Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuum and discrete models for unbalanced woven fabrics   The classical models used for describing the behavior of woven fabrics do not
fully account for the whole set of phenomena that occur during the testing of
such materials. This lack of precision is mainly due to the absence of energy
terms related to the microstructural properties of the fabric and, in
particular, to the bending stiffness of the yarns. In this paper it is shown
that in the unbalanced fabrics the different bending stiffnesses of the warp
and weft yarns produce macroscopic effects that are extremely visible as, for
example, the asymmetric S-shape during a Bias Extension Test (BET).
  We propose to introduce a constrained micromorphic model and a discrete model
that are able to account for i) the angle variation between warp and weft tows,
ii) the unbalance in the bending stiffness of the yarns and iii) the relative
slipping of the tows.
  The constrained micromorphic model is framed in the spirit of the Principle
of Virtual Powers for the equilibrium of continuum bodies. A suitable
constraint is introduced by means of Lagrange multipliers in the strain
energydens ity and the resulting constrained model tends a particular second
gradientone. The main advantage of using such constrained micromorphic model is
that the kinematical and traction boundary conditions that can be imposed on
the boundary of the considered body take a natural and unique meaning.
  The discrete model is set up by opportunely interconnecting Euler-Bernoulli
beams with different bending stiffnesses in the two directions by means of
rotational and translational elastic springs. The main advantage of such
discrete model is that the slipping of the tows is described in a rather
realistic way. Suitable numerical simulations are presented for both the
continuum and the discrete models and a comparison between the simulations and
the experimental results is made showing a definitely good agreement.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg