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- W2033382404 abstract "Abstract For time-independent materials which undergo non-linear deformations from some given reference configuration two (dual) hypotheses are considered. Firstly it is supposed that the work done to a given state of deformation is bounded below and that the bound is attainable on a physically possible path; secondly that the complementary work to a given state of stress is bounded above and that this bound too is attainable on a physically possible path. The consequences of these assumptions are analysed, and the results of Ponter and Martin [1] in the linear theory are generalized to account for non-linear deformations, due attention being paid to questions of stability. A non-linear elastic comparison material is defined whose strain energy is equal to the work done on a minimum path for the time-independent material. Extremum principles for non-linear elastic materials given in [2] are then applied to the comparison elastic material, and bounds are thereby placed on the work and complementary-work functional of the time-independent material. Corresponding overall properties of the time-independent and elastic materials are then compared by defining respective overall constitutive laws and overall stress and deformation variables. Following the definition of strengthening (weakening) of a non-linear elastic solid given by Ogden[2] a time-independent material is said to be strengthened (weakened) when its comparison elastic material is strengthened (weakened). Local and overall aspects of this definition are examined." @default.
- W2033382404 created "2016-06-24" @default.
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- W2033382404 date "1976-01-01" @default.
- W2033382404 modified "2023-09-27" @default.
- W2033382404 title "Local and overall extremal properties of time-independent materials and non-linear elastic comparison materials" @default.
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- W2033382404 doi "https://doi.org/10.1016/0020-7683(76)90050-0" @default.
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