Non-isothermal energy–momentum time integrations with drilling degrees of freedom of composites with viscoelastic fiber bundles and curvature–twist stiffness

Groß, Michael; Dietzsch, Julian; Röbiger, Chris

doi:10.1016/j.cma.2020.112973

Cited by 18 publications

(24 citation statements)

References 35 publications

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“…Besides taking one single family of fibres into account, these fibre-related gradient effects have been elaborated in [17] for woven fibre structures. In [18], fibre bundles have been examined with regard to fibre bending stiffness and twisting.…”

Section: Introductionmentioning

confidence: 99%

A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

2021

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It is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy function in order to capture the specific material properties in the fibre direction. While this model represents the transverse isotropy of a material, it cannot capture effects that result from a bending of the fibres and does not include any length scale that might allow the simulation of size effects. In this contribution, an enhanced approach is considered which relies on the introduction of higher-gradient contributions of the deformation map in the stored energy density function and which eventually allows accounting for fibre bending stiffness in simulations. The respective gradient fields are approximated by NURBS basis functions within an isogeometric finite element framework by taking advantage of their characteristic continuity properties. The isogeometric finite element approach that is presented in this contribution for fibre-reinforced composites with fibre bending stiffness accounts for finite deformations. It is shown that the proposed method is in accordance with semi-analytical solutions for a representative boundary value problem. In an additional example it is observed that the initial fibre orientation and the particular bending stiffness of the fibres influence the deformation as well as the stress response of the material.

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Section: Introductionmentioning

confidence: 99%

A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

2021

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“…In rotordynamical systems, fiber-reinforced materials with fiber rovings and cured matrix material have gained great significance for engineers. For instance, there are woven roving structures as for turbine blades in Reference [3], or structures with unidirectional ≈ 20mm RVE Anisotropy in [7] a b…”

Section: Introductionmentioning

confidence: 99%

“…Figure 1: Sketch of the cross-section of a body with rovings [4] (diagram a). In [7], the stiffness effect of such rovings is modelled by anisotropy with roving tension and curvature-twist stiffness (diagram b).…”

Section: Introductionmentioning

confidence: 99%

“…But, as a finite diameter of rovings leads to a stiffness with respect to a local flexure and twist, the continuum formulation has to allow for length scales in the strain energy. Such length scales can be introduced by gradient-based continuum formulations as in Reference [6], or by continuum formulations with local rotational degrees of freedom as in Reference [7]. By means of the latter formulation, the flexure and twist can be associated with independent length scales, such that a flexural and a torsional rigidity can be prescribed independently as in structures.…”

Section: Introductionmentioning

confidence: 99%

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Variational computational modelling of dynamical behaviour of fiber roving composites with inelastic anisotropic continua and thermomechanical coupling

Groß¹,

Dietzsch²,

Kalaimani³

et al. 2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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The nonlinear finite element method is a computational method in the variational simulation of material models for materials with and without microstructures [1]. Taking into account microstructures of engineering materials in their computational models is often worthwhile to improve numerical predictions [2]. An example is the modelling of fiber-reinforced materials, which are manufactured on the microscale by filaments or on the mesoscale by rovings, respectively. A macroscopic finite element simulation of both materials provides an anisotropic continuum model. However, fiber-reinforced materials based on rovings demand for continua with extended kinematics. A computational modelling of extended continua is possible by a mixed finite element method. In this contribution, we show the introduction of internal rotational degrees of freedom to model also a stiffness with respect to roving flexure and twist. Furthermore, a corresponding structure-preserving time integration is obtained. Numerical examples also demonstrate the additional continuum stiffness owing to the consideration of roving flexure and twist.

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“…F are presented in Reference [10], and references therein. The curvature-twist strain energy Ψ K also leads to a new contribution in the balance law of potential energy on a time step, given by…”

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confidence: 99%

Energy-Momentum Scheme with Drilling Degrees of Freedom for Composites with Curvature-Twist Stiffness

Groß¹,

Dietzsch²,

Kalaimani³

2021

14th WCCM-ECCOMAS Congress

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This paper is motivated by the increasing application of 3D fiber-reinforced composites in rotating systems [1]. In 2D fiber-reinforced composites, single fibers with a diameter in the range of micrometers are embedded in a matrix material. But, these composites are prone to delamination damage, wherefore the development of 3D composites has been undertaken. Here, fiber bundles are woven, knitted, braided or stitched, in order to fix the fibers before they are surrounded by a matrix material. From a material modelling point of view, these two kind of composites make a huge difference, because a fiber bundle has to be considered as a beam-like structure with curvature-twist (bending as well as twisting) stiffness, in addition to the usual stretching stiffness (cf. [2]). The former is then responsible for the increasing strength-to-weight ratio of 3D fiber-reinforced composites for thin-walled lightweight structures. Therefore, 3D fiber-reinforced composites demand for a bespoke simulation technique. We have to consider a representative volume element, in which secondary effects as a micro inertia and a curvature-twist stiffness must be taken into account. We introduce these secondary effects in a continuum formulation by means of independent drilling degrees of freedom (cf. [3]). The resulting nonisothermal constrained micropolar continuum is derived by a mixed principle of virtual power (cf. [4]). This variational principle simultaneously generates in the discrete setting a mixed B-bar method and a Galerkin-based energy-momentum scheme of higher order. We also take into account viscoelastic material behaviour, which arises from a mixture of organic and inorganic fibers in a polymeric matrix material. Representative numerical examples demonstrate the twisting and bending stiffness of the fiber bundles.

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Non-isothermal energy–momentum time integrations with drilling degrees of freedom of composites with viscoelastic fiber bundles and curvature–twist stiffness

Cited by 18 publications

References 35 publications

A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

Variational computational modelling of dynamical behaviour of fiber roving composites with inelastic anisotropic continua and thermomechanical coupling

Energy-Momentum Scheme with Drilling Degrees of Freedom for Composites with Curvature-Twist Stiffness

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