Bin Liu's blog

Published in Extreme Mechanics Letters: https://doi.org/10.1016/j.eml.2020.100685. Catastrophic failure of materials and structures due to unstable crack growth could be prevented if fracture toughness could be enhanced at will through structural design, but how can this be possible if fracture toughness is a material constant related to energy dissipation in the vicinity of a propagating crack tip.

Published in Extreme Mechanics Letters: https://doi.org/10.1016/j.eml.2019.100507. For more than half a century, physicists rejected the existence of two-dimensional (2D) materials since they theoretically underestimated the stability. However, the discovery of one-atom-thick graphene proved the inapplicability of this theory.

Published in Physcal Review Letters: https://doi.org/10.1103/PhysRevLett.122.045502. Many materials are anisotropic. However, there is no widely accepted measure for characterizing the degree of elastic anisotropy. Here, assuming that the limiting case of extreme anisotropy should possess a positive semidefinite stiffness matrix, we propose three criteria to evaluate measures of anisotropy and show that the existing measures in the literature do not satisfy all of the proposed criteria.

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories.

In our just published paper, we identify two ways to extract the energy (or power) flowing into a crack tip during propagation based on the power balance of areas enclosed by a stationary contour and a comoving contour. It is very interesting to find a contradiction that two corresponding energy release rates (ERRs), a surface-forming ERR and a local ERR, are different when stress singularity exists at a crack tip. Besides a rigorous mathematical interpretation, we deduce that the stress singularity leads to an accompanying kinetic energy at the crack tip.

In our recent paper, some interesting conclusions are found when we attempt to establish a standardized compliance matrices for general anisotropic materials. The abstract is as follows.

The J-integral based criterion is widely used in elastic-plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J-integral cannot be defined unambiguously.

Finite element method (FEM) with fixed representative volume element (RVE) encounters some difficulties in simulating the periodical postbuckling behaviors of infinite long beam or infinite large film on soft substrate under compression, because the wavelength and pattern of buckling are not known before simulation and will change with the increase of compression strain.

This paper investigates what is the largest magnetoelectric (ME) coefficient of ME composites, and how to realize it. From the standpoint of energy conservation, a theoretical analysis is carried out on an imaginary lever structure consisting of a magnetostrictive phase, a piezoelectric phase, and a rigid lever. This structure is a generalization of various composite layouts for optimization on ME effect.