Non-local structural mechanics and Peridynamics

Prof. Dr.-Ing. Christian WillbergORCID Symbol
Magdeburg-Stendal university of applied sciences

Kontakt: christian.willberg@h2.de

Bildreferenz

Lecture

Understanding of fractures is needed for

  • reducing experiments
  • fatigue prediction
  • crack growth and residual strength estimation

Assumptions in classical continuum mechanics

  • Continuous medium
  • 2x continuously differentiable
  • Conservation equations satisfied (momentum, angular momentum and energy)

Conservation of Momentum

Implications 1D

truss with 2 areas

,

no derivative exists at the position, where becomes

Reality is non-local

Peridynamics (PD)

  • material point
  • bond
  • neighbor
  • integral domain
  • horizon
  • deformed bond state
    ...

PD is a continuum formulation!

Model Conservation of Momentum Conservation of Angular Momentum
bond-based bond bond
ordinary state-based integral bond
non-ordinary state-based integral integral

Software

%%{init: { 'theme':'forest','quadrantChart': { 'pointLabelFontSize': '130%'} } }%% quadrantChart x-axis Low Functionalty --> High Functionalty y-axis Hard to use --> Simple to use Peridigm: [0.85, 0.2] PeriLab.jl: [0.7, 0.8] Peridynamics.jl: [0.5, 0.7] EMU: [0.95, 0.1] PeriPy: [0.2, 0.7] PeriPyDIC: [0.2, 0.6] LAMMPS: [0.3, 0.3] PeriFlakes: [0.35, 0.4] Relation-Based Software: [0.4, 0.25] BB_PD: [0.2, 0.50] PeriDEM: [0.13, 0.3]

Software


PeriLab Repository

  • install julia programming language
  • start julia
  • write in the console

using Pkg
Pkg.add("PeriLab")

Application - run julia

using PeriLab

PeriLab.get_examples() (optional)
PeriLab.main("examples/DCB/DCBmodel.yaml") (run run model)

Seminar

Theory
Examples for the seminar
Results