A computational homogenization framework for non-ordinary state-based peridynamics
Abstract
Peridynamic theory has been shown to possess the capabilities of describing phenomena that theories based on partial differential equations are not capable of describing. These phenomena include nonlocal interactions and presence of singularities in system responses. To exploit the capabilities offered by peridynamics in the homogenization of heterogenous media, a nonlocal computational homogenization theory based on peridynamic correspondence model (non-ordinary state-based peridynamics) is proposed. To set the development of the theory on a rigorous mathematical framework and to ensure consistency with the nonlocal nature of the peridynamic theory, a nonlocal vector calculus was used in the analysis of the nonlocal homogenization theory. The proposed theory is a two-scale micro–macro-homogenization strategy in which the constitutive relation at the macroscale is derived from explicit solution of a nonlocal volume constraint problem at the microscale. To justify the coupling between the two scales, nonlocal analogues of the stress and strain average theorems as well as the Hill–Mandel macrohomogeneity condition were derived. Validation of the proposed theory is achieved via numerical solution of Representative Volume Elements (RVE) from composite materials and comparing the results with those obtained by means of established methodologies.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 18, 2022
- Source ID
- 10.1007/s00366-021-01582-6
Entities
People
- Erkan Oterkus
- Selda Oterkus
- Wenxuan Xia
- Yakubu Kasimu Galadima
Organizations
- Air Force Office of Scientific Research
- Petroleum Technology Development Fund