Dipl.-Math. techn. Matthias Leuschner

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Former scientific employee

Dr.-Ing. Matthias Leuschner

(until Sep 2017)

Research objective (project DFG FR2702/3 - completed)

My work is dedicated to the field of homogenization for materials with a heterogeneous microstructure. Notable examples of such materials are particle- or fiber-reinforced composites which comprise multiple phases. Viscoplastic behavior of an individual phase or discontinuities of the displacement field at the phase boundaries lead to nonlinear problems and usually implicate tremendous numerical effort. The aim of my work is to develop reduced order methods that allow to find the solutions to such multiscale problems with reasonable accuracy at drastically reduced computational cost.

Related projects

CoSiMOR (Scientific Network)

Publications

[1] Felix Fritzen and Matthias Leuschner. Reduced basis hybrid computational homogenization based on a mixed incremental formulation. Computer Methods in Applied Mechanics and Engineering, 260(0):143-154, 2013. [ bib ]
[2] Felix Fritzen, Max Hodapp, and Matthias Leuschner. GPU accelerated computational homogenization based on a variational approach in a reduced basis framework. Computer Methods in Applied Mechanics and Engineering, 278(0):186-217, 2014. [ bib ]
[3] M. Leuschner, F. Fritzen, J.A.W. van Dommelen, and J.P.M. Hoefnagels. Potential-based constitutive models for cohesive interfaces: Theory, implementation and examples. Composites Part B: Engineering, 68(0):38-50, 2015. [ bib ]
[4] Felix Fritzen and Matthias Leuschner. Nonlinear reduced order homogenization of materials including cohesive interfaces. Computational Mechanics, 56(1):131-151, 2015. [ bib ]
[5] Matthias Leuschner and Felix Fritzen, Liang Xia, Matthias Leuschner and Piotr Breitkopf. Topology optimization of multiscale elastoviscoplastic structuresInternational Journal for Numerical Methods in Engineering, 106:430-453, 2016.
[6] Matthias Leuschner and Felix Fritzen. Reduced order homogenization for viscoplastic composite materials including dissipative imperfect interfaces. Mechanics of Materials, 104:121-138, 2017.
[7] Matthias Leuschner and Felix Fritzen. Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems. Computational Mechanics, (in press, 2017).
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