Low-order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

This article presents a novel finite element formulation for the Biot equation using low-order elements. Additionally, an extra degree of freedom is introduced to treat the volumetric locking steaming from the effective response of the medium; its balance equation is also stabilized. The accuracy of the proposed formulation is demonstrated by means of numerical analyses.Peer ReviewedPostprint (author's final draft

On discontinuous Galerkin methods

Discontinuous Galerkin methods have received considerable attention in recent years for applications to many problems in which convection and diffusion terms are present. Several alternatives for treating the diffusion flux effects have been introduced, as well as, for treatment of the convective flux terms. This report summarizes some of the treatments that have been proposed. It also considers how elementary finite volume methods may be considered as the most primative form of a discontinuous Galerkin method as well as how it may be formed as a finite element method. Several numerical examples are included in the report which summarize results for discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for diffusion-reaction problems, convection-diffusion problems, and a special problem with a turning point. We identify aspects which relate to accuracy as well as stability of the method

XFEM formulation with sub-interpolation, and equivalence to zero-thickness interface elements

This is the accepted version of the following article: Crusat L, Carol I, Garolera D. XFEM formulation with sub‐interpolation, and equivalence to zero‐thickness interface elements. Int J Numer Anal Methods Geomech. 2019;43:45–76. https://doi.org/10.1002/nag.2853, which has been published in final form at https://doi.org/10.1002/nag.2853This paper describes a particular formulation of the extended finite element method (XFEM) specifically conceived for application to existing discontinuities of fixed location, for instance, in geological media. The formulation is based on two nonstandard assumptions: (1) the use of sub-interpolation functions for each subdomain and (2) the use of fictitious displacement variables on the nodes across the discontinuity (instead of the more traditional jump variables). Thanks to the first of those assumptions, the proposed XFEM formulation may be shown to be equivalent to the standard finite element method with zero-thickness interface elements for the discontinuities (FEM+z). The said equivalence is theoretically proven for the case of quadrangular elements cut in two quadrangles by the discontinuity, and only approximate for other types of intersections of quadrangular or triangular elements, in which the XFEM formulation corresponds to a kinematically restricted version of the corresponding interface plus continuum scheme. The proposed XFEM formulation with sub-interpolation, also helps improving spurious oscillations of the results obtained with natural interpolation functions when the discontinuity runs skew to the mesh. A possible explanation for these oscillations is provided, which also explains the improvement observed with sub-interpolation. The paper also discusses the oscillations observed in the numerical results when some nodes are too close to the discontinuity and proposes the remedy of moving those nodes onto the discontinuity itself. All the aspects discussed are illustrated with some examples of application, the results of which are compared with closed-form analytical solutions or to existing XFEM results from the literature.Peer ReviewedPostprint (author's final draft

Finite calculus formulation for incompressible solids using linear triangles and tetrahedra

Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach is taken to overcome this undesirable effect. The starting point is a new setting of the governing differential equations using a finite calculus (FIC) formulation. The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem. The FIC approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective–diffusive and fluid flow problems. The same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to linear static problems as well as to the semi‐implicit and explicit 2D and 3D non‐linear transient dynamic analysis of an impact problem and a bulk forming process are presented

Obituary

Professor E. M. Alf Samuelsson from Chalmers University, Göteborg, Sweden, died on the 3rd of June 2005 at the age of 75 after a lengthy illness. Professor Samuelsson was an engineer with Professor Sven-Olof Asplund’s ConstructionCompany from 1952 to the time he joined Chalmers University in September 1954. In 1963 he completed his doctoral thesis with Professor Asplund on the subject of analysis of framedstructures by use of algebraic topology. He was beloved by students, colleagues and co-workersand was known as ‘Alf’ by all. Through his foresight and deep knowledge in many fields Alfcreated a strong group in Computational Mechanics at Chalmers University, which he led until his retirement in July 1994. Under his leadership the Department of Structural Mechanics flourished and has been widely recognized for its many scientific contributions. Alf supervised a large number of doctoral students of which nine have become professors. Alf was, formany years, the Dean of Research at Chalmers and has contributed much to the University’s development

Finite Element Modeling of Ultrasonic Inspection of Weldments

High performance weldments for critical service applications require 100% inspection. Balanced against the adaptability of the ultrasonic method for automated inspection are the difficulties encountered with nonhomogeneous and anisotropic materials. This research utilizes crystals and bicrystals of nickel to model austenitic weld metal, where the anisotropy produces scattering and mode conversion, making detection and measurement of actual defects difficult. Well characterized samples of Ni are produced in a levitation zone melting facility. Crystals in excess of 25 mm diameter and length are large enough to permit ultrasonic measurements of attenuation, wave speed, and spectral content. At the same time, the experiments are duplicated as finite element models for comparison purposes. Finite element models permit easy description of boundary conditions, geometry, and loading. Direct integration of the wave equation is done with the Newmark-Beta and Wilson-Theta Methods. The usual problem with the large number of degress of freedom can be alleviated with the use of Guyan reduction. Two-dimensional comparisons showing mode conversion and a plate with a flaw are made. The continued development of this computational tool should increase understanding of quantitative ultrasonic inspection

Computer simulation of breast reduction surgery

Background: Plastic surgery of the breast, particularly breast reduction, is considered difficult. It can become a challenge for a less experienced surgeon to understand exactly what to do when facing a particular type of breast and how to avoid unsatisfactory results. Methods: The goal of this study was to create a computer model of the breast that provides a basis for the simulation of breast surgery, particularly breast reduction. The reconstruction of elastic parameters is based on observations of the breast with the patient in different positions. Results: It is shown that several measurements with the patient in different positions allow one to choose the parameters of the model and determine the elastic coefficients of the breast and the skin. The geometry of the breast before and after surgery is simulated. A qualitative study of the incision parameters’ influence on the final geometry of the breast is presented. Conclusion: The developed methodology and software allow one to estimate the form of the breast after the surgery by knowing its form before surgery and taking into consideration the parameters of incision applied by the surgeon at the time of surgery. The described approach can be used for the qualitative and quantitative study of breast reduction surgery with a satisfactory result. Level of Evidence: V (This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors http://www.springer.com/00266.