Analysis Materials

All elements that refer to Beam Sections, 2D Properties or 3D Properties require an analysis material. This can either be an explicitly defined material or an implied material from a material grade. The latter are always assume to be elastic isotropic materials.

The Material Wizard should normally be used to define the analysis material properties.

Explicit analysis materials

The detailed properties are defined here:

Name

The name is only used as a convenient way of identifying a material.

Material Model

The following material models are the most common:

• Elastic isotropic
• Elastic orthotropic
• Elastic-plastic isotropic
• Fabric

Though GSA can also analyse the following materials with some solvers:

• Drucker-Prager
• Mohr-Coulomb

Young’s modulus, Poisson’s ratios, Shear modulus

Elastic isotropic material - Young’s modulus, Poisson’s ratio and shear modulus can have the following relationship

$$G = \frac{E}{2(1+\nu)}$$

However the shear modulus may be specified independently to allow for the non-isotropic nature of material such as timber. Note that the shear modulus can only be edited using the Material Wizard.

Elastic orthotropic material - there are three Young’s moduli, three Poisson’s ratios and three shear moduli need to be defined and they are:

The material properties are

$E_x$ - Young’s modulus in x direction

$E_{y}$ - Young’s modulus in y direction

$E_{z}$ - Young’s modulus in z direction

$ν_{xy}$ - Poisson’s ratio, y direction strain generated by unit strain in x direction

$ν_{yz}$ - Poisson’s ratio, z direction strain generated by unit strain in y direction

$ν_{zx}$ - Poisson’s ratio, x direction strain generated by unit strain in z direction

The other three Poisson’s ratios ($ν_{yx}$, $ν_{zy}$, $ν_{xz}$) can be calculated from the following relationships:

$$\frac{E_x}{E_y}=\frac{\nu_{xy}}{\nu_{yx}}\qquad\frac{E_y}{E_z}=\frac{\nu_{yz}}{\nu_{zy}}\qquad\frac{E_z}{E_x}=\frac{\nu_{zx}}{\nu_{xz}}$$

$G_{xy}$ - Shear modulus in xy plane

$G_{yz}$ - Shear modulus in yz plane

$G_{zx}$ - Shear modulus in zx plane

Note: If an element uses an orthotropic material, the parameters used by the element are:

Beam elements

$E_{x}$

$G_{xy}$, $G_{zx}$

Bar, Tie & Strut elements

$E_{x}$

2D shell and plate elements

$E_{x}$, $E_{y}$

$ν_{xy}$, $^*ν_{yx}$

$G_{xy}$, $G_{yz}$, $G_{zx}$

2D plane stress elements

$E_{x}$, $E_{y}$

$ν_{xy}$, $^*ν_{yx}$

$G_{xy}$

2D plane strain elements

$E_{x}$, $E_{y}$, $E_{z}$

$ν_{xy}$, $^*ν_{yx}$, $ν_{yz}$, $^*ν_{zy}$, $ν_{zx}$, $^*ν_{xz}$

$G_{xy}$

2D axisymmetric elements

$E_{x}$, $E_{y}$, $E_{z}$

$ν_{yz}$, $^*ν_{zy}$, $ν_{zx}$, $^*ν_{xz}$

$G_{xy}$

• these values are calculated by GSA from the $E$ values and the complementary Poisson’s ratio.

Elastic-plastic isotropic material - the Young’s modulus, Poisson’s ratios and shear modulus etc parameters are the same as elastic isotropic material.

Yield stress is the tensile and compressive strength of the material, ultimate stress is the maximum stress the material can sustain, but it is not used in any of the analysis at the moment, hardening modulus and hardening parameter are used to define the material hardening behavior that can be used by explicit time history analysis and explicit nonlinear analysis.  

In GsRelax nonlinear analysis, material plasticity is considered by beam, bar, tie and strut elements.  Elastic and perfectly plastic material model is assumed in the analysis, i.e. a bi-linear stress-strain curve is used and the second branch of the stress-strain curve is horizontal, There is no strain limit and the stress is limited to the yield stress.  Ultimate stress, hardening modulus and hardening parameter are not used in GsRelax nonlinear analysis.

In explicit time history analysis and explicit nonlinear analysis, material plasticity will be considered by all elements that uses elastic-plastic materials, the stress-strain curve is also bi-linear and the second branch of the curve can be horizontal if no hardening modulus is defined, if  hardening modulus is defined, the second branch of the curve is sloped up to reflect the strain hardening of the material.  Strain hardening can be considered by explicit analysis if they are defined.  The same as GsRelax analysis, the ultimate stress is not used in the analysis..  

Fabric material - Fabric material is only used for 2D fabric (membrane) element, since the element has no thickness, the unit of Young’s modulus and shear modulus of fabric material is force per unit length. Fabric material is orthotropic and the following properties need to be defined:

$E′_{x}$ - Young’s modulus in $x$ (warp) direction

$E′_{y}$ - Young’s modulus in $y$ (weft) direction

$ν_{xy}$ - Poisson’s ratio, $y$ direction strain generated by unit strain in $x$ direction

The other Poisson’s ratio ($ν_{yx}$) can be obtained from the following relationship:

$$\frac{E'_x}{E'_y}=\frac{\nu_{xy}}{\nu_{yx}}$$

Fabric material can be defined to take tensile force only (the default option) or take both tensile and compressive forces. If the check box “Allow compression” is checked, fabric will take compressive force, otherwise, it will take tensile force only.

Other options

Note that these may be available with only some material types.

Initialize Analysis Material from Design Material

This command is available from the wizard. You can set the material properties either from materials in a catalogue or from material grades in the model.

Density

The density of the material to be used in dynamic analysis to calculate masses and in other analysis to calculate gravity loads.

Temperature coefficient

The temperature coefficient of expansion which is used in conjunction with thermal loading. For orthotropic material, three coefficients need to be defined for $x$, $y$ & $z$ directions.

Damping Ratio

The damping ratio is used during a dynamic analysis to calculate an estimate of the modal damping ratio.

Yield stress

The stress at which the material first yields in nonlinear analyses. For design this may be a value specified by a design code.

Ultimate stress

The stress at which the material will break. This is used mainly for design purposes. This property is not used by the analysis options in GSA but can be when analysing in LS-DYNA.

Hardening modulus

Once the material has yielded it is assumed to follow a straight-line relationship between stress and strain. The slope of this line is the hardening modulus. This property is not used by the analysis options in GSA but can be when analysing in LS-DYNA.

Hardening parameter

This is used in nonlinear analysis to determine if the hardening model should be isotropic or kinematic. This property is not used by the analysis options in GSA but can be when analysing in LS-DYNA.

Allow Compression

This box should be unchecked if the fabric is to allowed to behave like a true fabric and not allow compression.

Cohesion, Friction angle, Dilation

Set the soil properties