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The peridynamic (PD) theory is a nonlocal reformulation of mechanics with various advantages over common approaches, mainly local continuum mechanics and molecular dynamics (MD). PD theory can capture phenomena at different dimensions, including nanoscale. However, limited studies have been performed by this theory in nanoscale, which have generally focused on the feasibility and accuracy of using PD in atomic-scale modeling. In the present study, based on the ordinary state-based peridynamic method, we investigate the fracture of pre-cracked single layer graphene sheets (SLGSs) under uniaxial tension. By simulating the exact atomic model of graphene, the failure strain and crack growth pattern in the zigzag and armchair directions in PD are compared with MD. We show that by considering some restrictions, these two methods have a good consistency with each other. Afterward, we study two different coarse-grained PD models and demonstrate this method can simulate the failure of graphene with acceptable accuracy. A significant reduction in simulation cost is an excellent point of the PD compared to the MD simulation model. Under these conditions, a massive atomic model with several million atoms can be easily simulated. [ABSTRACT FROM AUTHOR]

Peridynamics is a nonlocal formulation of solid mechanics capable of unguided modelling of crack initiation, propagation and fracture. Peridynamics is based upon integral equations, thereby avoiding spatial derivatives, which are not defined at discontinuities, such as crack surfaces. Rice's J-contour integral is a firmly established expression in classic continuum solid mechanics, used as a fracture characterizing parameter for both linear and nonlinear elastic materials. A corresponding nonlocal J-integral has previously been derived for peridynamic modelling, which is based on the calculation of a set of displacement derivatives and force interactions associated with the contour of the integral. In this paper, we present an alternative calculation of the classical linear elastic J-integral for use in peridynamics, by writing Rice's J-integral as a function entirely of displacement derivatives. The accuracy of the proposed J-integral on displacement formulation is investigated by applying it to the exact analytical displacement solution of an infinite specimen with a central crack and comparing the exact analytical expression of its J-integral K I 2 / E . Further comparison with a well-known peridynamic crack problem shows very good agreement. The suggested method is computationally efficient and further allows testing of the accuracy of a peridynamic model as such. [ABSTRACT FROM AUTHOR]

A continuum model of ductile fracture initiation is presented which is based on consideration of the work done on the system sufficient to cause release of the binding energy necessary for crack formation. The fracture criterion is posed for plastic materials with no pre-existing crack as a critical state reached when the energy release rate of the bulk system is balanced by the energy release rate associated with the fractured medium. Two fracture modes are considered which are commonly addressed in fracture mechanics: mode I crack opening perpendicular to the fracture plane and mode II shear rupture tangential to the fracture plane. A study of the use of the criterion for a plastic material with power law hardening is examined and compared with published experimental data and empirical criteria. [ABSTRACT FROM AUTHOR]

A new technique is presented to study fracture in nanomaterials by coupling quantum mechanics (QM) and continuum mechanics (CM). A key new feature of this method is that broken bonds are identified by a sharp decrease in electron density at the bond midpoint in the QM model. As fracture occurs, the crack tip position and crack path are updated from the broken bonds in the QM model. At each step in the simulation, the QM model is centered on the crack tip to adaptively follow the path. This adaptivity makes it possible to trace paths with complicated geometries. The method is applied to study the propagation of cracks in graphene which are initially perpendicular to zigzag and armchair edges. The simulations demonstrate that the growth of zigzag cracks is self-similar whereas armchair cracks advance in an irregular manner. The critical stress intensity factors for graphene were found to be 4.21 MPa $${\sqrt {\rm m}}$$ for zigzag cracks and 3.71 MPa $${\sqrt{\rm m}}$$ for armchair cracks, which is about 10% of that for steel. [ABSTRACT FROM AUTHOR]

In the paper, the results of numerical failure analysis of plain concrete beams loaded by impact three-point bending load are presented and discussed. The theoretical framework for the numerical analysis is continuum mechanics and irreversible thermodynamics. The spatial discretization is performed by the finite element method using update Lagrange formulation. Green–Lagrange stain tensor is used as a strain measure. To account for cracking and damage of concrete, the beam is modeled by the rate sensitive microplane model with the use of the so-called co-rotational stress tensor. Damage and cracking phenomena are modeled within the concept of smeared cracks. To assure objectivity of the analysis with respect to the size of the finite elements, crack band method is used. The contact-impact analysis is based on the mechanical interaction between two bodies—concrete beam (master) and dropping hammer (slave) falling on the mid span of the beam. The contact constrains are satisfied by Lagrange multiplier method, which is adapted for the explicit time integration scheme. To investigate the influence of loading rate on the failure mode of the beam parametric study is carried out. The numerical results are evaluated, discussed and compared with test results known from the literature. It is shown that the beam resistance and failure mode strongly depend on loading rate. For lower loading rates beam fails in bending (mode-I fracture). However, with increasing loading rate there is a transition of the failure mechanism from bending to shear. The results are in good agreement with theoretical and experimental results known from the literature. [ABSTRACT FROM AUTHOR]

A variational formulation of quasi-static brittle fracture in elastic solids at small strains is proposed and an associated finite element implementation is presented. On the theoretical side, a consistent thermodynamic framework for brittle crack propagation is outlined. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius–Planck inequality. Here, the canonical direction of the crack propagation associated with the classical Griffith criterion is the direction of the material configurational force which maximizes the local dissipation at the crack tip. On the numerical side, we first consider a standard finite element discretization in the two-dimensional space which yields a discrete formulation of the global dissipation in terms of configurational nodal forces. Next, consistent with the node-based setting, the discretization of the evolving crack discontinuity for two-dimensional problems is performed by the doubling of critical nodes and interface segments of the mesh. A crucial step for the success of this procedure is its embedding into a r-adaptive crack-segment re-orientation algorithm governed by configurational-force-based directional indicators. Here, successive crack propagation is performed by a staggered loading-release algorithm of energy minimization at frozen crack state followed by nodal releases at frozen deformation. We compare results obtained by the proposed formulation with other crack propagation criteria. The computational method proposed is extremely robust and shows an excellent performance for representative numerical simulations. [ABSTRACT FROM AUTHOR]

Due to the enormous difference in the scales involved in correlating the macroscopic properties with the micro- and nano-physical mechanisms of carbon nanotube-reinforced composites, multiscale mechanics analysis is of considerable interest. A hybrid atomistic/continuum mechanics method is established in the present paper to study the deformation and fracture behaviors of carbon nanotubes (CNTs) in composites. The unit cell containing a CNT embedded in a matrix is divided in three regions, which are simulated by the atomic-potential method, the continuum method based on the modified Cauchy–Born rule, and the classical continuum mechanics, respectively. The effect of CNT interaction is taken into account via the Mori–Tanaka effective field method of micromechanics. This method not only can predict the formation of Stone–Wales (5-7-7-5) defects, but also simulate the subsequent deformation and fracture process of CNTs. It is found that the critical strain of defect nucleation in a CNT is sensitive to its chiral angle but not to its diameter. The critical strain of Stone–Wales defect formation of zigzag CNTs is nearly twice that of armchair CNTs. Due to the constraint effect of matrix, the CNTs embedded in a composite are easier to fracture in comparison with those not embedded. With the increase in the Young’s modulus of the matrix, the critical breaking strain of CNTs decreases. [ABSTRACT FROM AUTHOR]