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===== Multiscale Simulation of Fracturing of Carbon-epoxy Braided composites =====

Two-dimensional triaxially braided composites (2DTBCs) can dissipate large amount of energy during fracturing. The biggest challenge remains in engineering this carbon-epoxy composite to optimize energy dissipation and to discover critical and sensitive factors affecting fracturing performance. The simulation started with the definition and dicretization of Repetitive Unit Cell (RUC), see Figure below

| {{:gallery:2dtbc_ruc.png?500}} |
| Images of 2DTBC and reconstructed RUCs with bias tow angles of 30<sup>o</sup>, 45<sup>o</sup> and 60<sup>o</sup>. Images from University of Michigan, prof. Waas' group.|

Since the fracture parameters are best manifested in the scaling properties and are the main parameters in the size effect law, the nominal strengths of three geometrically similar notched beams of three different sizes are simulated in a 3D finite element framework. A collection of RUCs was embeded in a notched beam, which creates a finely disretized region around the notch and a coarse disretization around, see Figure. Python script generated the embedded geometry with the help of hanging nodes and master-slave nodes. 

{{:gallery:2dtbc_multiscale.png?500}}

The simulation uses framework of damage mechanics. A fixed orientation of three perpendicular planes, aligned with material orientation axes, defines six damage variables; three for normal stress and three for shear. The material law handles the class //CompoDamageMat//. The left Figure shows the notched beam with embedded damaged RUCs, the right Figure force-displacement curve.

{{:gallery:60_beam_anim_small1.gif|}} {{:gallery:60_pd_anim1.gif|}} 

The Figure below depicts a detailed view of a process zone above the notch. The colors represent damage magnitude.

{{:gallery:damage_braiders_anim1.gif|}}

The left Figure shows a detail of the three-point beam bending test, the middle Figure prediction and simulation for three beam sizes, and the right Figure fitting to the the size effect law. 

{{:gallery:dsc00519a.jpg?170}} {{:gallery:30_rsize_pd_e.png?180}} {{:gallery:30_rsize_effectb.png?180}}

By fitting the size effect law, the fracture energy was found in the range 212 - 464 N/mm. For more information, see our article 
  * V. Šmilauer, C. G. Hoover, Z. P. Bažant, F. C. Caner, A. M. Waas, K. W. Shahwan: Multiscale Simulation of Fracture of Braided Composites via Repetitive Unit Cells, Engineering Fracture Mechanics, in press, 2011.

//Created 12/2010 by Vít Šmilauer. Acknowledgements belong to C. G. Hoover, B. Patzák, Z. P. Bažant, A. M. Waas and K. W. Shahwan.//