Overview

This package is an evolution of the somewhat cumbersome-to-use ep2-3De v1.0, and is entirely written in Julia. It is designed for rapid prototyping while maintaining reasonable production capabilities. It addresses the following key aspects:

• Updated Lagrangian explicit formulation for elastoplastic simulations.
• Supports both finite and infinitesimal deformation frameworks:
  • Finite deformation: employs logarithmic strains and Kirchhoff stresses.
  • Infinitesimal deformation: based on a Jaumann rate formulation.
• Compatible with multiple shape function bases:
  • Standard linear shape function $N_n(\boldsymbol{x}_p)$
  • GIMP shape function $S_n(\boldsymbol{x}_p)$
  • Boundary-modified cubic B-spline shape function $\phi_n(\boldsymbol{x}_p)$
• Provides mappings between nodes (denoted $n$ or $v$) and material points (denoted $p$), using:
  • FLIP with augmented mUSL procedure
  • TPIC with standard USL procedure

The solver can generate initial fields $f(\boldsymbol{x})$—such as the cohesion $c(\boldsymbol{x}_p)$ or internal friction angle $\varphi(\boldsymbol{x}_p)$—using random Gaussian fields, with $\boldsymbol{x}_p$ representing a material point’s coordinate.

<p align="center"> <img src="./assets/img/epII.png" alt="Plastic strain" style="width:80%;"/>> <br/> <em>Figure: Slumping dynamics (without volumetric locking corrections) showing the accumulated plastic strain $\epsilon_p^{\mathrm{acc}}$ after an elastic load of 8 s and an additional elasto-plastic load of ≈ 7 s.</em> </p>

<p align="center"> <img src="./assets/img/c0.png" alt="Initial cohesion field" style="width:80%;"/> <br/> <em>Figure: Initial cohesion field ( c0(\boldsymbol{x}p) ) with average ( \mu = 20 \,\text{kPa} ) and variance ( \sigma = \pm 5 \,\text{kPa} ).</em> </p>