3.5.1: Material Properties

The component “MatProps” lets one directly define isotropic and orthotropic materials. Use the dropdown menu at the bottom of the component to chose between ortho- and isotropic materials.

Isotropic Material Properties

Fig. 3.5.1.1: Definition of the properties of two isotropic materials via the “Material Properties” component

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IsotropicMaterialPropertiesComponent.gh

In Fig. 3.5.1.1 selection of the second material from the resulting list can be made (bottom right component) or selection from the default material table (top right component). Material isotropy means that the material’s behaviour does not change with direction. Karamba3D uses the following parameters to characterize an isotropic material (see fig. 3.5.1.1):

"Family"	Family name of the material (e.g. “steel”); is used for selecting materials from a list.
"Name"	Name of the material (e.g. “S235”); serves as identification when selecting materials from a list.
"Elem|Id"	An element with an identifier, a string containing an identifier or a regular expression that depicts the elements that shall have the specified material.
"Color"	Color of the material. In order to see it, enable “Materials” in submenu “Colors” of the “ModelView”-component, then enable “Cross section” in submenu “Render Settings” of the “BeamView”- and/or “ShellView”-component.
"E"	Young’s Modulus ($kN/cm^2$): characterizes the stiffness of the material.
"G12"	In-plane shear modulus ($kN/cm^2$): In case of isotropic materials the following constraint applies: $E/3<G_{12}<E/2$ . In case this condition is not fulfilled, the structure may show strange behaviour.
"G13"	Transverse shear modulus ($kN/cm^2$): Is the same as$G_{12}$in case of isotropic materials like e.g. steel. This value can be chosen independently from$E$. In case of e.g. wood, the value may be much smaller than$G_{12}$.
"gamma"	Specific weight ($kN/cm^3$)
"alphaT"	Coefficient of thermal expansion ($1/°C$)
"ft"	Tensile strength of the material ($kN/cm^2$) - a positive value
"fc"	Compressive strength of the material ($kN/cm^2$) - a negative value
"S-Hypo"	Index of the strength hypothesis to be used. Use 'Expand ValueLists' from the components context menu for selecting between these options: 0: Von Mises, 1: Tresca, 2: Rankine

In case of temperature changes materials expand or shorten. “alphaT” sets the increase of strain per degree Celsius of an unrestrained element. For steel the value is $1.0E 5(1.0E 5 = 1.-0 10−5 = 0.00001)$. Therefore an unrestrained steel rod of length $10 m$ lengthens by $1 mm$ under an increase of temperature of $10 °C$. “alphaT” enters calculations when temperature loads are present.

The utilization of cross sections as displayed by the “BeamView”-component (see section 3.6.7) is the ratio of actual stress and the tensile or compressive strength respectively. In case of shells, utilization is determined as the ratio of the result of the strength Hypotheses (as computed from the stresses in the shell) and the tensil or compressive strengh (see section 3.6.11).

Cross section optimization (see section 3.5.8) also makes use of the materials stength values. For reinforced concrete this may lead to excessive cross section thicknesses since concrete cross sections are handled as though being unreinforced. In order to get useful thickness values for reinforced conrete, one needs to scale up the concrete material's tensile strength.

Orthotropic Material Properties

Material orthotropy means that the material’s behaviour changes with direction. The material properties in two orthogonal directions fully characterize any orthotropic material. In Karamba3D orthotropic materials take effect only in shells. When supplied to beams, the material properties in the first direction are applied. For shells the first material direction corresponds to the local x-axis. See section 3.1.14 on how to set user defined local coordinate systems on shells.

Fig. 3.5.1.2: Definition of properties of an orthotropic material via the “Material Properties” component

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OrthotropicMaterialPropertiesComponent.gh

In fig. 3.5.1.2 an orthotropic material gets defined using a “Material Property”-component. Besides “Family”, “Name”, “Elem|Id” and “Color” it expects the following input:

"E1"	Young’s Modulus in the first direction ($kN/cm^2$)
"E2"	Young’s Modulus in the second direction ($kN/cm^2$)
"G12"	In-plane shear modulus ($kN/cm^2$): The value of is liable to a constraint which is further depicted below.
"nue12"	$v_{12}$ ​is the in-plane lateral contraction coefficient (also called Poisson’s ratio): In case$v_{12}=-1$(the default) the approximate formula of Huber [8] is applied to $v_{21}$​ calculated from​$E_1$, $E_2$ and $G_{12}$: $v_{12}​=\frac{E_1}{2.G_{12}}​​−\sqrt{\frac{E_2}{​E_1}}​​ ​$
"G31"	Transverse shear modulus in the first direction ($kN/cm^2$)
"G32"	Transverse shear modulus in the second direction ($kN/cm^2$)
"gamma"	Specific weight ( $kN/m^3$ )
"alphaT1"	Coefficient of thermal expansion in the first direction ( $1/°C$ )
"alphaT2"	Coefficient of thermal expansion in the second direction ( $1/°C$ )
"ft1"	Tensile strength of the material ($kN/cm^2$) in the first direction - a positive value
"ft2"	Tensile strength of the material ($kN/cm^2$) in the second direction - a positive value
"fc1"	Compressive strength of the material ($kN/cm^2$) in the first direction - a negative value
"fc2"	Compressive strength of the material ($kN/cm^2$) in the second direction - a negative value
"t12"	Shear strength ($kN/cm^2$) between first and second material direction.
"F12"	Tsai-Wu interaction coefficient
"S-Hypo"	Index of the strength hypothesis to be used. Use 'Expand ValueLists' from the components context menu for selecting between these options: 0: Von Mises, 1: Tresca, 2: Rankine, 3:TsaiWu

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assignMaterial.gh

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ShearStiffness_Of_Beams.gh