Material property definition
- @MATERIAL_PROPERTY_DEFINITION {
- @MATERIAL_PROPERTY_NAME {MatPropName} {
- @MATERIAL_PROPERTY_TYPE {MatType}
- @MATERIAL_DENSITY {ρ}
- @STIFFNESS_PROPERTIES {
- @YOUNG'S_MODULUS {E_{1}, E_{2}, E_{3}}
- @POISSON'S_RATIO {ν_{12}, ν_{13}, ν_{23}}
- @SHEAR_MODULUS {G_{12}, G_{13}, G_{23}}
- }
- @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 {σ_{1}^{aT}, σ_{2}^{aT}, σ_{3}^{aT}}
- @ALLOWABLE_COMPRESSIVE_STRESS {σ_{1}^{aC}, σ_{2}^{aC}, σ_{3}^{aC}}
- @ALLOWABLE_SHEAR_STRESS {τ_{12}^{a}, τ_{13}^{a}, τ_{23}^{a}}
- }
- @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.
- 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.
- Optionally, the first section defines the viscous characteristics of the material. Bulk, axial, and shear viscosities are defined.
- 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 = (e_{1}, e_{2}, e_{3}), is defined that reflects the possible existence of various planes of symmetry and/or orthotropy, as illustrated in fig. 1.
Notes
- Material mass properties are defined by a single parameter, the material density, ρ.
- 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: E_{1}, E_{2}, and E_{3} along unit vectors e_{1}, e_{2}, and e_{3}, respectively; three Poisson's ratios: ν_{12}, ν_{13}, and ν_{23}; and three shearing moduli: G_{12}, G_{13}, and G_{23}. Thus, for an orthotropic material, the following nine properties are required.
- Young's moduli: E_{1}, E_{2}, and E_{3}.
- Shear moduli: G_{12}, G_{13}, and G_{23}.
- Poisson's ratios: ν_{12}, ν_{13}, and ν_{23}.
- 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 (e_{2}, e_{3}) is selected as the plane of isotropy. In this case, E_{3} = E_{2}, G_{13} = G_{12}, and ν_{13} = ν_{12}: in view of the isotropy in plane (e_{2}, e_{3}), subscripts (.)_{2} and (.)_{3} can be interchanged. Furthermore, the isotropy of plane (e_{2}, e_{3}) implies G_{23} = E_{2}/[2(1 + ν_{23})]. For these materials, the following five properties are required.
- Young's moduli: E_{1} and E_{2}.
- Shear moduli: G_{12}.
- Poisson's ratios: ν_{12} and ν_{23}.
- MatType = ISOTROPIC. An isotropic elastic material has identical properties in all directions. In this case, the isotropy of the material implies E_{1} = E_{2} = E_{3} = E, ν_{12} = ν_{13} = ν_{23} = ν, and G_{12} = G_{13} = G_{23} = E/[2(1 + ν)]. For these materials, the following two properties are required,
- Young's modulus: E.
- 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.
- 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.
- 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.
- Bulk viscosity: ξ,
- 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.
- ALLOWABLE_TENSILE_STRESS: σ_{1}^{aT}, σ_{2}^{aT} and σ_{3}^{aT}, along unit vectors e_{1}, e_{2}, and e_{3}, respectively.
- ALLOWABLE_COMPRESSIVE_STRESS: σ_{1}^{aC}, σ_{2}^{aC}, and σ_{3}^{aC}, along unit vectors e_{1}, e_{2}, and e_{3}, respectively.
- ALLOWABLE_SHEAR_STRESS: τ_{12}^{a}, τ_{13}^{a}, and τ_{23}^{a}.
For different types of materials, the required number of strength properties is different.
- If MatType = ORTHOTROPIC, all nine strength properties are required.
- Tension strength: σ_{1}^{aT}, σ_{2}^{aT}, and σ_{3}^{aT}.
- Compression strength: σ_{1}^{aC}, σ_{2}^{aC}, and σ_{3}^{aC}.
- Shear strength: τ_{12}^{a}, τ_{13}^{a}, and τ_{23}^{a}.
- If MatType = TRANSVERSELY_ISOTROPIC, σ_{3}^{aT} = σ_{2}^{aT}, σ_{3}^{aC} = σ_{2}^{aC} and τ_{13}^{a} = τ_{12}^{a}: in view of the isotropy in plane (e_{2}, e_{3}), subscripts (.)_{2} and (.)_{3} can be interchanged. Furthermore, the isotropy of plane (e_{2}, e_{3}) implies τ_{23}^{a} = σ_{2}^{aT}/√3. The following five properties are required.
- Tension strength: σ_{1}^{aT} and σ_{2}^{aT}.
- Compression strength: σ_{1}^{aC} and σ_{2}^{aC}.
- Shear strength: τ_{12}^{a}.
- If MatType = ISOTROPIC, σ_{1}^{aT} = σ_{2}^{aT} = σ_{3}^{aT} = σ^{a}, σ_{1}^{aC} = σ_{2}^{aC} = σ_{3}^{aC} = σ^{a} and τ_{12}^{a} = τ_{13}^{a} = τ_{23}^{a} = σ^{a}/ √ 3. A single property is required.
- Tension strength: σ^{a}.