Higher order finite elements in space and time for anisotropic simulations with variational integrators. Application of an efficient GPU implementation

Bartelt, Matthias; Klöckner, Oliver; Dietzsch, Julian; Groß, Michael

doi:10.1016/j.matcom.2019.09.018

Cited by 2 publications

(3 citation statements)

References 10 publications

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“…The material model is based on a nonlinear NEO-HOOKE model with an additional fiber reinforced material part, compare Eq. 7 (see also [3]). The fiber direction is given by a.…”

Section: Examplementioning

confidence: 92%

Determination of the effective 2D material stiffness matrix using ABAQUS

Horn

Bartelt

Wulf

et al. 2021

Proc Appl Math and Mech

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A cross-scale homogenization approach for multi-phase materials is to calculate an effective material stiffness in the smaller scale for the multiple states. These detailed results are used to identify a calculation rule for the effective material stiffness in the larger scale. The calculation of the stiffness matrix using ABAQUS for 3D finite elements was already described by [1]. This can be transferred to the calculation of the 2D stiffness matrix in R 3×3 without much effort. However, some 2D elements in ABAQUS require the specification of a matrix in R 4×4. In this article, the methods for calculating this type of stiffness matrix in 2D are presented.

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“…The material model is based on a nonlinear NEO-HOOKE model with an additional fiber reinforced material part, compare Eq. 7 (see also [3]). The fiber direction is given by a.…”

Section: Examplementioning

confidence: 92%

Determination of the effective 2D material stiffness matrix using ABAQUS

Horn

Bartelt

Wulf

et al. 2021

Proc Appl Math and Mech

View full text Add to dashboard Cite

show abstract

“…For this purpose a CPE4 element was assigned to each cell and the entire simulation space was designed as a 2D representative volume element (2D-RVE) with periodic boundary conditions analogous to Goldberg et al [ 28 ]. A different Neo-Hooke material law was assigned to each phase and the crystalline phase was additionally anisotropically stiffened in order to consider the direction-dependent properties of the lamellae—see also [ 29 , 30 ]:

where

is the direction of the lamellae,

the deformation gradient,

, and

the second Piola–Kirchhoff tensor. Thus, the total stress at each cell is computed as follows, taking into account the phase distributions present at the cells:

…”

Section: Predicting the Materials Behavior Under Consideration Of The Micro- And Nanoscalementioning

confidence: 99%

“…For this purpose a CPE4 element was assigned to each cell and the entire simulation space was designed as a 2D representative volume element (2D-RVE) with periodic boundary conditions analogous to Goldberg et al [28]. A different Neo-Hooke material law was assigned to each phase and the crystalline phase was additionally anisotropically stiffened in order to consider the direction-dependent properties of the lamellae-see also [29,30]:…”

Section: Predicting the Materials Behavior Under Consideration Of The Micro-and Nanoscalementioning

confidence: 99%

Multiscale Simulation of Semi-Crystalline Polymers to Predict Mechanical Properties

et al. 2021

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A multiscale simulation method for the determination of mechanical properties of semi-crystalline polymers is presented. First, a four-phase model of crystallization of semi-crystalline polymers is introduced, which is based on the crystallization model of Strobl. From this, a simulation on the nanoscale is derived, which models the formation of lamellae and spherulites during the cooling of the polymer by using a cellular automaton. In the solidified state, mechanical properties are assigned to the formed phases and thus the mechanical behavior of the nanoscale is determined by a finite element (FE) simulation. At this scale, simulations can only be performed up to a simulation range of a few square micrometers. Therefore, the dependence of the mechanical properties on the degree of crystallization is determined by means of homogenization. At the microscale, the cooling of the polymer is simulated by a cellular automaton according to evolution equations. In combination with the mechanical properties determined by homogenization, the mechanical behavior of a macroscopic component can be predicted.

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Higher order finite elements in space and time for anisotropic simulations with variational integrators. Application of an efficient GPU implementation

Cited by 2 publications

References 10 publications

Determination of the effective 2D material stiffness matrix using ABAQUS

Determination of the effective 2D material stiffness matrix using ABAQUS

Multiscale Simulation of Semi-Crystalline Polymers to Predict Mechanical Properties

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