| Author | Kamlun Shek |
|---|---|
| Title | Finite Deformation Plasticity for Composite Structures: Computational Models and Adaptive Strategies |
| Year | 1997 |
| School | Mechanical Engineering |
| Institution | RPI |
| Abstract | This thesis generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains. Starting from the double scale asymptotic expansion for the displacement and eigenstrain fields, this study derives close form expressions relating arbitrary eigenstrains to the mechanical fields in the phases. Computational models and adaptive modeling strategies for obtaining an approximate solution to a boundary value problem describing the finite deformation plasticity of heterogeneous structures are developed. A nearly optimal mathematical model consists of an averaging scheme based on approximating eigenstrains and elastic concentration factors in each micro phase by a constant in the macro problem subdomains where modeling errors are small, whereas elsewhere, a more detailed mathematical model based on piecewise constant approximation of eigenstrains and elastic concentration factors is utilized. The methodology is developed within the framework of "statistically homogeneous" composite material and local periodicity assumptions. For numerical examples considered, the CPU time obtained by means of the adaptive 2/n-point scheme was 30 seconds on a SPARC 10/51 station as opposed to 7 hours using classical mathematical homogenization theory. At the same time, the maximum error in the microscope fields in the critical unit cell was only 3.5% in comparison with the classical mathematical homogenization theory. |
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