A space-time upscaling technique for modeling high-cycle fatigue-damage of short-fiber reinforced composites

Magino, Nicola; Köbler, Jonathan; Andrä, Heiko; Welschinger, Fabian; Müller, Ralf; Schneider, Matti

doi:10.1016/j.compscitech.2022.109340

Cited by 14 publications

(10 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As stated in the beginning, computational micromechanics has evolved rapidly in the last two decades, and rather complex inelastic constitutive models may be treated on long time scales. [16][17][18] Thus, there is an immediate interest whether the confidence in regular-grid-based homogenization methods is justified when inelastic materials are considered. Mathematically speaking, this entails the question of superconvergence of the effective stresses under inelastic homogenization and computationally feasible approximations.…”

Section: State Of the Artmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials

Schneider

Wicht

2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

We provide theoretical investigations and empirical evidence that the effective stresses in computational homogenization of inelastic materials converge with a higher rate than the local solution fields. Due to the complexity of industrial-scale microstructures, computational homogenization methods often utilize a rather crude approximation of the microstructure, favoring regular grids over accurate boundary representations. As the accuracy of such an approach has been under continuous verification for decades, it appears astonishing that this strategy is successful in homogenization, but is seldom used on component scale. A part of the puzzle has been solved recently, as it was shown that the effective elastic properties converge with twice the rate of the local strain and stress fields. Thus, although the local mechanical fields may be inaccurate, the averaging process leads to a cancellation of errors and improves the accuracy of the effective properties significantly. Unfortunately, the original argument is based on energetic considerations. The straightforward extension to the inelastic setting provides superconvergence of (pseudoelastic) potentials, but does not cover the primary quantity of interest: the effective stress tensor. The purpose of the work at hand is twofold. On the one hand, we provide extensive numerical experiments on the convergence rate of local and effective quantities for computational homogenization methods based on the fast Fourier transform. These indicate the superconvergence effect to be valid for effective stresses, as well. Moreover, we provide theoretical justification for such a superconvergence based on an argument that avoids energetic reasoning.

show abstract

Section: State Of the Artmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials

Schneider

Wicht

2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another effect which we observe in fatigue experiments on short-fiber reinforced PBT is its frequency dependence. To realize the fatigue experiments in the shortest possible time, experiments at different loading amplitudes are often performed at different frequencies [74,75] to avoid self-heating of the material at high loading amplitudes. The choice of a different frequency also influences the measured dynamic modulus.…”

Section: In Fatigue Experimentsmentioning

confidence: 99%

“…Note that the damage evolution is directly formulated in cycle space in the work at hand. For a discussion of the evolution in time space and damage evolution under loading and unloading, we refer to Magino et al [75].…”

Section: Materials Modelmentioning

confidence: 99%

“…The applied damage model does not account for localization effects by construction and is therefore unable to represent a negative second derivative in the stiffness degradation. Rather, we focus on the reproduction of the approximately linear trends in the stable stiffness degradation [75,98]. The damage processes leading to the stiffness degradation within the last decade of the fatigue process are most likely already localized.…”

Section: Experiments Versus Computational Predictionsmentioning

confidence: 99%

See 1 more Smart Citation

Accounting for viscoelastic effects in a multiscale fatigue model for the degradation of the dynamic stiffness of short-fiber reinforced thermoplastics

et al. 2022

Self Cite

View full text Add to dashboard Cite

Under fatigue loading, the stiffness decrease in short-fiber reinforced polymers reflects the gradual degradation of the material. Thus, both measuring and modeling this stiffness is critical to investigate and understand the entire fatigue process. Besides evolving damage, viscoelastic effects within the polymer influence the measured dynamic stiffness. In this paper, we study the influence of a linear viscoelastic material model for the matrix on the obtained dynamic stiffness and extend an elastic multiscale fatigue-damage model to viscoelasticity. Our contribution is two-fold. First, we revisit the complex-valued elastic models known in the literature to predict the asymptotic periodic orbit of a viscoelastic material. For small phase shifts in an isotropic linear viscoelastic material, we show through numerical experiments that a real-valued computation of an “elastic” material is sufficient to approximate the dynamic stiffness of a microstructure with a generalized Maxwell material and equal Poisson’s ratios in every element as matrix, reinforced by elastic inclusions. This makes standard solvers applicable to fiber-reinforced thermoplastics. Secondly, we propose a viscoelastic fatigue-damage model for the thermoplastic matrix based on decoupling of the time scales where viscoelastic and fatigue-damage effects manifest. We demonstrate the capability of the multiscale model to predict the dynamic stiffness evolution under fatigue loading of short-fiber reinforced polybutylene terephthalate (PBT) by a validation with experimental results.

show abstract

Assumed strain methods in micromechanics, laminate composite voxels and level sets

Lendvai,

Schneider

2024

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

This work deals with the composite voxel method, which—in its original form—furnishes voxels containing more than one material with a surrogate material law accounting for the heterogeneity in the voxel. We show that the laminate composite voxel technique naturally arises as an assumed strain method, that is, the general framework introduced by Simo‐Rifai, for a specific choice of enhanced strain field. As a consequence, laminate composite voxels may be regarded as a kinematic assumption within a discretization scheme rather than a part of material modeling, as suggested originally. We discuss how to seamlessly integrate composite voxels into the framework of a level‐set description of the microstructure, in particular the accurate and efficient computation of normals and cut‐volume fractions. In contrast to more traditional strategies based on subvoxelizations, the introduced method avoids systematic errors when computing composite voxel properties. We demonstrate the applicability of the developed technology for a number of relevant computational examples.

show abstract

A space-time upscaling technique for modeling high-cycle fatigue-damage of short-fiber reinforced composites

Cited by 14 publications

References 61 publications

Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials

Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials

Accounting for viscoelastic effects in a multiscale fatigue model for the degradation of the dynamic stiffness of short-fiber reinforced thermoplastics

Assumed strain methods in micromechanics, laminate composite voxels and level sets

Contact Info

Product

Resources

About