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| Original file line number | Diff line number | Diff line change |
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| # # Wave propagation across material interface | ||
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| # Based on the [wave propagation tutorial](@ref tut_wave), this tutorial features a | ||
| # displacement wave crossing a material interface, as investigated in | ||
| # [Partmann2024AAM](@cite). This means that a bar containing two sections with different | ||
| # material properties is regarded. | ||
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| # First import the Peridynamics.jl package: | ||
| using Peridynamics | ||
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| # Then the geometric parameters are set, which are the same as in the wave propagation | ||
| # tutorial. | ||
| # These are the length `lx`, width and height `lyz` of the cuboid as well as the number | ||
| # of points in the width `npyz`, which determines the point spacing `Δx`. | ||
| lx = 0.2 | ||
| lyz = 0.002 | ||
| npyz = 4 | ||
| Δx = lyz / npyz | ||
| # With these parameters we now create a body, here using the non-ordinary state-based | ||
| # correspondence formulation. | ||
| pos, vol = uniform_box(lx, lyz, lyz, Δx) | ||
| body = Body(NOSBMaterial(), pos, vol) | ||
| # Again, failure is not allowed in the whole body. | ||
| failure_permit!(body, false) | ||
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| # Then the material parameters for one half of the body are assigned to the whole body | ||
| # first. | ||
| material!(body, horizon=3.015Δx, rho=7850.0, E=210e9, nu=0.25, epsilon_c=0.01) | ||
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| # Now a point set containing the other half of all points is created. | ||
| point_set!(x -> x < 0, body, :set1) | ||
| #  | ||
| # The parameters for this point set are then overwritten with their new parameters. | ||
| material!(body, :set1, horizon=3.015Δx, rho=7850.0, E=105e9, nu=0.25, epsilon_c=0.01) | ||
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| # Except for the Young's modulus, these are the same in both sections: | ||
| # | ||
| # | material parameter | value | | ||
| # |:--------|:-------------| | ||
| # | Horizon $ δ $ | $3.015 \cdot Δx$ | | ||
| # | Density $ρ$ | $ 7850\,\mathrm{kg}\,\mathrm{m}^{-3}$ | | ||
| # | Young's modulus $E_I$ | $ 105 \, \mathrm{GPa}$ | | ||
| # | Young's modulus $E_{II}$ | $ 210 \, \mathrm{GPa}$ | | ||
| # | Poisson's ratio $ν$ | $0.25$ | | ||
| # | critical strain $ε_c$ | $0.01$ | | ||
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| # To employ the boundary conditions creating a displacement wave, the point set `:left` is | ||
| # created: | ||
| point_set!(x -> x < -lx / 2 + 1.2Δx, body, :left) | ||
| # As in the wave propagation tutorial, the applied velocity boundary condition is | ||
| # ```math | ||
| # {v}_x (t) = | ||
| # \begin{cases} | ||
| # v_\mathrm{max} \cdot \sin(2\pi \cdot \frac{t}{T}) \qquad | ||
| # & \forall \; 0 \leq t \leq T \\ | ||
| # 0 &\text{else.} | ||
| # \end{cases} | ||
| # ``` | ||
| #  | ||
| T, vmax = 1.0e-5, 2.0 | ||
| velocity_bc!(t -> t < T ? vmax * sin(2π / T * t) : 0.0, body, :left, :x) | ||
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| # The Velocity Verlet algorithm is used as time integration method and 2000 time steps | ||
| # are calculated: | ||
| vv = VelocityVerlet(steps=2000) | ||
| # Finally the job is defined and submitted. | ||
| #md # ```julia | ||
| #md # job = Job(body, vv; path="results/xwave_interface") | ||
| #md # submit(job) | ||
| #md # ``` | ||
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| # The following video shows the results for the displacement in x-direction $u_x$ and the | ||
| # first entry of the | ||
| # stress tensor, i.e. the normal stress in x-direction $\sigma_{11}$. | ||
| # ```@raw html | ||
| # <video controls loop="true"> | ||
| # <source src="https://github.com/user-attachments/assets/d7e600ee-cad8-40f9-99f4-e96ac05585d6" /> | ||
| # </video> | ||
| # ``` |
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