Intercorrelated random fields with bounds and the Bayesian identification of their parameters: Application to linear elastic struts and fibers

in International Journal for Numerical Methods in Engineering (2022), 123(15), 3418-3463

Many materials and structures consist of numerous slender struts or fibers. Due to the manufacturing processes of different types of struts and the growth processes of natural fibers, their mechanical ... [more ▼]

Many materials and structures consist of numerous slender struts or fibers. Due to the manufacturing processes of different types of struts and the growth processes of natural fibers, their mechanical response frequently fluctuates from strut to strut, as well as locally within each strut. In associated mechanical models each strut is often represented by a string of beam elements, since the use of conventional three-dimensional finite elements renders the simulations computationally inefficient. The parameter input fields of each string of beam elements are ideally such that the local fluctuations and fluctuations between individual strings of beam elements are accurately captured. The goal of this study is to capture these fluctuations in several intercorrelated bounded random fields. Two formulations to describe the intercorrelations between each random field, as well as the case without any intercorrelation, are investigated. As only a few sets of input fields are available (due to time constraints of the supposed experimental techniques), the identification of the random fields’ parameters involves substantial uncertainties. A probabilistic identification approach based on Bayes’ theorem is employed to treat the involved uncertainties. [less ▲]

Implementation of a new strain split to model unilateral contact within the phase field method

in International Journal for Numerical Methods in Engineering (2020)

A new orthogonal decomposition of strain tensor into compressive/tensile parts is implemented in the phase eld model to maintain the physical crack propagation behavior. An e cient operator split scheme ... [more ▼]

A new orthogonal decomposition of strain tensor into compressive/tensile parts is implemented in the phase eld model to maintain the physical crack propagation behavior. An e cient operator split scheme with the introduction of projection tensors is proposed to facilitate the numerical implementation of the new spectral decomposition. Formulations of the present failure model accounting the unilateral contact condition are given analytically and explicitly, which implies an extremely robust computational model. In particular, compared to the existing models, the present framework is general, which can be applied to all possible elastic behavior, such as isotropic, orthotropic, and totally anisotropic elastic material. A detailed comparison of fracture response predicted by the present models with the literature approaches is then provided. It is shown that orthogonal decomposition is able to simulate various failure scenarios. Especially, this formulation shows a very remarkably prediction compared to experimental observation for the case of compression load. [less ▲]

An adaptive variational Quasicontinuum methodology for lattice networks with localized damage

in International Journal for Numerical Methods in Engineering (2017), 112(2),

Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso‐structures of materials such as 3D‐printed structures and foams. This contribution deals with the ... [more ▼]

Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso‐structures of materials such as 3D‐printed structures and foams. This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture. Lattice networks naturally incorporate non‐locality, large deformations and dissipative mechanisms taking place inside fracture zones. Because the physically relevant length scales are significantly larger than those of individual interactions, discrete models are computationally expensive. The Quasicontinuum (QC) method is a multiscale approach specifically constructed for discrete models. This method reduces the computational cost by fully resolving the underlying lattice only in regions of interest, while coarsening elsewhere. In this contribution, the (variational) QC is applied to damageable lattices for engineering‐scale predictions. To deal with the spatially evolving fracture zone, an adaptive scheme is proposed. Implications induced by the adaptive procedure are discussed from the energy‐consistency point of view, and theoretical considerations are demonstrated on two examples. The first one serves as a proof of concept, illustrates the consistency of the adaptive schemes and presents errors in energies. The second one demonstrates the performance of the adaptive QC scheme for a more complex problem. [less ▲]

Stable 3D XFEM/vector-level sets for non-planar 3D crack propagation and comparison of enrichment schemes

in International Journal for Numerical Methods in Engineering (2017)

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting ... [more ▼]

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near-tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, i.e., the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach significantly simplifies implementation and reduces the computational cost associated with numerical integration. The two dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for non-planar crack propagation problems. [less ▲]

A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities

in International Journal for Numerical Methods in Engineering (2017), 110(3), 203-226

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms ... [more ▼]

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrixes can be computed by smoothing technique. This is accomplished by combining the Green’s divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion. [less ▲]

Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods

in International Journal for Numerical Methods in Engineering (2015), 104(13), 1173-1199

We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally ... [more ▼]

We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM.We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the O.dof s/1:1 in case of the conventional polygonal FEM, while it scales as O.dof s/0:7 in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. [less ▲]

Extended space-time finite elements for landslide dynamics

in International Journal for Numerical Methods in Engineering (2013), 93(3), 329-354

The paper introduces a methodology for numerical simulation of landslides experiencing considerable deformations and topological changes. Within an interface capturing approach, all interfaces are ... [more ▼]

The paper introduces a methodology for numerical simulation of landslides experiencing considerable deformations and topological changes. Within an interface capturing approach, all interfaces are implicitly described by specifically defined level-set functions allowing arbitrarily evolving complex topologies. The transient interface evolution is obtained by solving the level-set equation driven by the physical velocity field for all three level-set functions in a block Jacobi approach. The three boundary-coupled fluid-like continua involved are modeled as incompressible, governed by a generalized non-Newtonian material law taking into account capillary pressure at moving fluid-fluid interfaces. The weighted residual formulation of the level-set equations and the fluid equations is discretized with finite elements in space and time using velocity and pressure as unknown variables. Non-smooth solution characteristics are represented by enriched approximations to fluid velocity (weak discontinuity) and fluid pressure (strong discontinuity). Special attention is given to the construction of enriched approximations for elements containing evolving triple junctions. Numerical examples of three-fluid tank sloshing and air-water-liquefied soil landslides demonstrate the potential and applicability of the method in geotechnical investigations. © 2012 John Wiley & Sons, Ltd. [less ▲]

Local/global model order reduction strategy for the simulation of quasi-brittle fracture

in International Journal for Numerical Methods in Engineering (2012), 89(2), 154-179

This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and ... [more ▼]

This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and propagation while concentrating the computational effort where it is most needed, that is, in the localization zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe damage and cracking) is solved for in a reduced space computed by the classical proper orthogonal decomposition while the local (master) degrees of freedom (associated with the part of the structure where most of the damage is taking place) are fully resolved. Both domains are coupled through a local/global technique. This method circumvents the difficulties associated with model order reduction for the simulation of highly nonlinear mechanical failure and offers an alternative or complementary approach to the development of multiscale fracture simulators. © 2011 John Wiley & Sons, Ltd. [less ▲]

Extended Finite Element Method

in International Journal for Numerical Methods in Engineering (2011), 86(4-5), 403

[No abstract available]

Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling

in International Journal for Numerical Methods in Engineering (2011), 86(2), 249-268

Fracture modelling using numerical methods is well-advanced in 2D using techniques such as the extended finite element method (XFEM). The use of meshless methods for these problems lags somewhat behind ... [more ▼]

Fracture modelling using numerical methods is well-advanced in 2D using techniques such as the extended finite element method (XFEM). The use of meshless methods for these problems lags somewhat behind, but the potential benefits of no meshing (particularly in 3D) prompt continued research into their development. In methods where the crack face is not explicitly modelled (as the edge of an element for instance), two procedures are instead used to associate the displacement jump with the crack surface: the visibility criterion and the diffraction method. The visibility criterion is simple to implement and efficient to compute, especially with the help of level set coordinates. However, spurious discontinuities have been reported around crack tips using the visibility criterion, whereas implementing the diffraction method in 3D is much more complicated than the visibility criterion. In this paper, a tying procedure is proposed to remove the difficulty with the visibility criterion so that crack tip closure can be ensured while the advantages of the visibility criterion can be preserved. The formulation is based on the use of level set coordinates and the element-free Galerkin method, and is generally applicable for single or multiple crack problems in 2D or 3D. The paper explains the formulation and provides verification of the method against a number of 2D crack problems. [less ▲]