Analytical Homogenization Estimates For The Transient And Steady-State Response Of Elasto-Viscoplastic Polycrystals
In this work, we develop analytical homogenization estimates for the macroscopic response and field statistics of elasto-viscoplastic polycrystals in the transient and steady-state regimes. In Chapter 2, we use the iterated fully optimized second-order homogenization method for the steady-state resp...
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| Format: | Thesis |
| Language: | English |
| Published: |
2021
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| Online Access: | https://repository.upenn.edu/handle/20.500.14332/31146 https://hdl.handle.net/20.500.14332/31146 |
| Summary: | In this work, we develop analytical homogenization estimates for the macroscopic response and field statistics of elasto-viscoplastic polycrystals in the transient and steady-state regimes. In Chapter 2, we use the iterated fully optimized second-order homogenization method for the steady-state response of porous polycrystals composed of large randomly distributed pores in a fine-grained polycrystalline matrix, with grains described by crystal viscoplasticity. The method is then used to estimate the effects of microstructure on the macroscopic response of sea ice. The key finding here is that the brine-air inclusions induce macroscopic compressibility, which is significantly affected by the porosity, pore geometry, and crystallographic texture of polycrystalline ice. Comparisons with experimental results demonstrate the capabilities of the model, especially in capturing the dilatational response of sea ice under combined hydrostatic and deviatoric loading. In Chapter 3, we generalize the model to account for the finite-strain response of porous polycrystals with pressurized pores and characterize the effects from microstructural evolution on the macroscopic response under general loading conditions. In particular, we investigate the effects of pore pressure, as well as morphological and crystallographic textures of the polycrystalline matrix, under plane strain and axisymmetric loading conditions. We find that the pore pressure can significantly harden the macroscopic response, especially for negative triaxialities, while having minimal effects for positive triaxialities. On the other hand, the crystallographic textures impact the responses of porous polycrystals for low and moderate positive triaxialities, as deduced by appropriate comparisons with porous untextured polycrystals. Moreover, different textures are developed for different loading conditions, which in turn induces significant sensitivity of the macroscopic response on loading conditions. However, for large positive triaxialities, the macroscopic ... |
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