
AbstractSimple derivation of the dual conservation integrals in small strain elasticity is presented, without the aid of Noether’s theorem on invariant variational principles. The derived integrals are related to the release rates of the potential and complementary potential energy associated with the defect motion. The analysis corrects the errors in earlier derivation of the relationship between the dual integrals and the release rates of the complementary potential energy. Selected examples in plane and anti-plane strain illustrate the calculation of dual integrals and their application. It is shown that the evaluation of dual integrals is of similar complexity to that of classical integrals, so that either can be used to determine the stress intensity factors or the forces between defects, without solving the corresponding boundary value problems. An advantage of combining the two calculations is discussed.
Energy momentum tensor, Mechanical Engineering, Applied Mathematics, Conservation integrals, Condensed Matter Physics, Potential energy, Materials Science(all), Mechanics of Materials, Modelling and Simulation, Dual integrals, Complementary energy
Energy momentum tensor, Mechanical Engineering, Applied Mathematics, Conservation integrals, Condensed Matter Physics, Potential energy, Materials Science(all), Mechanics of Materials, Modelling and Simulation, Dual integrals, Complementary energy
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 12 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
