Deformation of 2d Logo

We consider a Peridynamic simulation of Soft material using RNP Peridynamic model (Regularized Nonlinear Peridynamic) developed and studied in Lipton 2016 and Jha and Lipton 2018. RNP model is implemented in class RNPBond.

Units are SI units, e.g. length is in
meter
, mass is inkg
, force is inN
, and time is insecond
. 
Elastic properties of material are as follows:
 Shear modulus
G = 35.2E+03 Pa
 Poisson ratio
$\nu$ = 0.25
 Density
$\rho$ = 1011.204 kg/$m^3$
 Shear modulus

Fracture properties of material are as follows:
 Critical energy release rate
$G_c$ = 9.998E+02 J/$m^2$
 Critical energy release rate

For above elastic properties and fracture properties, we can compute the parameters in Peridynamic material model. This has been described in detail in RNPBond::computeParameters.

We consider a triangular mesh for “NLM” logo. It is contained in the box
[0, 2.75 m] x [0, 1.5 m]
. 
Horizon is
$\epsilon$ = 0.1 m
and mesh size ish = 0.025 m
. 
Time domain
 Final time
T = 0.01
 Time steps
N = 50000
 Output frequency of simulation data:
N/100
 Final time

Boundary condition

We apply body force along horizontal axis on whole material domain.

Force is given by $f_x(x,y,t) = f t sin(n\pi x/L_x)$ where
n = 3
andf = 1.5E+09
.


We specify
Displacement
,Velocity
,Force
andDamage_Z
as output candidates.
Mesh
We obtain mesh using Gmsh
library with mesh size h = 0.025
.
Results
We show damage plot at time t = 0.008, 0.009, 0.01 seconds
.
Video of simulation: