Doctoral defence Brian Nyvang Legarth

Non-linear Mechanics of Anisotropic Materials – failure and homogenization

Ass. Professor Brian Nyvang Legarth
Technical University of Denmark


Professor A. Amine Benzerga, Texas A&M University, College Station, USA

Professor Odd Sture Hopperstad, NTNU, Trondheim, Norge

Both opponents are appointed by DTU and have been part of the assessment committee with the chairman also appointed by DTU, Professor
Professor Jesper Henri Hattel, DTU Mechanical Engineering

Unofficial opponents are to address the moderator:

Provost Rasmus Larsen
Building 101A
Technical University of Denmark
Tel.: 45 25 71 42

A copy of the dissertation can be obtained by contacting:

Anna-Maria Lund
Office of Research and Relations
Building 101A
Technical University of Denmark
Tel.: 45 25 71 42


Non-linear Mechanics of Anisotropic Materials – failure and homogenization English summary

This thesis deals with numerical simulations of anisotropic materials. Advanced numerical modeling techniques are developed and adopted to study the mechanical behavior of non-linear materials. Special focus is on anisotropic plasticity and the results narrow into three topics:

  1. Failure in homogeneous materials
  2. Failure in inhomogeneous materials
  3. Homogenization of materials

A significant amount of the work deals with size effects and an anisotropic plasticity model accounting for size effects is proposed. Anisotropy is characterized by its severity and its orientation and both topics are treated in the thesis. The orientation of plastic anisotropy greatly defines how severe the effect of plastic anisotropy is, as the local stress field changes with this orientation. Both initiation of cracking and actual crack growth are delayed for an off-axis orientation of plastic anisotropy in homogeneous materials. For the inhomogeneous materials failure under transverse load often occurs along weak interfaces, but eventually it shifts to cracking away from the interface due to a redistribution of the load. Such load redistribution caused by a second phase inclusion is utilized to determine a configuration for improved in-situ measurements of interfacial normal strength under transverse load. If the second phase is substituted by a hole the effect is less pronounced as the presence of holes affects the transverse compressive strength more than that in transverse tension.

Finally, a homogenization scheme for aligned fiber composites is developed. Based on this, an anisotropic pressure dependent plasticity model is formulated, in which the yield surface does not shrink under hydro-static loading. Instead, the yield surface is rotated relatively to the hydro-static axis, such that a hydro-static load causes plastic deformations. By this homogenization scheme fiber composites can efficiently be treated as pressure dependent homogeneous materials. Hence, throughout the thesis it is shown, that the orientation of anisotropy generally plays an important role in several different non-linear cases.



Mon 18 Jun 18
14:00 - 18:00




DTU, Lyngby Campus

Anker Engelunds Vej 1

Building 101 A

Meeting room 1, 1st floor