A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

Kerfriden, Pierre; Claus, Susanne; Mihai, Iulia

doi:10.1186/s40323-020-00154-5

Cited by 20 publications

(29 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All of those mentioned previous works do not introduce additional degrees of freedom for the reinforcements, but instead incorporate the beam stiffness contributions into the stiffness matrices of the solid elements. Alternatively, the beam degrees of freedom can be kept in the discrete system, which introduces the need for kinematic coupling constraints acting on the beams and solid [2,11,17,18,51]. A collocation method is used in [11] to couple 1D beams into a 3D matrix.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

et al. 2020

View full text Add to dashboard Cite

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to account for the reinforcements, while still being able to capture complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.

show abstract

Section: Introductionmentioning

confidence: 99%

“…A collocation method is used in [11] to couple 1D beams into a 3D matrix. In [18], a CutFEM approach is employed to embed 1D structural elements without bending stiffness into a 3D matrix material. The application of 1D-3D coupling can also be found in other fields than solid mechanics [9,19,20].…”

Section: Introductionmentioning

confidence: 99%

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Finally, a series of other prospects could also be envisioned such as adaptive refinement for materials with multi-scale micro-structures [10,36], extension to multi-phase (> 2) materials using more advanced modellings such as those based on the Cut-FEM method [28]. In addition, we recall that the threshold value used for characterizing the geometric level-set is a user-defined parameter herein and is one of the crucial parameters.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, they allow for an accurate description of the mechanical fields while saving a large amount of degrees of freedom compared to standard low-order boundary fitted strategies. This certainly explains their current popularity in the computational mechanics community for the analysis of geometrically complex objects (see [21,22,23,24,25,26,27,28] to name a few). In the current study, we choose to resort to immersed isogeometric analysis [29,30,31,32,33] which provides a natural framework for performing fictitious domain analysis using smooth higher-order functions.…”

Section: Introductionmentioning

confidence: 99%

Adjusting fictitious domain parameters for fairly priced image-based modeling: Application to the regularization of Digital Image Correlation

Rouwane

Bouclier

Passieux

et al. 2021

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

The integration of numerical simulation and experimental measurements in cellular materials at the sub-cellular scale is a real challenge. On the experimental side, the almost absence of texture makes displacement fields measurement tricky. On the simulation side, it requires the construction of reliable and specimen-specific geometric and mechanical models from digital images. For this purpose, high order based fictitious domain approaches have proven to be an efficient alternative to boundary conforming finite elements for the analysis of geometrically complex objects. A number of discretization parameters needs to be set by the user by making a trade-off between accuracy and computational cost. In addition to numerical errors (interpolation, integration etc.), there are additional geometric and model errors due to the pixelation of the image (e.g., quantization, sampling, noise). In the literature, discretization parameters are often analyzed without taking pixelation into account, which can lead to over-calculations. In this paper, these parameters are adjusted to obtain (a) the best possible accuracy (bounded by pixelation errors) while (b) ensuring minimal complexity (concept of fair price). In order to analyze the different sources of error, various two-dimensional synthetic experiments are generated by mimicking the image acquisition process from high-resolution numerical simulations considered as a reference. The approach leads to a modeling that outperforms conventional approaches both in terms of accuracy and complexity. Eventually, it is shown that the presented image-based models provide a unique opportunity to assist digital volume correlation and allow the measurement of relevant local kinematics within cellular materials.

show abstract

“…1D structural models account only for internal elastic energy contributions from axial tension, e.g. [13,17,20,25,26,43,50]. Work on the 1D-3D coupling between beams, i.e.…”

Section: Introductionmentioning

confidence: 99%

Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

2021

View full text Add to dashboard Cite

The present article proposes a mortar-type finite element formulation for consistently embedding curved, slender beams into 3D solid volumes. Following the fundamental kinematic assumption of undeformable cross-section s, the beams are identified as 1D Cosserat continua with pointwise six (translational and rotational) degrees of freedom describing the cross-section (centroid) position and orientation. A consistent 1D-3D coupling scheme for this problem type is proposed, requiring to enforce both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions within the 3D solid. While the rotation tensor defined by the polar decomposition of the deformation gradient appears as a natural choice and will even be demonstrated to represent these material directions in a $$L_2$$ L 2 -optimal manner, several alternative triad definitions are investigated. Such alternatives potentially allow for a more efficient numerical evaluation. Moreover, objective (i.e. frame-invariant) rotational coupling constraints between beam and solid orientations are formulated and enforced in a variationally consistent manner based on either a penalty potential or a Lagrange multiplier potential. Eventually, finite element discretization of the solid domain, the embedded beams, which are modeled on basis of the geometrically exact beam theory, and the Lagrange multiplier field associated with the coupling constraints results in an embedded mortar-type formulation for rotational and translational constraint enforcement denoted as full beam-to-solid volume coupling (BTS-FULL) scheme. Based on elementary numerical test cases, it is demonstrated that a consistent spatial convergence behavior can be achieved and potential locking effects can be avoided, if the proposed BTS-FULL scheme is combined with a suitable solid triad definition. Eventually, real-life engineering applications are considered to illustrate the importance of consistently coupling both translational and rotational degrees of freedom as well as the upscaling potential of the proposed formulation. This allows the investigation of complex mechanical systems such as fiber-reinforced composite materials, containing a large number of curved, slender fibers with arbitrary orientation embedded in a matrix material.

show abstract

A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

Cited by 20 publications

References 26 publications

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

Adjusting fictitious domain parameters for fairly priced image-based modeling: Application to the regularization of Digital Image Correlation

Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

Contact Info

Product

Resources

About