By Lewis G.N.

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44(13), 2007, 4442–4471. 17. , Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation. Int. J. Numer. Methods Engng. 55, 2002, 1285–1322. 18. , Materially uniform simple bodies with inhomogeneities. Arch. Rational Mech. Anal. 27, 1967, 1–32. 19. , Non-Linear Elastic Deformations. Dover, 1997. 20. Ortiz, M. , Nonconvex energy minimization and dislocation structures in ductile single crystals. J. Mech. Phys. Solids 47, 1999, 397–462.

Andriyana, A. , Prediction of fatigue life improvement in natural rubber using configurational stress. Int. J. Solids Struct. 44, 2007, 2079–2092. 2. , Applications of an energy-momentum tensor in non-linear elastostatics. J. Elast. 5, 1975, 249–258. 3. Epstein, M. , (1990) The energy-momentum tensor and material uniformity in finite elasticity. Acta Mech. 83, 1990, 127–133. 4. , The force on an elastic singularity. Phil. Trans. R. Soc. Lond. A 244, 1951, 87–112. 5. , The elastic energy-momentum tensor.

Due to the overall incompatibility of the locally defined material isomorphism, dislocation structures are included in these modelling approaches – either in terms of the corresponding inelastic connection, or in terms of the corresponding dislocation density tensor; see, for example, [15, 23]. In general, such dislocation-related quantities can be used to enhance field or evolution equations for the underlying material isomorphism, or additionally be incorporated as arguments into energy potentials; see, for instance, [14] and references cited therein, or [5, 6, 9, 27].