In recent years, various models of gradient elasticity, gradient plasticity and gradient dislocation dynamics have been advanced to model phenomena and experimental observations not captured by classical local theories for nearly homogeneous materials and configurations. A unifying procedure based on the introduction of the Laplacian and bi-Laplacian operators in classical continuum mechanics and metal physics theories is proposed herein. It is also shown that fractional/fractal and stochastic effects can be easily incorporated in the proposed methodology. Specific examples on nanograin heterogeneous materials and components are discussed and comparisons with related experiments are made.
[References: E.C. Aifantis, Gradient Extension of Classical Material Models: From Nuclear & Condensed Matter Scales to Earth & Cosmological Scales, In: E. Ghavanloo et al (eds), Size-Dependent Continuum Mechanics Approaches, Springer Tracts in Mechanical Engineering, Springer, 417-452, 2021;
E.C. Aifantis, Material mechanics & Hussein Zbib: A Tribute to his memory, J. Engng. Mater. Technol., accepted, 2021.]