P14 – Passage from Atomistic-to-Continuum for Quasistatic and Dynamic Crack Growth (P14 GRK 2423 FRASCAL)

Third Party Funds Group - Sub project

Acronym: P14 GRK 2423 FRASCAL

Start date : 01.04.2019

End date : 30.09.2023

Extension date: 31.12.2027

Overall project details

Overall project

Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics (FRASCAL) (GRK 2423 FRASCAL) Jan. 1, 2019 - Dec. 31, 2027

Project details

Scientific Abstract

We extend the rigorous identification of Griffith models from atomistic systems governed by Lennard-Jones interactions [FrSc15a] to general lattice systems including long-range and multi-body interactions. Here, we will apply techniques from the paper [BaBrCi20] and complement their analysis by showing the Cauchy-Born rule in the setting of small displacements. Applying the Gamma-convergence approach to composite materials, we also aim at studying the influence of different mesoscopic on the macroscopic fracture properties. This connects our perspective to projects P8 and P11. Our main goal is then to establish existence of an atomistic continuous–time evolution and relate it rigorously to continuum quasi-static evolutions [FrLa03, FrSo18] by means of evolutionary Gamma-convergence for rate-independent systems. Here, a key issue consists in verifying stability of unilateral minimisers along the irreversible fracture process.


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