| Full text | |
| Author(s): |
Adair R. Aguiar
[1]
;
Túlio V. Berbert Patriota
[2]
;
Gianni Royer-Carfagni
[3]
;
Alan B. Seitenfuss
[1]
Total Authors: 4
|
| Affiliation: | [1] Univ Sao Paulo, Dept Engn Estrutural, Sao Carlos, SP - Brazil
[2] Politecnico di Milano. Dipartamento de Meccanica - Itália
[3] Univ Parma, Dipartamento Ingn & Architettura, Parma - Italy
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES; v. 15, n. 10 2018-10-22. |
| Abstract | |
Abstract The peridynamic theory is an extension of the classical continuum mechanics theory. The peridynamic governing equations involve integrals of interaction forces between near particles separated by finite distances. These forces depend upon the relative displacements between material points within a body. On the other hand, the classical governing equations involve the divergence of a tensor field, which depends upon the spatial derivatives of displacements. Thus, the peridynamic governing equations are valid not only in the interior of a body, but also on its boundary, which may include a Griffith crack, and on interfaces between two bodies with different mechanical properties. Near the boundary, the solution of a peridynamic problem may be very different from the classical solution. In this work, we investigate the behavior of the displacement field of a unidimensional linearly elastic bar of length L near its ends in the context of the peridynamic theory. The bar is in equilibrium without body force, is fixed at one end, and is subjected to an imposed displacement at the other end. The bar has micromodulus C, which is related to the Young's modulus E in the classical theory and is given by different expressions found in the literature. We find that, depending on the expression of C, the displacement field may be singular near the ends, which is in contrast to the linear behavior of the displacement field observed in the classical linear elasticity. In spite of the above, we show that the peridynamic displacement field converges to its classical counterpart as a length scale, called peridynamic horizon, tends to zero. (AU) | |
| FAPESP's process: | 16/12529-4 - Study of torsion of cylindrical shaft in the context of the peridynamic theory |
| Grantee: | Túlio Vinícius Berbert Patriota |
| Support Opportunities: | Scholarships in Brazil - Scientific Initiation |
| FAPESP's process: | 16/12217-2 - Peridynamic theory in the modelling of the Post-Breakage phase of structural glass |
| Grantee: | Adair Roberto Aguiar |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |