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• Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

  M. Arroyo, T. Belytschko

  Physical review B: condensed matter and material physics (2004). Vol. 69 (11), pp. 115415-1, 115415-11

  
  

  Abstract

  A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based on an extension of the Cauchy-Born rule called the exponential Cauchy-Born rule. The continuum object replacing the graphene sheet is a surface without thickness. The method systematically addresses both the characterization of the small strain elasticity of nanotubes and the simulation at large strains. Elastic moduli are explicitly expressed in terms of the functional form of the interatomic potential. The expression for the flexural stiffness of graphene sheets, which cannot be obtained from standard crystal elasticity, is derived. We also show that simulations with the continuum model combined with the finite element method agree very well with zero temperature atomistic calculations involving severe deformations.

  Abstract
  A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based [...]

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• Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes

  M. Arroyo, T. Belytschko

  Int. J. Numer. Meth. Engng. (2004). Vol. 59 (3), pp. 419-456

  
  

  Abstract

  The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved monolayer lattices by means of the exponential Cauchy–Born rule. The constitutive model for a two‐dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the underlying atomistic model. The resulting hyper‐elastic potential depends on the stretch and the curvature of the surface, as well as on internal elastic variables describing the rearrangements of the crystal within the unit cell. Coarse grained calculations of carbon nanotubes (CNTs) are performed by discretizing this continuum mechanics theory by finite elements. A smooth discrete representation of the surface is required, and subdivision finite elements, proposed for thin‐shell analysis, are used. A detailed set of numerical experiments, in which the continuum/finite element solutions are compared to the corresponding full atomistic calculations of CNTs, involving very large deformations and geometric instabilities, demonstrates the accuracy of the proposed approach. Simulations for large multi‐million systems illustrate the computational savings which can be achieved

  Abstract
  The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard [...]

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• Nonlinear mechanical response and rippling of thick multi-walled carbon nanotubes

  M. Arroyo, T. Belytschko

  Physical review letters (2003). Vol. 91 (21), pp. 215505-1, 221505-4

  
  

  Abstract

  The measured drop of the effective bending stiffness of multiwalled carbon nanotubes (MWCNTs) with increasing diameter is investigated by a generalized local quasicontinuum method. The previous hypothesis that this reduction is due to a rippling mode is confirmed by the calculations. The observed ripples result from a complex three-dimensional deformation similar to theYoshimura buckling pattern. It is found that thick MWCNTs exhibit a well-defined nonlinear moment-curvature relation, even for small deformations, governed by the interplay of strain energy relaxation and intertube interactions. Rippling deformations are also predicted for MWCNTs subject to torsion, resulting in an effective torsional modulus much smaller than that predicted by linear elasticity.

  Abstract
  The measured drop of the effective bending stiffness of multiwalled carbon nanotubes (MWCNTs) with increasing diameter is investigated by a generalized local quasicontinuum [...]

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• A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes

  M. Arroyo, T. Belytschko

  Mechanics of materials (2003). Vol. 35 (3-6), pp. 193-215

  
  

  Abstract

  A finite deformation hyper-elastic membrane theory based on inter-atomic potentials for crystalline films composed of a single atomic layer is developed. For this purpose, an extension of the standard Born rule that exploits the differential geometry concept of the exponential map is proposed to deal with the curvature of surfaces. The exponential map is approximated locally and strain measures based on the stretch and the curvature of the membrane arise. The methodology is first particularized to atomic chains in two dimensions, and then to graphene sheets. A reduced model for the transverse mechanics of carbon nanotubes is developed in detail. This model is a hyper-elastic constrained membrane which fully exploits the symmetry of the transverse deformation. Additionally, a continuum version of the non-bonded interactions is provided. The continuum model is discretized using finite elements and very good agreement with molecular mechanics simulations is obtained. Finally, several simulations illustrate the strong effect of the van der Waals interactions in the transverse deformation of carbon nanotubes.

  Abstract
  A finite deformation hyper-elastic membrane theory based on inter-atomic potentials for crystalline films composed of a single atomic layer is developed. For this purpose, [...]

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• An atomistic-based finite deformation membrane for single layer crystalline films

  M. Arroyo, T. Belytschko

  Journal of the Mechanics and Physics of Solids (2002). Vol. 50 (9), pp. 1941-1977

  
  

  Abstract

  A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based on the exponential map is proposed. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of the curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical methods, the exponential map is locally approximated. The effectiveness of our approach is demonstrated by numerical studies of carbon nanotubes. Deformed configurations as well as equilibrium energies of atomistic simulations are compared with those provided by the continuum membrane resulting from this method discretized by finite elements.

  Abstract
  A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based [...]

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• Explicit finite deformation stress integration of the elasto-plastic constitutive equations

  L. Monforte, M. Arroyo, A. Gens, J. Carbonell

  (2014). Computer Methods and Recent Advances in Geomechanics - Proceedings of the 14th Int. Conference of International Association for Computer Methods and Recent Advances in Geomechanics, IACMAG 2014". Kyoto: CRC Press Taylor & Francis Group, p. 267-272.

  
  

  Abstract

  In this work, an explicit integration scheme for hyperelastic-based finite strains elasto-plasticity is presented. One step update equations are obtained from the large deformation multiplicative elasto-plasticity theory, where an exponential variation of the plastic deformation gradient is assumed. In addition, the material tangent matrix is presented and has the same formal structure as the usual small strains elasto-plastic tangent matrix. In purely elastic regime, the proposal reduces to the usual large deformation elasticity equations. Routines to alleviate the main drawbacks of explicit methods are outlined, such as a yield surface drift correction scheme and an adaptive substepping method. Several examples of typical geotechnical tests using the Houlsby hyperelastic model along with the Modified Cam Clay plastic model are discussed. Results from a convergence test suggest that, using an adaptive substepping scheme, the error of the local problem is independent of the step size.

  Abstract
  In this work, an explicit integration scheme for hyperelastic-based finite strains elasto-plasticity is presented. One step update equations are obtained from the large deformation [...]

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• Evaluation of Multilayer Pavement Viscoelastic Properties from Falling Weight Deflectometer using Neural Networks

  J. González, J. Carbonell, W. Bijsterveld

  (2016). Chapters 16. In Materials and Infrastructures 1 (eds J.‐M. Torrenti and F. La Torre).

  
  

  Abstract

  The surface deflection caused by the falling weight deflectometer (FWD) is a dynamic problem usually treated as a static problem. This chapter presents a dynamic solution of the backcalculation problem using a viscoelastic model, introducing a viscosity variable. The calibration process is based on the numerical simulation of the FWD test to approximate the deflection curves obtained in the road track. Description of the experimental curves and the hypothesis of the numerical problem assumed are also described. The samples used to train and validate the artificial neural network (ANN) are conformed by four values per curve times the number of geophones, the input data, while the output data are five Young moduli and five viscosities. The backcalculation process is based on experimental tests from the FWD and calibrated using an FEM simulation of the problem.

  Abstract
  The surface deflection caused by the falling weight deflectometer (FWD) is a dynamic problem usually treated as a static problem. This chapter presents a dynamic solution [...]

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• The particle finite element method (PFEM) in thermo‐mechanical problems

  J. Rodríguez, J. Carbonell, J. Cante, J. Oliver

  Int. J. Numer. Meth. Engng. (2015). (preprint) Vol. 107 (9), pp. 733-785

  
  

  Abstract

  The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo‐mechanical problems. In particular, the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes, and thermal effects. The framework of the numerical scheme is based on the particle finite element method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (α − shape method), in this work, the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function. The description of the thermo‐mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u‐p mixed formulation, with a stabilization of the pressure term via the polynomial pressure projection, is proposed. One of the novelties of this work is the use of a combination between the isothermal split and the so‐called IMPL‐EX hybrid integration technique to enhance the robustness and reduce the typical iteration number of the fully implicit Newton–Raphson solution algorithm. The new set of numerical tools implemented in the PFEM algorithm, including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo‐mechanical problems. Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking‐free element type and different time integration schemes for thermo‐mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example.

  Abstract
  The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo‐mechanical problems. In particular, [...]

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• Numerical simulation of undrained insertion problems in geotechnical engineering with the Particle Finite Element Method (PFEM)

  L. Monforte, M. Arroyo, J. Carbonell, A. Gens

  Computers and Geotechnics (2017). (preprint)Vol. 82, pp. 144-156

  
  

  Abstract

  The paper presents total-stress numerical analyses of large-displacement soil-structure interaction problems in geomechanics using the Particle Finite Element Method (PFEM). This method is characterized by frequent remeshing and the use of low order finite elements to evaluate the solution. Several important features of the method are: (i) a mixed formulation (displacement-mean pressure) stabilized numerically to alleviate the volumetric locking effects that are characteristic of low order elements when the medium is incompressible, (ii) a penalty method to prescribe the contact constraints between a rigid body and a deformable media combined with an implicit scheme to solve the tangential contact constraint, (iii) an explicit algorithm with adaptive substepping and correction of the yield surface drift to integrate the finite-strain multiplicative elasto-plastic constitutive relationship, and (iv) the mapping schemes to transfer information between successive discretizations. The performance of the method is demonstrated by several numerical examples, of increasing complexity, ranging from the insertion of a rigid strip footing to a rough cone penetration test. It is shown that the proposed method requires fewer computational resources than other numerical approaches addressing the same type of problems.

  Abstract
  The paper presents total-stress numerical analyses of large-displacement soil-structure interaction problems in geomechanics using the Particle Finite [...]

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• Damage analysis of masonry structures subjected to rockfalls

  O. Mavrouli, P. Giannopoulos, J. Carbonell, C. Syrmakezis

  Landslides (2017). (preprint) Vol. 14 (3), pp. 891-904

  
  

  Abstract

  Masonry structures present substantial vulnerability to rockfalls. The methodologies for the damage quantification of masonry structures subjected to rockfalls are scarce. An analytical procedure for the damage assessment of masonry structures is presented. The procedure comprises three stages: (1) determination of the rockfall impact actions which are applied to a masonry structure, in terms of external forces, using the particle finite element method (PFEM), (2) evaluation of the mechanical properties, modelling of the masonry structure, and calculation of the internal stresses, using the finite element method (FEM), (3) assessment of the damage due to the rockfall actions, applying a failure criterion adapted to masonries, and calculation of the damage in terms of the percentage of the damaged wall surface. Three real rockfall events and their impact on buildings are analysed. A sensitivity analysis of the proposed procedure is then used to identify the variables that mostly affect the extent of the wall damage, which are the masonry width, the tensile strength, the block diameter and lastly, velocity.

  Abstract
  Masonry structures present substantial vulnerability to rockfalls. The methodologies for the damage quantification of masonry structures subjected to rockfalls are scarce. [...]

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