A variational free-discontinuity formulation of brittle fracture was given by Francfortand Marigo [1], where the total energy is minimized with respect to the crackgeometry and the displacement field simultaneously. The entire evolution of cracksincluding their initiation and branching is determined by this minimization principlerequiring no further criterion. However, a direct numerical discretization of themodel faces considerable difficulties as the displacement field is discontinuous inthe presence of cracks.

A Continuum Phase Field Model for Fracture

Generation of 3D representative volume elements for heterogeneous materials: a review

The applicability of voxel meshes to model the mechanical behavior of woven composites at the mesoscopic scale is studied and compared to consistent Finite Element (FE) meshes. The methods are illustrated by mechanically modeling a Representative Unit Cell (RUC) of a composite made of four layers of glass fiber plain weave fabric embedded in an epoxy matrix. Mesh convergence is studied to determine the minimum element size necessary to obtain a correct yarn volume fraction. The comparison between both methods is based on (i) homogenized macroscopic elastic properties, (ii) local stress fields, and (iii) first damage prediction. Even if a good agreement is obtained for the elastic properties, the stress concentrations due to the steplike shape of voxels induce significant differences between both methods in terms of first damage prediction.

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Comparison between voxel and consistent meso-scale models of woven composites

Damage investigation and modeling of 3D woven ceramic matrix composites from X-ray tomography in-situ tensile tests

We present a finite element discrete model for pantographic lattices, based on a continuous Euler–Bernoulli beam for modeling the fibers composing the pantographic sheet. This model takes into account large displacements, rotations and deformations; the Euler–Bernoulli beam is described by using nonlinear interpolation functions, a Green–Lagrange strain for elongation and a curvature depending on elongation. On the basis of the introduced discrete model of a pantographic lattice, we perform some numerical simulations. We then compare the obtained results to an experimental BIAS extension test on a pantograph printed with polyamide PA2200. The pantographic structures involved in the numerical as well as in the experimental investigations are not proper fabrics: They are composed by just a few fibers for theoretically allowing the use of the Euler–Bernoulli beam theory in the description of the fibers. We compare the experiments to numerical simulations in which we allow the fibers to elastically slide one with respect to the other in correspondence of the interconnecting pivot. We present as result a very good agreement between the numerical simulation, based on the introduced model, and the experimental measures.

A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler–Bernoulli beams

A new automated method to generate smooth Finite Element meshes for the meso-scale representation of textile composites unit cells with preformed and compacted reinforcements is presented. The reinforcement geometry is obtained from textile geometry preprocessors or by modeling of the preforming step. It is then transformed into a geometric model of the entire composite unit cell, taking into account the real yarn shape after preforming and compaction, the contact interactions between the yarns, as well as the resulting local variations of fiber volume fraction. A consistent mesh of the complete cell, conformal between the parts, is ensured, without the need for inserting artificial matrix layers between the yarns. The methodology is illustrated by mechanical modeling of the representative unit cell of a multi-layer composite with a compacted and nested woven reinforcement.

Consistent Finite Element mesh generation for meso-scale modeling of textile composites with preformed and compacted reinforcements

Experimental characterization and numerical modeling of damage at the mesoscopic scale of woven polymer matrix composites under quasi-static tensile loading

This paper presents a viscoelastic temperature- and degree-of-cure-dependent constitutive model for an epoxy resin. Multi-temperature relaxation tests on fully and partially cured rectangular epoxy...

Martin Hirsekorn

Papers

Comparison between voxel and consistent meso-scale models of woven composites

Consistent Finite Element mesh generation for meso-scale modeling of textile composites with preformed and compacted reinforcements

Experimental characterization and numerical modeling of damage at the mesoscopic scale of woven polymer matrix composites under quasi-static tensile loading

Viscoelastic behavior of an epoxy resin during cure below the glass transition temperature: Characterization and modeling:

On the influence of fabric layer shifts on the strain distributions in a multi-layer woven composite