Antonio J. Gil

The bending of single layer graphene sheets: the lattice versus continuum approach

The out-of-plane bending behaviour of single layer graphene sheets (SLGSs) is investigated using a special equivalent atomistic-continuum model, where the C-C bonds are represented by deep shear bending and axial stretching beams and the graphene properties by a homogenization approach. SLGS models represented by circular and rectangular plates are subjected to linear and nonlinear geometric point loading, similar to what is induced by an atomic force microscope (AFM) tip. The graphene models are developed using both a lattice and a continuum finite element discretization of the partial differential equations describing the mechanics of the graphene. The minimization of the potential energy allows us to identify the thickness, elastic parameters and force/displacement histories of the plates, in good agreement with other molecular dynamic (MD) and experimental results. We note a substantial equivalence of the linear elastic mechanical properties exhibited by circular and rectangular sheets, while some differences in the nonlinear geometric elastic regime for the two geometrical configurations are observed. Enhanced flexibility of SLGSs is observed by comparing the nondimensional force versus displacement relations derived in this work and the analogous ones related to equivalent plates with conventional isotropic materials.

The formation of wrinkles in single-layer graphene sheets under nanoindentation

We investigate the formation of wrinkles and bulging in single-layer graphene sheets using an equivalent atomistic continuum nonlinear hyperelastic theory for nanoindentation and nanopressurization. We show that nonlinear geometrical effects play a key role in the development of wrinkles. Without abandoning the classical tension field membrane theory, we develop an enhanced model based upon the minimization of a relaxed energy functional in conjunction with nonlinear finite hyperelasticity. Formation of wrinkles are observed in rectangular graphene sheets due to the combination of induced membrane tension and edge effects under external pressure.

A vertex centred Finite Volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics

A vertex centred Finite Volume algorithm is presented for the numerical simulation of fast transient dynamics problems involving large deformations. A mixed formulation based upon the use of the linear momentum, the deformation gradient tensor and the total energy as conservation variables is discretised in space using linear triangles and tetrahedra in two-dimensional and three-dimensional computations, respectively. The scheme is implemented using central differences for the evaluation of the interface fluxes in conjunction with the Jameson-Schmidt-Turkel (JST) artificial dissipation term. The discretisation in time is performed by using a Total Variational Diminishing (TVD) two-stage Runge-Kutta time integrator. The JST algorithm is adapted in order to ensure the preservation of linear and angular momenta. The framework results in a low order computationally efficient solver for solid dynamics, which proves to be very competitive in nearly incompressible scenarios and bending dominated applications.

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

A vertex centred Jameson-Schmidt-Turkel (JST) finite volume algorithm was recently introduced by the authors (Aguirre et al., 2014 1) in the context of fast solid isothermal dynamics. The spatial discretisation scheme was constructed upon a Lagrangian two-field mixed (linear momentum and the deformation gradient) formulation presented as a system of conservation laws 2-4. In this paper, the formulation is further enhanced by introducing a novel upwind vertex centred finite volume algorithm with three key novelties. First, a conservation law for the volume map is incorporated into the existing two-field system to extend the range of applications towards the incompressibility limit (Gil et al., 2014 5). Second, the use of a linearised Riemann solver and reconstruction limiters is derived for the stabilisation of the scheme together with an efficient edge-based implementation. Third, the treatment of thermo-mechanical processes through a Mie-Gruneisen equation of state is incorporated in the proposed formulation. For completeness, the study of the eigenvalue structure of the resulting system of conservation laws is carried out to demonstrate hyperbolicity and obtain the correct time step bounds for non-isothermal processes. A series of numerical examples are presented in order to assess the robustness of the proposed methodology. The overall scheme shows excellent behaviour in shock and bending dominated nearly incompressible scenarios without spurious pressure oscillations, yielding second order of convergence for both velocities and stresses.

An enhanced Immersed Structural Potential Method for fluid-structure interaction

Within the group of immersed boundary methods employed for the numerical simulation of fluid-structure interaction problems, the Immersed Structural Potential Method (ISPM) was recently introduced (Gil et al., 2010) [1] in order to overcome some of the shortcomings of existing immersed methodologies. In the ISPM, an incompressible immersed solid is modelled as a deviatoric strain energy functional whose spatial gradient defines a fluid-structure interaction force field in the Navier-Stokes equations used to resolve the underlying incompressible Newtonian viscous fluid. In this paper, two enhancements of the methodology are presented. First, the introduction of a new family of spline-based kernel functions for the transfer of information between both physics. In contrast to classical IBM kernels, these new kernels are shown not to introduce spurious oscillations in the solution. Second, the use of tensorised Gaussian quadrature rules that allow for accurate and efficient numerical integration of the immersed structural potential. A series of numerical examples will be presented in order to demonstrate the capabilities of the enhanced methodology and to draw some key comparisons against other existing immersed methodologies in terms of accuracy, preservation of the incompressibility constraint and computational speed.

A two-step Taylor-Galerkin formulation for fast dynamics

Purpose – The purpose of this paper is to present a new stabilised low-order finite element methodology for large strain fast dynamics. Design/methodology/approach – The numerical technique describing the motion is formulated upon the mixed set of first-order hyperbolic conservation laws already presented by Lee et al. (2013) where the main variables are the linear momentum, the deformation gradient tensor and the total energy. The mixed formulation is discretised using the standard explicit two-step Taylor-Galerkin (2TG) approach, which has been successfully employed in computational fluid dynamics (CFD). Unfortunately, the results display non-physical spurious (or hourglassing) modes, leading to the breakdown of the numerical scheme. For this reason, the 2TG methodology is further improved by means of two ingredients, namely a curl-free projection of the deformation gradient tensor and the inclusion of an additional stiffness stabilisation term. Findings – A series of numerical examples are carried out ...

Computer Simulation of Superplastic Forming in Restorative Dentistry

Superplastic forming of dental prostheses using Ti-6Al-4V alloy is a recent innovation. Such prostheses are lightweight and strong and can be produced using low cost dies made from standard dental casting investment materials. In contrast to the volume production of SPF components a dental prostheses is unique to each patient and the SPF pressure cycle required to form the prosthesis equally unique. Consequently it is necessary to employ computer simulation to reduce trial and error experimentation. This paper will summarise the computer simulation of the process and subsequent experimental validation. Both geometric and finite element simulation methods will be discussed with an emphasis on the pressure cycle algorithm contained in the latter method.

F.E.M. for Prestressed Saint Venant-Kirchhoff Hyperelastic Membranes

This chapter presents a complete numerical formulation for the nonlinear structural analysis of prestressed membranes with applications in Civil Engineering. These sort of membranes can be considered to undergo large deformations but moderate strains, consequently nonlinear continuum mechanics principles for large deformation of prestressed bodies will be employed in order to proceed with the analysis. The constitutive law adopted for the material will be the one corresponding to a prestressed hyperelastic Saint Venant-Kirchhoff model. To carry out the computational resolution of the structural problem, the Finite Element Method (FEM) will be implemented according to a Total Lagrangian Formulation (TLF), by means of the Direct Core Congruential Formulation (DCCF). Eventually, some numerical examples will be introduced to verify the accuracy and robustness of the aforementioned formulation.

Finite element modelling of thin metal sheet forming

Abstract: This chapter reviews the finite element simulation of superplastic forming processes. Both the traditional flow formulation and the incremental flow formulation are presented. The chapter reviews the finite element discretisation of the equilibrium equations describing the motion of a forming sheet including available strategies for the evaluation of a correct forming pressure, which is often one of the key outputs of the simulation. A number of examples are given in relation to applications in the aerospace industry as well as more recent applications in the biomedical field.

Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design: Transient nonlinear acousto-magneto-mechanical coupling in MRI

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