Material property definition

@MATERIAL_PROPERTY_DEFINITION {
@MATERIAL_PROPERTY_NAME {MatPropName} {
@MATERIAL_PROPERTY_TYPE {MatType}
@MATERIAL_DENSITY {ρ}
@STIFFNESS_PROPERTIES {
@YOUNG'S_MODULUS {E1, E2, E3}
@POISSON'S_RATIO {ν12, ν13, ν23}
@SHEAR_MODULUS {G12, G13, G23}
}
@VISCOSITY_PROPERTIES {
@BRANCH_PROPERTIES {
@RELAXATION_TIME {τ}
@DAMPING_COEFFICIENT {μ}
@BULK_VISCOSITY {ξ}
@SHEAR_VISCOSITY {η}
}
}
@STRENGTH_PROPERTIES {
@FAILURE_CRITERION_TYPE {FacType}
@ALLOWABLE_TENSILE_STRESS {σ1aT, σ2aT, σ3aT}
@ALLOWABLE_COMPRESSIVE_STRESS {σ1aC, σ2aC, σ3aC}
@ALLOWABLE_SHEAR_STRESS {τ12a, τ13a, τ23a}
}
@COMMENTS {CommentText}
}
}

Introduction

Figure 1. Orthotropic, transversely isotropic and isotropic materials.

The mass, stiffness, viscous, and strength properties of materials are defined in this section. Three data sections are used to define all the properties.

  1. The first section defines the stiffness characteristics of the material. Young's moduli, Poisson's ratios, and shear moduli are defined. Materials to be defined are assumed to be linear elastic materials and are further subdivided into three distinct types: isotropic, orthotropic, and transversely isotropic.
  2. Optionally, the first section defines the viscous characteristics of the material. Bulk, axial, and shear viscosities are defined.
  3. The last section defines the strength characteristics of the material. Allowable tensile, compressive, and shear stresses are defined together with a failure criterion.

Material properties are used for the characterization of lay-ups, which characterize the physical properties of plates and shells in NormalBuilder, and the physical properties of beams SectionBuilder.

In each case, a material basis, E = (e1, e2, e3), is defined that reflects the possible existence of various planes of symmetry and/or orthotropy, as illustrated in fig. 1.

Notes

  1. Material mass properties are defined by a single parameter, the material density, ρ.
  2. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.

Stiffness properties

Material stiffness properties involve Young's moduli, shear moduli, and Poisson's ratios. The flag MatType can take one the following three values.

  • MatType = ORTHOTROPIC. An orthotropic material possess two orthogonal planes of symmetry, implying the existence of a third, as described in fig. 1. The material stiffness properties are characterized by three distinct Young's moduli: E1, E2 and E3 along unit vectors e1, e2 and e3, respectively; three Poisson's ratios: ν12, ν13 and ν23; and three shearing moduli: G12, G13 and G23. Thus, for an orthotropic material, the following nine properties are required.
    1. Young's moduli: E1, E2 and E3.
    2. Shear moduli: G12, G13 and G23.
    3. Poisson's ratios: ν12, ν13 and ν23.
  • MatType = TRANSVERSELY_ISOTROPIC. A transversely isotropic material possess two orthogonal planes of symmetry and an additional plane of material isotropy, i.e., properties are identical in all directions in this plane. As illustrated in fig. 1, plane (e2, e3) is selected as the plane of isotropy. In this case, E3 = E2, G13 = G12 and ν13 = ν12: in view of the isotropy in plane (e2, e3), subscripts (.)2 and (.)3 can be interchanged. Furthermore, the isotropy of plane (e2, e3) implies G23 = E2/[2(1 + ν23)]. For these materials, the following five properties are required.
    1. Young's moduli: E1 and E2.
    2. Shear moduli: G12.
    3. Poisson's ratios: ν12 and ν23.
  • MatType = ISOTROPIC. An isotropic elastic material has identical properties in all directions. In this case, the isotropy of the material implies E1 = E2 = E3 = E, ν12 = ν13 = ν23 = ν, and G12 = G13 = G23 = E/[2(1 + ν)]. For these materials, the following two properties are required,
    1. Young's modulus: E.
    2. Poisson's ratios: ν.

Viscosity properties

Material viscosity properties involve time constants, bulk, shear, and axial viscosity coefficients. Viscoelasticity of the material is modeled based on a generalized Maxwell model. Each branch of the model is associated with a relaxation time constant, τ. The properties of each branch are defined in two mutually exclusive manners.

  1. If the damping coefficient, μ, is defined, the viscosity matrix in the corresponding branch is defined as D = μC, where C is the material stiffness matrix.
  2. If no damping coefficient is defined, the bulk and shear viscosities of the material must be defined for the branch. An isotropic viscous material has identical properties in all directions. For these materials, the following two viscosity properties are required.
    1. Bulk viscosity: ξ,
    2. Shear viscosity: η.

Failure criterion

To predict strength, a failure criterion is selected by means of parameter FacType, which can take the following values.

  • If FacType = HOFFMANN, the Hoffmann criterion will be used.
  • If FacType = MAXIMUM_STRAIN, the maximum strain criterion will be used.
  • If FacType = MAXIMUM_STRESS, the maximum stress criterion will be used.
  • If FacType = TSAI_WU, the Tsai-Wu criterion will be used.
  • If FacType = VON_MISES, the von Mises criterion will be used.

Allowable stresses

The failure criteria depend on a number of material strength parameters. In general, up to nine different parameters can be defined.

  1. ALLOWABLE_TENSILE_STRESS: σ1aT, σ2aT and σ3aT, along unit vectors e1, e2 and e3, respectively.
  2. ALLOWABLE_COMPRESSIVE_STRESS: σ1aC, σ2aC and σ3aC, along unit vectors e1, e2 and e3, respectively.
  3. ALLOWABLE_SHEAR_STRESS: τ12a, τ13a and τ23a.

For different types of materials, the required number of strength properties is different.

  1. If MatType = ORTHOTROPIC, all nine strength properties are required.
    • Tension strength: σ1aT, σ2aT and σ3aT.
    • Compression strength: σ1aC2aC and σ3aC.
    • Shear strength: τ12a, τ13a and τ23a.
  2. If MatType = TRANSVERSELY_ISOTROPIC, σ3aT = σ2aT, σ3aC = σ2aC and τ13a = τ12a: in view of the isotropy in the (e2, e3) plane, the subscripts (.)2 and (.)3 can be interchanged. Furthermore, the isotropy of plane (e2, e3) implies τ23a = σ2aT/√3. The following five properties are required.
    • Tension strength: σ1aT and σ2aT.
    • Compression strength: σ1aC and σ2aC.
    • Shear strength: τ12a.
  3. If MatType = ISOTROPIC, σ1aT = σ2aT = σ3aT = σa, σ1aC = σ2aC = σ3aC = σa and τ12a = τ13a = τ23a = σa/ √ 3. A single property is required.
    • Tension strength: σa.