Javier Bonet

A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications

This paper presents a simple linear tetrahedron element that can be used in explicit dynamics applications involving nearly incompressible materials or incompressible materials modelled using a penalty formulation. The element prevents volumetric locking by defining nodal volumes and evaluating average nodal pressures in terms of these volumes. Two well-known examples relating to the impact of elasto–plastic bars are used to demonstrate the ability of the element to model large isochoric strains without locking.

Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications

This papers summarizes two linear tetrahedral FE formulations that have been recently proposed to overcome volumetric locking in nearly incompressible explicit dynamic applications. In particular, the average nodal pressure (ANP) technique described by Bonet and Burton (Communications in Numerical Methods in Engineering 1998; 14:437–449) is briefly reviewed. In addition, the split-based formulation proposed by Zienkiewicz et al. (International Journal for Numerical Methods in Engineering 1998; 43:565–583) is described here in terms of a time integration of the nodal Jacobian. This will make it simple to compare both techniques and will enable a new combined method to be presented. The paper will then discuss the stability constraints that each technique places on the timestep size. A von-Neuman stability analysis on simple 1-D uniform meshes will show that the ANP element permits the use of much larger timesteps than the split based formulations. Finally, numerical examples corroborating in 3-D this analytical conclusions will be presented. Copyright

Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson's Equation

We present a method for Poissons equation that computes guaranteed upper and lower bounds for the values of piecewise-polynomial linear functional outputs of the exact weak solution of the infinite-dimensional continuum problem with piecewise-polynomial forcing. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a constrained minimization problem. Localization is achieved by Lagrangian relaxation and the bounds are computed by appeal to a local dual problem. The proposed method computes approximate Lagrange multipliers using traditional finite element approximations to calculate a primal and an adjoint solution along with well-known hybridization techniques to calculate interelement continuity multipliers. The computed bounds hold uniformly for any level of refinement, and in the asymptotic convergence regime of the finite element method, the bound gap decreases at twice the rate of the energy norm measure of the error in the finite element solution. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity that is linear in the number of elements in the finite element discretization. The elemental contributions to the bound gap are always positive and hence lend themselves to be used as adaptive indicators, as we demonstrate with a numerical example.

Multiple-Fluid SPH Simulation Using a Mixture Model

This article presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is captured by using an improved mixture model, and a stable and accurate SPH formulation is rigorously derived to resolve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of real-world multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction, etc. Moreover, the new multiple-fluid SPH scheme can be readily integrated into existing state-of-the-art SPH simulators, and the multiple-fluid simulation is easy to set up. Various examples are presented to demonstrate the effectiveness of our approach.

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.

A review of the numerical analysis of superplastic forming

Abstract This paper reviews the literature on the numerical simulation of superplastic forming (SPF). After introducing the phenomena of superplasticity and superplastic constitutive equations, non finite element analyses are reviewed. The finite element method of solution to SPF simulation is then examined within the context of the standard flow formulation. However non steady state SPF is not ideally suited to a standard flow formulation and an alternative, incremental flow formulation is discussed.

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 ...