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Thematic Einstein Semester on
Energy-based mathematical methods for reactive multiphase flows

TES-Seminar on Energy-based Mathematical Methods and Thermodynamics

Thursday, 3 pm – 4.30 pm CET ( UTC + 1)

The seminar is held online in Zoom. In order to receive the Zoom-links to attend the talks, please register using the button below.

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Seminar

A discontinuous Galerkin method for phase field approximations of dynamic fracture

Speaker: Christian Wieners (KIT)

Date: November 19, 2020

 

Abstract: We present a new numerical method for dynamic fracture at small strains which is based on a discontinuous Galerkin approximation of a first order formulation for elastic waves and where the fracture is approximated by a phase field driven by a stress based fracture criterion.
The staggered algorithm in time combines the implicit midpoint rule for the wave propagation followed by an implicit Euler step for the phase field evolution. Then, driven by a stress based fracture criterion, the material is degradated, and the waves are reflected at the diffusive interface.
Then method is evaluated in detail in one dimension, and then we demonstrate in a 2D application the fracture evolution with multiple fractures initiated by reflections.
This is joint work with Kerstin Weinberg, Siegen.

Multiscale Thermodynamics

Speaker: Miroslav Grmela (Polytechnique Montréal)

Date: November 26, 2020

 

Abstract: Multiscale thermodynamics is a theory of relations among levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case but it is applicable to both static and time evolving processes in externally and internally driven macroscopic systems that are far from equilibrium and are investigated on microscopic, mesoscopic, and macroscopic levels. In this talk we formulate the multiscale thermodynamics, explain its origin, and illustrate it in mesoscopic dynamics that combines levels, see [1] for more details.

 

[1] M. Grmela: Multiscale Thermodynamics. arxiv-preprint 2020.

Equilibrium for multiphase solids with Eulerian interfaces

Speaker: Martin Kružík (Czech Technical University)

Date: December 10, 2020

Abstract: We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove the existence of energy minimizing equilibrium states and Γ-convergence of diffuse-interface approximations to the sharp-interface limit.
This is a joint work with D. Grandi, E. Mainini and U. Stefanelli.

 

TBA

Speaker: Denis Matignon (ISAE)

Date: January 14, 2021

Abstract: TBA