A theory of anisotropic healing and damage mechanics of materials

Self-healing smart materials have emerged into the research arena and have been deployed in industrial and biomedical applications, in which the modelling techniques and predicting schemes are crucial for designers to optimize these smart materials. In practice, plastic deformation is coupled with damage and healing in these systems, which necessitates a coupled formulation for characterization. The thermodynamics of inelastic deformation, damage and healing processes are incorporated here to establish the coupled constitutive equations for healing materials. This thermodynamic consistent formulation provides the designers with the ability to predict the irregular inelastic deformation of glassy polymers and damage and healing patterns for a highly anisotropic self-healing system. Moreover, the lack of a physically consistent method to measure and calibrate the healing process in the literature is addressed here. Within the continuum damage mechanics (CDM) framework, the physics of damage and healing processes is used to introduce the healing effect into the CDM concept and a set of two new anisotropic damage–healing variables are derived. These novel damage–healing variables together with the proposed thermodynamic consistent coupled theory constitute a well-structured method for accurately predicting the degradation and healing mechanisms in material systems. The inelastic and damage response for a shape memory polymer-based self-healing system is captured herein. While the healing experimental results are limited in the literature, the proposed theory provides the mathematical competency to capture the most nonlinear responses.

Further investigation of crystal hardening inequalities in (110) channel die compression

A set of geometrically based FCC crystal slip-systems hardening inequalities is analytically investigated in (110) channel die compression for all lateral constraint directions between and , following previous analyses of the other two distinct orientation ranges in (110) compression. With all critical slip systems active, it is proved that these inequalities uniquely predict initial lattice stability and finite crystal shearing only in the horizontal channel plane, consistent with experiments for this range of orientations. (The earlier analyses had predicted load-axis stability in both orientation ranges, and lattice stability in one, also commonly found experimentally.) Moreover, it is established that the lateral constraint stress predicted by the hardening inequalities will be less than that given by classic Taylor hardening as this stress evolves with deformation. It is further shown, taking into account experimental stress–strain curves and latent hardening experiments for aluminium and copper, that lattice stability generally can be expected to very large deformations, except perhaps for lateral constraint orientations near the end of the range, which result is consistent with experiment. In appendix A, the possibilities of solutions with a critical slip system inactive are investigated, and predictions of a power law rate-dependent plasticity model are analysed for comparison with the results based on the hardening inequalities.