Optimization of Textile-Like Materials via Homogenization and Beam Approximations

Orlik, Julia; Panasenko, Grigory; Shiryaev, V. V.

doi:10.1137/15m1017193

Cited by 25 publications

(21 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This method has been applied to a large number of different types of problems. We mention only a few of them which deal with periodic structures in the framework of the linear elasticity (see [3,[16][17][18][19][20][21]26]). As general references on the theory of beams or structures made of beams, we refer to [2,7,22,23,29,30].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of Stable Structures Made of Beams

Griso

Khilkova

Orlik

et al. 2021

J Elast

Self Cite

View full text Add to dashboard Cite

In this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

show abstract

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of Stable Structures Made of Beams

Griso

Khilkova

Orlik

et al. 2021

J Elast

Self Cite

View full text Add to dashboard Cite

show abstract

“…The simulation is performed with varying friction coefficient µ. In [21], structure (pattern) optimization with state constraints (a desired stress or pressure profile in the fabric) for knitted fabrics is presented. In the paper, meshes in the knitting pattern are parametrized in a very simple way, corresponding to the knitting machine control parameters such as the stich-height, distance between needles and prestress in the yarns during the production in the machine.…”

Section: Simulation Of Textiles With Stretchable Yarnsmentioning

confidence: 99%

“…The derived mathematical framework is exemplified by our recent numerical simulations for multiple different textiles. Additionally, our currently developed simulation tool, TexMath (Version 0.4.0) [20], is presented, which allows us to systematically optimize textiles with respect to their desired functional behavior [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Recent Efforts in Modeling and Simulation of Textiles

et al. 2021

Self Cite

View full text Add to dashboard Cite

In many textiles and fiber structures, the behavior of the material is determined by the structural arrangements of the fibers, their thickness and cross-section, as well as their material properties. Textiles are thin plates made of thin long yarns in frictional contact with each other that are connected via a rule defined by a looping diagram. The yarns themselves are stretchable or non-stretchable. All these structural parameters of a textile define its macroscopic behavior. Its folding is determined by all these parameters and the kind of the boundary fixation or loading direction. The next influencing characteristic is the value of the loading. The same textile can behave similar to a shell and work just for bending, or behave as a membrane with large tension deformations under different magnitudes of the loading forces. In our research, bounds on the loading and frictional parameters for both types of behavior are found. Additionally, algorithms for the computation of effective textile properties based on the structural information are proposed. Further focus of our research is the nature of folding, induced by pre-strain in yarns and some in-plane restriction of the textile movements, or by the local knitting or weaving pattern and the yarn’s cross-sections. Further investigations concern different applications with spacer fabrics. Structural parameters influencing the macroscopic fabric behavior are investigated and a way for optimization is proposed. An overview of our published mathematical and numerical papers with developed algorithms is given and our numerical tools based on these theoretical results are demonstrated.

show abstract

“…The thickness of fibers is small compared to their length. Thus, the dimension of the auxiliary problems in the representative cell can be reduced further by an asymptotic approach with respect to the fiber thickness [ 19 , 22 , 23 , 24 ]. Finally, it is numerically solved by the finite element method with frictional contact [ 20 , 21 ], and extended to visco-elastic relaxation [ 25 , 26 ].…”

Section: Introductionmentioning

confidence: 99%

Simulation of Leather Visco-Elastic Behavior Based on Collagen Fiber-Bundle Properties and a Meso-Structure Network Model

et al. 2021

Self Cite

View full text Add to dashboard Cite

Simulation-based prediction of mechanical properties is highly desirable for optimal choice and treatment of leather. Nowadays, this is state-of-the-art for many man-made materials. For the natural material leather, this task is however much more demanding due to the leather’s high variability and its extremely intricate structure. Here, essential geometric features of the leather’s meso-scale are derived from 3D images obtained by micro-computed tomography and subsumed in a parameterizable structural model. That is, the fiber-bundle structure is modeled. The structure model is combined with bundle properties derived from tensile tests. Then the effective leather visco-elastic properties are simulated numerically in the finite element representation of the bundle structure model with sliding contacts between bundles. The simulation results are validated experimentally for two animal types, several tanning procedures, and varying sample positions within the hide. Finally, a complete workflow for assessing leather quality by multi-scale simulation of elastic and visco-elastic properties is established and validated.

show abstract

Optimization of Textile-Like Materials via Homogenization and Beam Approximations

Cited by 25 publications

References 12 publications

Asymptotic Behavior of Stable Structures Made of Beams

Asymptotic Behavior of Stable Structures Made of Beams

Recent Efforts in Modeling and Simulation of Textiles

Simulation of Leather Visco-Elastic Behavior Based on Collagen Fiber-Bundle Properties and a Meso-Structure Network Model

Contact Info

Product

Resources

About