4LM30 - Multiscale modelling for polymer mechanics

sands

The course will give an introduction to/repetition of the most common and important simulation techniques, namely to

  • Molecular Dynamics (MD) simulations (particle-based),
  • Metropolis Monte Carlo (MC) simulations (particle-based),
  • Finite Element Method (FEM) (continuum),

 that are used nowadays to model and predict the thermo-mechanical properties of polymers. To that end, the course will include the following subtopics:

  • Controlling the temperature and pressure with thermo- and barostats (MD, MC);
  • Imposing external deformation and temperature gradients (MD, FEM);
  • Calculation of the mechanical and thermal response (stress tensor and heat flux) (MD);
  • Implementation of constitutive material models for hyper-elastic, visco-elastic, and visco-plastic behavior (FEM);
  • Coupling of particle-based and continuum scales (MD, MC, FEM), using nonequilibrium thermodynamics.

In order to increase the accuracy and efficiency of the simulations, the course covers also

  • Time-integration schemes (Euler, Verlet) (MD);
  • Efficient energy and force calculations for large systems (neighbour lists and cell lists) (MD, MC);
  • Averages and the usefulness of fluctuations (MC);
  • Boundary conditions, periodic or free (MD, MC, FEM);
  • Calculation of stresses and tangential stiffness (FEM);
  • Mesh-convergence (FEM).

Implementation of material models is done in Matlab (MD, MC, FEM), and Marc Mentat (FEM). The above simulation techniques will be applied to study and predict the behavior of polymers.

learning objectives

The focus of this course is on modeling the mechanical behavior of polymers in the solid state. Of particular interest is the combination different length scales to arrive at mechanical models that built on the underlying structure. To that end, several numerical techniques are discussed, namely Molecular Dynamics, Metropolis Monte Carlo, and Finite Element Modeling. The coupling of different levels of description can be achieved either sequentially (by pre-calculation of input parameters for a coarser scale) or concurrently. In the latter case, we will make use of techniques from non-equilibrium thermodynamics. All these procedures will be applied to the mechanical behavior of solid polymers. This course continues/builds on the Bachelor elective course 4LB00 Strength & Structure.