10.2 Stress_Model: Linear Orthotropic Elasticity Model

ORTHOTROPIC_ELASTIC

Material_name = ORTHOTROPIC_ELASTIC

Material_set_number = mset , etc...

Note Variable Name Type Default Description

• Keywords Read Method

Material_set_number integer [1] Material set number Numat

Mass_density real [0.0] Mass density

Youngs_modulus real [0.0] Young's modulus E

Poissons_ratio real [0.0] Poisson's ratio

(1) Modulus_coefficient_C11 real [0.0] Modulus coefficient C11

Modulus_coefficient_C22 real [0.0] Modulus coefficient C22

Modulus_coefficient_C33 real [0.0] Modulus coefficient C33

Modulus_coefficient_C44 real [0.0] Modulus coefficient C44

Modulus_coefficient_C55 real [0.0] Modulus coefficient C55

Modulus_coefficient_C66 real [0.0] Modulus coefficient C66

Modulus_coefficient_C12 real [0.0] Modulus coefficient C12 (= C21)

Modulus_coefficient_C23 real [0.0] Modulus coefficient C23 (= C32)

Modulus_coefficient_C13 real [0.0] Modulus coefficient C13 (= C31)

(2) Reference_direction_axes:

n_x(1), n_y(1), n_z(1) real [ref.axes] Material axes (if needed)

n_x(2), n_y(2), n_z(2)

n_x(3), n_y(3), n_z(3)

(3) Mass_damping real [0.0] Mass matrix Rayleigh damping coefficient

(3) Stiffness_damping real [0.0] Stiffness matrix Rayleigh damping coefficient

(4) Solid_mass_density real [0.0] Mass density (Solid Phase)

(4) Fluid_mass_density real [0.0] Mass density (Fluid Phase)

(4) Fluid_bulk_modulus real [0.0] Bulk modulus (Fluid Phase)

(4) Porosity real [0.0] Porosity

(4) Ref_fluid_pressure real [0.0] Reference pore-fluid pressure

(4) Pressure_load_time integer [0] Pore-fluid pressure load time function

(cont’d)

(cont'd)

Note Variable Name Type Default Description

(5) Initial_stress

initial_stress_11 real [0.0] Component 11 ()

initial_stress_22 real [0.0] Component 22 ()

initial_stress_33 real [0.0] Component 33 ()

initial_stress_12 real [0.0] Component 12 ()

initial_stress_23 real [0.0] Component 23 ()

initial_stress_31 real [0.0] Component 31 ()

• List Read Method

Material data must follow in the form:

< m, E(m), Pois(m), (m), (m), (m), (m), Pf(m) >

< C11(m), C22(m), …, C66(m) >

< C12(m), C23(m), C13(m) >

< i, n(1, m, i), n(2, m, i), n(3, m, i), i = 1 >

< i, n(1, m, i), n(2, m, i), n(3, m, i), i = 2 >

< i, n(1, m, i), n(2, m, i), n(3, m, i), i = 3 >

< Dampm (m), Dampk (m) >

< (Stres(i, m), i = 1, 6) >

< terminate with a blank record >.

Notes/

(1) If (C11*C22*...*C44 0) the material defaults to an isotropic linear elastic model using Young's modulus and Poisson's ratio.

(2) Default is n₁ = e₁ = {1, 0, 0}, n₂ = e₂ = {0, 1, 0}, and n₃ = e₃ = {0, 0, 1} where [e₁, e₂, e₃] is the triad of unit base vectors used for the reference rectangular Cartesian axes. The orthotropic elasticity tensor E, is referred to the global coordinate axes via the rotation:

E'_ijkl = E_klmn R_ki R_lj R_mk R_nl

where R = [n₁, n₂, n₃]. Note that the orthotropic direction vectors are restricted to be orthogonal to each other, viz.,

n_I ^. n_J = _IJ

(3) The element damping matrix is computed as:

c = Rayleigh_mass_damp*m + Rayleigh_stiffness_damp*k

(4) Only applicable to porous media models.

(5) Tensile stresses are positive.

Notes . .