Implicit-explicit Integration Scheme Research Articles

A stable mesh-independent approach for numerical modelling of structured soils at large strains

We describe the large strain implementation of an elasto-plastic model for structured soils into G-PFEM, a code developed for geotechnical simulations using the Particle Finite Element Method. The constitutive model is appropriate for naturally structured clays, cement-improved soils and soft rocks. Structure may result in brittle behavior even in contractive paths; as a result, localized failure modes are expected in most applications. To avoid the pathological mesh-dependence that may accompany strain localization, a nonlocal reformulation of the model is employed. The resulting constitutive model is incorporated into a numerical code by means of a local explicit stress integration technique. To ensure computability this is hosted within a more general Implicit-Explicit integration scheme (IMPLEX). The good performance of these techniques is illustrated by means of element tests and boundary value problems.

Numerical modeling of steel fiber reinforced concrete with a discrete and explicit representation of steel fibers

This work presents a novel numerical model based on the use of coupling finite elements to simulate the behavior of steel fiber reinforced concrete (SFRC) with a discrete and explicit representation of steel fibers. The material is described as a composite made up by three phases: concrete, discrete discontinuous fibers and fiber-matrix interface. The steel fibers are modeled using two-node finite elements (truss elements) with a one-dimensional elastoplastic constitutive model. They are positioned using an isotropic uniform random distribution, considering the wall effect of the mold. A non-rigid coupling procedure is proposed for modeling the complex nonlinear behavior of the fiber-matrix interface by adopting an appropriate constitutive damage model to describe the relation between the shear stress (adherence stress) and the relative sliding between the matrix and each fiber individually. An isotropic damage model including two independent scalar damage variables for describing the concrete behavior under tension and compression is considered. To increase the computability and robustness of the continuum damage models used to simulate matrix and interface behavior, an implicit-explicit integration scheme is used. Numerical examples involving a single fiber and a cloud of fibers are performed. Comparisons with experimental results demonstrate that the application of the numerical strategy for modeling the behavior of SFRC is highly promising and may constitute an important tool for better understanding the effects of the different aspects involved in the failure process of this material.

Symbolic multibody methods for real-time simulation of railway vehicles

In this work, recently developed state-of-the-art symbolic multibody methods are tested to accurately model a complex railway vehicle. The model is generated using a symbolic implementation of the principle of virtual power. Creep forces are modeled using a direct symbolic implementation of the standard linear Kalker model. No simplifications, such as base parameter reduction, partial-linearization or lookup tables for contact kinematics, are used. An Implicit–Explicit integration scheme is proposed to efficiently deal with the stiff creep dynamics. Real-time performance is achieved: the CPU time required for a very robust $1~\text{ms}$ integration time step is 203 μs.

A robust numerical framework for simulating localized failure and fracture propagation in frictional materials

A computationally robust framework for simulating geomaterial failure patterns is presented in this paper. Finite element simulations which feature the use of embedded discontinuities to track material failure are known to suffer from convergence issues due to a lack of robustness. Oftentimes, complex time step-cutting schemes or arc-length methods are required in order to achieve convergence. This may invariably limit the complexity of constitutive models available for use in tracking nonlinear material behavior. To this end, we use an implicit–explicit integration scheme [Impl–Ex (Oliver et al. in Comput Methods Appl Mech Eng 195(52):7093–7114, 2006)] coupled with a novel constitutive model which allows for combined opening and shearing displacement in tension, as well as frictional sliding in compression. We show that this framework is suitable for capturing complex fracture patterns in geomaterial structures without the need for elaborate continuance schemes.

On the use of finite elements with a high aspect ratio for modeling cracks in quasi-brittle materials

A new technique for modeling cracks in quasi-brittle materials based on the use of interface solid finite elements is presented. This strategy named mesh fragmentation technique consists in introducing sets of standard low-order solid finite elements with a high aspect ratio in between regular (or bulk) elements of the mesh to fill the very thin gaps left by the mesh fragmentation procedure. The conception of this strategy is supported by the fact that, as the aspect ratio of a standard low-order solid finite element increases, the element strains also increase, approaching the same kinematics as the Continuum Strong Discontinuity Approach. As a consequence, the analyses can be performed integrally in the context of the continuum mechanics, and complex crack patterns can be simulated without the need of tracking algorithms. A tension damage constitutive relation between stresses and strains is proposed to describe crack formation and propagation. This constitutive model is integrated using an implicit–explicit integration scheme to avoid convergence drawbacks, commonly found in problems involving discontinuities. 2D and 3D numerical analyses are performed to show the applicability of the presented technique. Relevant aspects such as the influence of the thickness of the interface elements and mesh objectivity are investigated. The results show that the technique is able to predict satisfactorily the behavior of structural members involving different crack patterns, including multiple cracks, without significant mesh dependency provided that unstructured meshes are used.

A modified implicit–explicit integration scheme: an application to elastoplasticity problems

In this paper, a novel modified version of the implicit–explicit integration scheme (IMPL-EX) proposed by Oliver (Comput Methods Appl Mech Eng 197:1865–1889, 2008) is presented. This modified approach has as its main difference with respect to the standard IMPL-EX the choice of internal variables to be updated. In the modified approach what is updated are the plastic strain tensor components, instead of the plastic multiplier. This choice of update, as will be shown, has the advantage of making the algorithm stiffness matrix constant, while keeping all the advantages that comes with the standard IMPL-EX already pointed out by Oliver in (Comput Methods Appl Mech Eng 197:1865–1889, 2008) and (Comput Methods Appl Mech Eng 195:7093–7114, 2006). The scope of the paper will be restricted to the application of the proposed scheme to elastoplasticity problems. Due to what is exposed above the authors named the proposed method by Modified IMPL-EX. To assess the algorithm proposed, a few verification examples, with closed-form solutions, for elastoplasticity problems are presented and the Modified IMPL-EX results are compared with the results obtained by the implicit integration scheme.

Study of the formability of steels

In the present contribution, a new advanced Gurson model [1] is developed. This new model is an extension of the initial one, to the plastic anisotropy and the mixed (isotropic+ kinematic) hardening of the fully dense matrix. The nucleation and the growth phases are considered by integrating the empirical laws developed by Bouaziz et al. [2] in this new model. These laws, identified on the basis of X-ray microtomography results, display the triaxiality effect on the nucleation and the growth of cavities. This advanced Gurson model is implemented into a finite element code by using an implicit-explicit integration scheme. FE simulations study the behavior of a sample submitted to tensile test and assess the influence of nucleation and growth laws on the formability of this sample.