""" Transversely isotropic elasticity (thermomechanical) ==================================================== """ import numpy as np import simcoon as sim import matplotlib.pyplot as plt import os plt.rcParams["figure.figsize"] = (18, 10) ################################################################################### # In thermoelastic transversely isotropic materials, the following parameters # are required: # # 1. The density :math:`\rho` # 2. The specific heat :math:`c_p` # 3. The axis of transverse isotropy (1, 2, or 3) # 4. The longitudinal Young modulus :math:`E_L` # 5. The transverse Young modulus :math:`E_T` # 6. The Poisson ratio :math:`\nu_{TL}` # 7. The Poisson ratio :math:`\nu_{TT}` # 8. The shear modulus :math:`G_{LT}` # 9. The longitudinal thermal expansion coefficient :math:`\alpha_L` # 10. The transverse thermal expansion coefficient :math:`\alpha_T` # # The elastic stiffness tensor for a transversely isotropic material with axis 1 # as the symmetry axis is written in the Voigt notation formalism as: # # .. math:: # # \mathbf{L} = \begin{pmatrix} # L_{1111} & L_{1122} & L_{1122} & 0 & 0 & 0 \\ # L_{1122} & L_{2222} & L_{2233} & 0 & 0 & 0 \\ # L_{1122} & L_{2233} & L_{2222} & 0 & 0 & 0 \\ # 0 & 0 & 0 & L_{1212} & 0 & 0 \\ # 0 & 0 & 0 & 0 & L_{1212} & 0 \\ # 0 & 0 & 0 & 0 & 0 & L_{2323} # \end{pmatrix} # # The thermal expansion tensor is: # # .. math:: # # \boldsymbol{\alpha} = \begin{pmatrix} # \alpha_L & 0 & 0 \\ # 0 & \alpha_T & 0 \\ # 0 & 0 & \alpha_T # \end{pmatrix} umat_name = "ELIST" # 5 character code for transversely isotropic elastic subroutine nstatev = 1 # Number of internal variables # Material parameters rho = 4.4 # Density c_p = 0.656 # Specific heat capacity axis = 1 # Symmetry axis E_L = 4500.0 # Longitudinal Young's modulus (MPa) E_T = 2300.0 # Transverse Young's modulus (MPa) nu_TL = 0.05 # Poisson ratio (transverse-longitudinal) nu_TT = 0.3 # Poisson ratio (transverse-transverse) G_LT = 2700.0 # Shear modulus (longitudinal-transverse) (MPa) alpha_L = 1.0e-5 # Thermal expansion (longitudinal) alpha_T = 2.5e-5 # Thermal expansion (transverse) psi_rve = 0.0 theta_rve = 0.0 phi_rve = 0.0 solver_type = 0 corate_type = 2 props = np.array([rho, c_p, axis, E_L, E_T, nu_TL, nu_TT, G_LT, alpha_L, alpha_T]) path_data = "../data" path_results = "results" ################################################################################### # Loading in direction 1 # ~~~~~~~~~~~~~~~~~~~~~~~~ # # First we apply a uniaxial stress loading along direction 1 (the symmetry axis). pathfile = "THERM_ELISO_path_1.txt" outputfile_1 = "results_THERM_ELIST_1.txt" sim.solver( umat_name, props, nstatev, psi_rve, theta_rve, phi_rve, solver_type, corate_type, path_data, path_results, pathfile, outputfile_1, ) outputfile_macro_1 = os.path.join(path_results, "results_THERM_ELIST_1_global-0.txt") ################################################################################### # Loading in direction 2 # ~~~~~~~~~~~~~~~~~~~~~~~~ # # Then we apply a uniaxial stress loading along direction 2 (the transverse direction). pathfile = "THERM_ELISO_path_2.txt" outputfile_2 = "results_THERM_ELIST_2.txt" sim.solver( umat_name, props, nstatev, psi_rve, theta_rve, phi_rve, solver_type, corate_type, path_data, path_results, pathfile, outputfile_2, ) outputfile_macro_2 = os.path.join(path_results, "results_THERM_ELIST_2_global-0.txt") ################################################################################### # Plotting the results -- Loading direction 1 # ----------------------------------------------- # # We plot the stress-strain curve, the temperature evolution, and the work terms # for loading along direction 1. fig = plt.figure() # Get the data e11, e22, e33, e12, e13, e23, s11, s22, s33, s12, s13, s23 = np.loadtxt( outputfile_macro_1, usecols=(8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19), unpack=True, ) time, T, Q, r = np.loadtxt(outputfile_macro_1, usecols=(4, 5, 6, 7), unpack=True) Wm, Wm_r, Wm_ir, Wm_d, Wt, Wt_r, Wt_ir = np.loadtxt( outputfile_macro_1, usecols=(20, 21, 22, 23, 24, 25, 26), unpack=True ) # Stress vs Strain ax = fig.add_subplot(2, 2, 1) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel(r"Strain $\varepsilon_{11}$", size=15) plt.ylabel(r"Stress $\sigma_{11}$ (MPa)", size=15) plt.plot(e11, s11, c="black", label="direction 1") plt.legend(loc="best") # Temperature vs Time ax = fig.add_subplot(2, 2, 2) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"Temperature $\theta$ (K)", size=15) plt.plot(time, T, c="black", label="temperature") plt.legend(loc="best") # Mechanical work vs Time ax = fig.add_subplot(2, 2, 3) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_m$", size=15) plt.plot(time, Wm, c="black", label=r"$W_m$") plt.plot(time, Wm_r, c="green", label=r"$W_m^r$") plt.plot(time, Wm_ir, c="blue", label=r"$W_m^{ir}$") plt.plot(time, Wm_d, c="red", label=r"$W_m^d$") plt.legend(loc="best") # Thermal work vs Time ax = fig.add_subplot(2, 2, 4) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_t$", size=15) plt.plot(time, Wt, c="black", label=r"$W_t$") plt.plot(time, Wt_r, c="green", label=r"$W_t^r$") plt.plot(time, Wt_ir, c="blue", label=r"$W_t^{ir}$") plt.legend(loc="best") plt.show() ################################################################################### # Plotting the results -- Loading direction 2 # ----------------------------------------------- # # We plot the stress-strain curve, the temperature evolution, and the work terms # for loading along direction 2. fig = plt.figure() # Get the data e11, e22, e33, e12, e13, e23, s11, s22, s33, s12, s13, s23 = np.loadtxt( outputfile_macro_2, usecols=(8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19), unpack=True, ) time, T, Q, r = np.loadtxt(outputfile_macro_2, usecols=(4, 5, 6, 7), unpack=True) Wm, Wm_r, Wm_ir, Wm_d, Wt, Wt_r, Wt_ir = np.loadtxt( outputfile_macro_2, usecols=(20, 21, 22, 23, 24, 25, 26), unpack=True ) # Stress vs Strain ax = fig.add_subplot(2, 2, 1) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel(r"Strain $\varepsilon_{22}$", size=15) plt.ylabel(r"Stress $\sigma_{22}$ (MPa)", size=15) plt.plot(e22, s22, c="black", label="direction 2") plt.legend(loc="best") # Temperature vs Time ax = fig.add_subplot(2, 2, 2) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"Temperature $\theta$ (K)", size=15) plt.plot(time, T, c="black", label="temperature") plt.legend(loc="best") # Mechanical work vs Time ax = fig.add_subplot(2, 2, 3) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_m$", size=15) plt.plot(time, Wm, c="black", label=r"$W_m$") plt.plot(time, Wm_r, c="green", label=r"$W_m^r$") plt.plot(time, Wm_ir, c="blue", label=r"$W_m^{ir}$") plt.plot(time, Wm_d, c="red", label=r"$W_m^d$") plt.legend(loc="best") # Thermal work vs Time ax = fig.add_subplot(2, 2, 4) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_t$", size=15) plt.plot(time, Wt, c="black", label=r"$W_t$") plt.plot(time, Wt_r, c="green", label=r"$W_t^r$") plt.plot(time, Wt_ir, c="blue", label=r"$W_t^{ir}$") plt.legend(loc="best") plt.show()