Generalized identification procedures for mixed-mode loading

Develop more general identification procedures for the length scale parameter of simplified strain gradient elasticity under mixed-mode loading conditions, using failure criteria and constitutive relations appropriate to complex stress states.

Background

The identification methodology in the paper is based on pure Mode I loading and the maximum-principal-stress criterion applied to regularized strain-gradient-elasticity stresses. The authors note that complex stress states and mixed-mode loading may require both more sophisticated failure criteria and constitutive relations beyond the one-parameter simplified theory.

Accordingly, the development of identification procedures applicable to mixed-mode conditions is explicitly left unresolved. This problem concerns extending parameter identification itself, rather than merely validating the Mode I procedures experimentally.

References

More sophisticated failure criteria may be required for complex stress states and mixed-mode loading. Also, more general constitutive relations of SGE then those given by Eq. eq:stress may be required. The present study is therefore restricted to pure Mode I within the simplified SGE, while the development of more general identification procedures for mixed-mode conditions is left for future investigation.

— Identification of the length scale parameter of simplified strain gradient elasticity from standard Mode I fracture tests  (2608.21016 - Solyaev et al., 21 Aug 2026) in Section 5, Methodology for the length scale parameter identification