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For an isotropic hyperelastic material, the function relates the energy stored in an elastic material, and thus the stress–strain relationship, only to the three strain (elongation) components, thus disregarding the deformation history, heat dissipation, stress relaxation etc.
The Gent hyperelastic material model [1] is a phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. In this model, the strain energy density function is designed such that it has a singularity when the first invariant of the left Cauchy-Green deformation tensor reaches a limiting value .
The higher the energy density of the fuel, the more energy may be stored or transported for the same amount of volume. The energy of a fuel per unit mass is called its specific energy. The adjacent figure shows the gravimetric and volumetric energy density of some fuels and storage technologies (modified from the Gasoline article).
Instead, the relationship between applied stress and strain is initially linear, but at a certain point the stress–strain curve will plateau. The neo-Hookean model does not account for the dissipative release of energy as heat while straining the material, and perfect elasticity is assumed at all stages of deformation.
For rubber and biological materials, more sophisticated models are necessary. Such materials may exhibit a non-linear stress–strain behaviour at modest strains, or are elastic up to huge strains. These complex non-linear stress–strain behaviours need to be accommodated by specifically tailored strain-energy density functions.
In a molecule, strain energy is released when the constituent atoms are allowed to rearrange themselves in a chemical reaction. [1] The external work done on an elastic member in causing it to distort from its unstressed state is transformed into strain energy which is a form of potential energy.
Energy densities table Storage type Specific energy (MJ/kg) Energy density (MJ/L) Peak recovery efficiency % Practical recovery efficiency % Arbitrary Antimatter: 89,875,517,874: depends on density: Deuterium–tritium fusion: 576,000,000 [1] Uranium-235 fissile isotope: 144,000,000 [1] 1,500,000,000
Maximum distortion energy theory (von Mises yield criterion) also referred to as octahedral shear stress theory. [4] – This theory proposes that the total strain energy can be separated into two components: the volumetric ( hydrostatic ) strain energy and the shape (distortion or shear ) strain energy.