A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization

A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

Elastoplastic consolidation at finite strain. Part 2: finite element implementation and numerical examples

A mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. A two-field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations. The constitutive model for the solid phase is represented by modified Cam—Clay theory formulated in the Kirchhoff principal stress space, and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches. The constitutive model for fluid flow is represented by a generalized Darcy's law formulated with respect to the current configuration. The finite element model is fully amenable to exact linearization. Numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses. The paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability.

Preface : (Boundary Element Method) Computers and Structures 83 (2005)

The Boundary Element Method is a powerful numerical technique well rooted in everyday engineering practice. This is shown by boundary element methods included in the most important commercial computer packages and in the continuous publication of books composed to explain the features of the method to beginners or practicing engineers. Our first paper in Computers & Structures on Boundary Elements was published in 1979 (C & S 10, pp. 351–362), so this Special Issue is for us not only the accomplishment of our obligation to show other colleagues the possibilities of a numerical technique in which we believe, but also the celebration of our particular silver jubilee with this Journal.

The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography. The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results.

Modelling of corrosion-induced cover cracking in reinforced concrete by an embedded cohesive crack finite element

Corrosion of a reinforcement bar leads to expansive pressure on the surrounding concrete that provokes internal cracking and, eventually, spalling and delamination. Here, an embedded cohesive crack 2D finite element is applied for simulating the cracking process. In addition, four simplified analytical models are introduced for comparative purposes. Under some assumptions about rust properties, corrosion rate, and particularly, the accommodation of oxide products within the open cracks generated in the process, the proposed FE model is able to estimate time to surface cracking quite accurately. Moreover, emerging cracking patterns are in reasonably good agreement with expectations. As a practical case, a prototype application of the model to an actual bridge deck is reported.

An efficient nonlinear transformation for the numerical computation of the singular integrals appearing in the 2-D Boundary Element Method

We discuss several methods, based on coordinate transformations, for the evaluation of singular and quasisingular integrals in the direct Boundary Element Method. An intrinsec error of some of these methods is detected. Two new transformations are suggested which improve on those currently available.

Goal-oriented self-adaptive hp-strategies for finite element analysis of electromagnetic scattering and radiation problems

In this paper, a fully automatic goal-oriented hp-adaptive finite element strategy for open region electromagnetic problems (radiation and scattering) is presented. The methodology leads to exponential rates of convergence in terms of an upper bound of an user-prescribed quantity of interest. Thus, the adaptivity may be guided to provide an optimal error, not globally for the field in the whole finite element domain, but for specific parameters of engineering interest. For instance, the error on the numerical computation of the S-parameters of an antenna array, the field radiated by an antenna, or the Radar Cross Section on given directions, can be minimized. The efficiency of the approach is illustrated with several numerical simulations with two dimensional problem domains. Results include the comparison with the previously developed energy-norm based hp-adaptivity.

Application of the Boundary Element Method to the Analysis of Bridge Abutments

The B.E. technique is applied to an interesting dynamic problem: the interaction between bridges and their abutments. Several two-dimensional cases have been tested in relation with previously published analytical results. A three-dimensional case is also shown and different considerations in relation with the accuracy of the method are described.

Finite Element Analysis Model of a Contactless Transformer for Battery Chargers in Electric Vehicles

A contactless transformer model is proposed in this paper using Finite Element Analysis (FEA). This model can be used to simulate Inductive Coupling Power Transfer (ICPT) systems with good accuracy of the transformer and reduce the fabrication time of these systems. The model not only takes into account the geometry of the windings but also the frequency effects in them. As the transformer does not have a magnetic core, it is complicated to model because the flux is expanded in the area around the windings. In order to obtain a very accurate model, it is necessary to use a 2D/3D field solver.

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.

Finite element simulation of sandwich panels of laminated plaster and rockwool under mixed mode fracture

Sandwich panels of laminated gypsum and rock wool have shown large pathology of cracking due to excessive slabs deflection. Currently the most widespread use of this material is as vertical elements of division or partition, with no structural function, what justifies that there are no studies on the mechanism of fracture and mechanical properties related to it. Therefore, and in order to reduce the cracking problem, it is necessary to progress in the simulation and prediction of the behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability.

Simplified Finite Element Assessment of Beams With and Without Shear Deformation

This paper presents a simplified finite element (FE) methodology for solving accurately beam models with (Timoshenko) and without (Bernoulli-Euler) shear deformation. Special emphasis is made on showing how it is possible to obtain the exact solution on the nodes and a good accuracy inside the element. The proposed simplifying concept, denominated as the equivalent distributed load (EDL) of any order, is based on the use of Legendre orthogonal polynomials to approximate the original or acting load for computing the results between the nodes. The 1-span beam examples show that this is a promising procedure that allows the aim of using either one FE and an EDL of slightly higher order or by using an slightly larger number of FEs leaving the EDL in the lowest possible order assumed by definition to be equal to 4 independently of how irregular the beam is loaded.

Finite element simulation of sandwich panels of plasterboard and rock wool under mixed mode fracture

This paper presents the results of research on mixed mode fracture of sandwich panels of plasterboard and rock wool. The experimental data of the performed tests are supplied. The specimens were made from commercial panels. Asymmetrical three-point bending tests were performed on notched specimens. Three sizes of geometrically similar specimens were tested for studying the size effect. The paper also includes the numerical simulation of the experimental results by using an embedded cohesive crack model.The involved parameters for modelling are previously measured by standardised tests.

Letters to the editor [An implementation of the Boundary Element Method for zoned media with stress discontinuities, T.J. Rudolphi, 1983]

En esta carta al editor, el profesor D. Enrique Alarcón Álvarez comenta el artículo de Thomas J. Rudolphi "An implementation of the Boundary Element Method for zoned media with stress discontinuities" publicado en la revista "International Journal for Numerical Methods in Engineering" Vol. 19, Nº 1, pags. 1–15, enero 1983.

A C1 finite element for Kirchhoff plate bending

After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented.. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.