Multiphysics Simulation of Multifunctional Soft Materials

HyperFEM is a library within the Gridap ecosystem designed for the simulation of multiphysics problems involving multifunctional hyperelastic materials. The ultimate goal of HyperFEM is to provide a high-level, expressive, and rapid prototyping tool that accelerates the modeling stages of Thermo–Electro–Magneto–Mechanical multiphysics problems. To this end, it includes a comprehensive library of analytically derived constitutive models formulated through tensor algebra. In addition, HyperFEM provides abstractions for monolithic and staggered solution schemes, extending Gridap’s capabilities in the context of nonlinear solid mechanics.

Installation

Open the Julia REPL, type ] to enter package mode, and install as follows

pkg> add https://github.com/MultiSimOLab/HyperFEM

Usage

First, include the main HyperFEM module:

using HyperFEM

Example of a Monolithic implementation for the simulation of Nonlinear ElectroMechanical deformation of dielectric elastomers

using HyperFEM
using Gridap, GridapGmsh, GridapSolvers, DrWatson
using GridapSolvers.NonlinearSolvers
using Gridap.FESpaces
using WriteVTK


simdir = datadir("sims", "Static_ElectroMechanical")
setupfolder(simdir)

geomodel = GmshDiscreteModel("./test/models/test_static_EM.msh")

# Constitutive model
physmodel_mec = NeoHookean3D(λ=10.0, μ=1.0)
physmodel_elec = IdealDielectric(ε=1.0)
physmodel= physmodel_mec+physmodel_elec

# Setup integration
order = 1
degree = 2 * order
Ω = Triangulation(geomodel)
dΩ = Measure(Ω, degree)

# Dirichlet boundary conditions 
evolu(Λ) = 1.0
dir_u_tags = ["fixedup"]
dir_u_values = [[0.0, 0.0, 0.0]]
dir_u_timesteps = [evolu]
Du = DirichletBC(dir_u_tags, dir_u_values, dir_u_timesteps)

evolφ(Λ) = Λ
dir_φ_tags = ["midsuf", "topsuf"]
dir_φ_values = [0.0, 0.1]
dir_φ_timesteps = [evolφ, evolφ]
Dφ = DirichletBC(dir_φ_tags, dir_φ_values, dir_φ_timesteps)

D_bc = MultiFieldBC([Du, Dφ])

# Finite Elements
reffeu = ReferenceFE(lagrangian, VectorValue{3,Float64}, order)
reffeφ = ReferenceFE(lagrangian, Float64, order)

# Test FE Spaces
Vu = TestFESpace(geomodel, reffeu, D_bc.BoundaryCondition[1], conformity=:H1)
Vφ = TestFESpace(geomodel, reffeφ, D_bc.BoundaryCondition[2], conformity=:H1)

# Trial FE Spaces
Uu = TrialFESpace(Vu, D_bc.BoundaryCondition[1], 1.0)
Uφ = TrialFESpace(Vφ, D_bc.BoundaryCondition[2], 1.0)

# Multifield FE Spaces
V = MultiFieldFESpace([Vu, Vφ])
U = MultiFieldFESpace([Uu, Uφ])

# Kinematic Description
km=Kinematics(Mechano,Solid)
ke=Kinematics(Electro,Solid)

# residual and jacobian function of load factor
res(Λ) = ((u, φ), (v, vφ)) -> residual(physmodel, (km,ke),(u, φ), (v, vφ), dΩ)
jac(Λ) = ((u, φ), (du, dφ), (v, vφ)) -> jacobian(physmodel, (km,ke), (u, φ), (du, dφ), (v,vφ),dΩ)

# nonlinear solver
ls = LUSolver()
nls_ = NewtonSolver(ls; maxiter=20, atol=1.e-10, rtol=1.e-8, verbose=true)

# Computational model
comp_model = StaticNonlinearModel(res, jac, U, V, D_bc; nls=nls_)

# Postprocessor to save results
function driverpost(post; Ω=Ω, U=U)
    state = post.comp_model.caches[3]
    Λ_ = post.iter

    xh = FEFunction(U, state)
    uh = xh[1]
    φh = xh[2]
    pvd = post.cachevtk[3]
    filePath = post.cachevtk[2]

    if post.cachevtk[1]
        pvd[Λ_] = createvtk(Ω,filePath * "/TIME_$Λ_" * ".vtu",cellfields=["u" => uh, "φ" => φh])
    end
end

post_model = PostProcessor(comp_model, driverpost; is_vtk=true, filepath=simdir)

# Solve
x = solve!(comp_model; stepping=(nsteps=5, maxbisec=5), post=post_model)

HyperFEM Gallery

       

How to cite HyperFEM

In order to give credit to the HyperFEM contributors, we ask that you please reference the paper:

In process

along with the required citations for Gridap.

Project funded by:

• Grants PID2022-141957OA-C22/PID2022-141957OB-C22 funded by MCIN/AEI/ 10.13039/501100011033 and by ''ERDF A way of making Europe''

       

Contact

Contact the project administrator Jesús Martínez-Frutos for further questions about licenses and terms of use.