期刊
出版社
ROYAL SOC
DOI: 10.1098/rspa.2014.0403
关键词
nonlinear elasticity; defects; geometrical mechanics; residual stress
资金
- AFOSR [FA9550-12-1-0290]
- NSF [CMMI 1042559, CMMI 1130856]
- Reintegration Grant under EC Framework VII
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1130856] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1162002] Funding Source: National Science Foundation
The geometrical formulation of continuum mechanics provides us with a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometrical structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space. Here, we consider the problem of discombinations (a new term that we introduce in this paper), that is, a combined distribution of fields of dislocations, disclinations and point defects. Given a discombination, we compute the geometrical characteristics of the material manifold (curvature, torsion, non-metricity), its Cartan's moving frames and structural equations. This identification provides a powerful algorithm to solve semi-inverse problems with non-elastic components. As an example, we calculate the residual stress field of a cylindrically symmetric distribution of discombinations in an infinite circular cylindrical bar made of an incompressible hyperelastic isotropic elastic solid.
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