>3.0.CO;2-6 |
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| Keywords | Hybrid and mixed finite element formulations Legendre polynomials Non-local damage models |
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| References | Silva, Castro (bib36) 2004 Pereira, Freitas (bib32) 2000; 74 C.M. Silva, L.M.S.S. Castro, Hybrid–mixed stress formulation with continuum damage models. in: P.R.M. Lyra, S.M.B.A. da Silva, F.S. Magnani et al. (Eds.), XXV CILAMCE, Gráfica Bagaço, 2004. C. LaBorderie, Phenomenes unilateraux dans un materiau endommageable: modelisation et application a l’analyse de structures en beton, Ph.D. Thesis, Université Paris 6, Paris, 1991. Silva, Castro (bib41) 2007; 85 C. Comi, U. Perego, A bi-dissapative damage model for concrete with applications to dam engineering, in: ECCOMAS 2000, 2000. Silva, Castro (bib34) 2003 C.M. Silva, L.M.S.S. Castro, Hybrid and mixed finite element formulations for softening materials, in: C. Mota Soares, et al. (Eds.), ECCM-2006, APMTAC, 2006. 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| Title | Continuum damage models with non-conventional finite element formulations |
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