User login


You are here

Bin Liu's blog

Bin Liu's picture

Intrinsic-to-extrinsic transition in fracture toughness through structural design: A lesson from nature

Published in Extreme Mechanics Letters: 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.

Bin Liu's picture

Why are most 2D lattices hexagonal? The stability of 2D lattices predicted by a simple mechanics model

Published in Extreme Mechanics Letters: 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.

Bin Liu's picture

Criteria for selecting a reasonable and better measure of anisotropy

Published in Physcal Review Letters: 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.

Bin Liu's picture

How to Realize Volume Conservation During Finite Plastic Deformation

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.

Bin Liu's picture

The surface-forming energy release rate versus the local energy release rate

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.

Bin Liu's picture

Objective Fracture Parameters and a Paradox for Interface Cracks

Due to the oscillatory singular stress field around a crack tip, interface fracture has some peculiar features. This paper is focused on two of them. One can be reflected by a proposed paradox that geometrically similar structures with interface cracks under similar loadings may have different failure behaviors. The other one is that the existing fracture parameters of the oscillatory singular stress field, such as a complex stress intensity factor, exhibit some nonobjectivity because their phase angle depends on an arbitrarily chosen length.

Bin Liu's picture

The widely used tensile stiffness ratio is not a correct measure of anisotropy degree

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.

Bin Liu's picture

The surface-forming energy release rate based fracture criterion for elastic-plastic crack propagation and interpretation on paradox of Rice

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.

Bin Liu's picture

Adaptive periodical representative volume element for simulating periodical postbuckling behavior

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.

Bin Liu's picture

The theoretical ultimate magnetoelectric coefficients of magnetoelectric composites by optimization design

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.

Bin Liu's picture

Mechanics interpretation on the bending stiffness and wrinkled pattern of graphene.

In this paper we attempt to answer two questions on graphene from a mechanic’s viewpoint: why does this one-atom-thick monolayer have finite bending stiffness to ensure its stability? and what is its wrinkle mechanism? As for the first question, it is found that the repulsive residual internal moment in the bond angle can lead to a nonzero bending stiffness, which makes the graphene flat. Together with long-range attraction among atoms, such as van der Waals forces, a graphene prefers to have a self-buckling wrinkled configuration with many waves.

Bin Liu's picture

Kinetic Energy-Based Temperature Computation in Non-Equilibrium Molecular Dynamics Simulation

      The velocities of atoms in MD simulation are not objective quantities, which depend on the choice of the reference frame and sample size. In our previous study (node/3181), we discussed how to overcome this non-objectivity and compute the atomic stress objectively. In this blog, our newly published paper on temperature computation is attached, and the abstract is as follows.

Bin Liu's picture

Direct influence of residual stress on the bending stiffness of cantilever beams

Although the cantilever beam has been widely used as a sensor to measure various physical quantities, important issues such as how residual stress affects its bending stiffness and what are the underlying physical origins have not been fully understood. We perform both theoretical analyses and finite-element simulations to demonstrate for the first time that without changing the material tangent stiffness, residual stress within the beam can directly influence the bending stiffness of the beam. This direct influence arises from two origins: geometry nonlinearity and Poisson’s ratio effect.

Bin Liu's picture

An effective bead-spring model for polymer simulation

An effective bead-spring model combining the advantages of large time steps of traditional bead-rod models and computational rigor of traditional bead-spring models is proposed to simulate the dynamic behaviors of flexible polymer chains with arbitrary longitudinal stiffness. The proposed model can be used to simulate many types of polymer chains or networks with different chain elasticity via a unified integration scheme with reasonably large time steps. The paper can be found at

Subscribe to RSS - Bin Liu's blog

Recent comments

More comments


Subscribe to Syndicate