Mechanical behavior of solids in the vicinity of singular points
| Grant number: | 07/03753-9 |
| Support type: | Regular Research Grants |
| Duration: | September 01, 2007 - August 31, 2009 |
| Field of knowledge: | Engineering - Civil Engineering |
| Principal Investigator: | Adair Roberto Aguiar |
| Grantee: | Adair Roberto Aguiar |
| Home Institution: | Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
Abstract
The classical theory of linear elasticity predicts spurious phenomena, such as the self-intersection of matter, in the vicinity of interior points of disks and spheres and of corners and tips of cracks on the boundary of elastic solids. The self-intersection phenomenon is associated with the violation of the kinematical condition that the Jacobian determinant of the deformation field is positive everywhere inside the solid. This anomalous behavior has not been treated adequately in the literature. One way to avoid this behavior combines the classical theory of linear elasticity with the imposition of the local injectivity constraint by means of a Lagrange multiplier technique. The associated constrained minimization problem is highly nonlinear and, in general, requires a numerical solution. In previous work, we have used this constrained minimization theory together with a penalty formulation in the numerical investigation of problems for which we have assumed a priori that the solution is rotationally symmetric with respect to an interior point of the solid. In this project, we want to investigate classes of materials that are more general than the classes considered previously and to extend the penalty formulation to treat full 2D problems, without considering, a priori, any type of simetria. This penalty formulation has the advantage of being mathematically appealling and computationally simple to implement. The results obtained in this investigation will be compared with the results obtained in previous investigations and with other results available in the literature. (AU)