NUMERICAL AND ASYMPTOTIC INVESTIGATION OF A BIFURCATION PHENOMENON IN A CLASS OF HYPERELASTIC LAMINATES
Adair Aguiar (University of São Paulo), Leslie Pérez-Fernández (Institute of Physics and Mathematics, Federal University of Pelotas, RS, Brazil), Edmar Prado (Dept. of Struct. Engnrng, São Carlos School of Engnrng, University of São Paulo)
SES Medal Symposium in honor of D.J. Steigmann
Tue 4:20 - 5:40
MacMillan 115
This work concerns the behavior of two-phase periodic laminates composed of homogeneous, isotropic, and hyperelastic layers in equilibrium in the absence of body force and subjected to finite deformations on their boundaries. The effective behavior of the laminates is studied elsewhere in the literature ([1]) using the tangent second-order homogenization method. In the case of a laminate made of a penalty compressible Neo-Hookean material and subjected to pure shear deformation on its boundary, results of that study indicate that the rotation of the layers may lead to a reduction in the overall stiffness of the laminates and that this phenomenon may be related to a possible loss of strong ellipticity of the macroscopic behavior of the laminate. Here, the Asymptotic Homogenization Method (AHM) is employed to obtain similar results for a laminate made of a different type of compressible Neo-Hookean material and subjected to the same boundary conditions. Using the Finite Element Method (FEM), the rotation of the layers at the center of the laminate is calculated and compared to the corresponding rotation obtained via AHM. The rotation angles are very close to each other up to a critical shear deformation, after which, the angle obtained via FEM changes abruptly from the angle obtained via AHM, indicating a bifurcation-like behavior. In addition, results obtained from the asymptotic analysis indicate that layers, at the microscopic level, may soften, even though no softening occurs in homogeneous solids made of the layer materials and under the same boundary conditions. Reference: Lopez-Pamies, O., Ponte Castañeda, P. (2009). Mechanics of Materials 41:4, 364--374. Acknowledgements: Brazilian National Council for Scientific and Technological Development, CNPq, Procs. 504778/2009-9 and 314410/2009-0,and the Coordination for the Improvement of Higher Education Personnel (CAPES) are gratefully acknowledged.