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Safety operation of important civil structures such as bridges can be estimated by using fracture analysis. Since the analytical methods are not capable of solving many complicated engineering problems, numerical methods have been increasingly adopted. In this paper, a part of isotropic material which contains a crack is considered as a partial model and the proposed model quality is evaluated. EXtended IsoGeometric Analysis (XIGA) is a new developed numerical approach [1, 2] which benefits from advantages of its origins: eXtended Finite Element Method (XFEM) and IsoGeometric Analysis (IGA). It is capable of simulating crack propagation problems with no remeshing necessity and capturing singular field at the crack tip by using the crack tip enrichment functions. Also, exact representation of geometry is possible using only few elements. XIGA has also been successfully applied for fracture analysis of cracked orthotropic bodies [3] and for simulation of curved cracks [4]. XIGA applies NURBS functions for both geometry description and solution field approximation. The drawback of NURBS functions is that local refinement cannot be defined regarding that it is based on tensorproduct constructs unless multiple patches are used which has also some limitations. In this contribution, the XIGA is further developed to make the local refinement feasible by using Tspline basis functions. Adopting a recovery based error estimator in the proposed approach for evaluation of the model quality and performing the adaptive processes is in progress. Finally, some numerical examples with available analytical solutions are investigated by the developed scheme.
We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.
This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.
The distinguishing structural feature of single-layered black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger–Weber potential for single-layered black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layered black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layered black phosphorus that has been reported in ab initio calculations.
The lattice dynamics properties are investigated for twisting bilayer graphene. There are big jumps for the inter-layer potential at twisting angle θ=0° and 60°, implying the stability of Bernal-stacking and the instability of AA-stacking structures, while a long platform in [8,55]° indicates the ease of twisting bilayer graphene in this wide angle range. Significant frequency shifts are observed for the z breathing mode around θ=0° and 60°, while the frequency is a constant in a wide range [8,55]°. Using the z breathing mode, a mechanical nanoresonator is proposed to operate on a robust resonant frequency in terahertz range.
The upper limit of the thermal conductivity and the mechanical strength are predicted for the polyethylene chain, by performing the ab initio calculation and applying the quantum mechanical non-equilibrium Green’s function approach. Specially, there are two main findings from our calculation: (1) the thermal conductivity can reach a high value of 310 Wm−1 K−1 in a 100 nm polyethylene chain at room temperature and the thermal conductivity increases with the length of the chain; (2) the Young’s modulus in the polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can sustain 32.85%±0.05% (ultimate) strain before undergoing structural phase transition into gaseous ethylene.
This paper presents several aspects of characterization of welding heat source parameters in Goldak’s double ellipsoidal model using Sysweld simulation of welding of two overlapping beads on a substrate steel plate. The overlap percentages ranged from 40% to 80% in increments of 10%. The new material properties of the fused metal were characterized using Weldware and their continuous cooling transformation curves. The convective and radiative heat transfer coefficients as well as the cooling time t8/5 were estimated using numerical formulations from relevant standards. The effects of the simulation geometry and mesh discretization were evaluated in terms of the factor F provided in Sysweld. Eventually, the parameters of Goldak’s double ellipsoidal heat source model were determined for the welding simulation of overlapping beads on the plate and the simulated bead geometry, extent of the molten pool and the HAZ were compared with the macrographs of cross-sections of the experimental weldments. The results showed excellent matching, thus verifying this methodology for determination of welding heat source parameters.
Explicit solutions for the cohesive energy between carbon nanotubes, graphene and substrates are obtained through continuum modeling of the van der Waals interaction between them. The dependence of the cohesive energy on their size, spacing and crossing angles is analyzed. Checking against full atom molecular dynamics calculations and available experimental results shows that the continuum solution has high accuracy. The equilibrium distances between the nanotubes, graphene and substrates with minimum cohesive energy are also provided explicitly. The obtained analytical solution should be of great help for understanding the interaction between the nanostructures and substrates, and designing composites and nanoelectromechanical systems.