Fabric Law for Elastic Orthotropic
Shells (LAW19 and LAW58)
Two elastic linear models and a nonlinear model exist in Radioss.
Fabric Linear Law for Elastic
Orthotropic Shells (LAW19)
A material is orthotropic if its behavior is symmetrical with respect to two orthogonal
plans. The fabric law enables to model this kind of behavior. This law is only available for
shell elements and can be used to model an airbag fabric. Many of the concepts for this law
are the same as for LAW14 which is appropriate for composite solids. If axes 1 and 2
represent the orthotropy directions, the constitutive matrix is defined in terms of material properties:
where the subscripts denote the orthotropy axes. As the matrix is symmetric:
Therefore, six independent material properties are the input of the material:
Young's modulus in direction 1
Young's modulus in direction 2
12
Poisson's ratio
, ,
Shear moduli for each direction
The coordinates of a global vector is used to
define direction 1 of the local coordinate system of orthotropy.
The angle is the angle between the local direction 1 (fiber direction)
and the projection of the global vector as shown in Figure 1.Figure 1. Fiber Direction Orientation
The shell normal defines the positive direction for . Since fabrics have different compression and tension
behavior, an elastic modulus reduction factor, RE, is defined that changes the
elastic properties of compression. The formulation for the fabric law has a
reduction if < 0 as shown in Figure 2.Figure 2. Elastic Compression Modulus Reduction
Fabric Nonlinear Law for Elastic
Anisotropic Shells (LAW58)
This law is used with Radioss standard shell elements and
anisotropic layered property (TYPE16). The fiber directions (warp and weft) define the local
axes of anisotropy. Material characteristics are determined independently in these axes.
Fibers are nonlinear elastic and follow the equation:
The shear in fabric material is only supposed to be function of the angle between current
fiber directions (axes of anisotropy):
and
, with
Where,
Shear lock angle
Tangent shear modulus at
Shear modulus at = 0
If = 0, the default value is calculated to avoid shear modulus
discontinuity at : = .
Figure 3. Elastic Compression Modulus Reduction
Where, is an initial angle between fibers defined in the shell
property (TYPE16).
The warp and weft fiber are coupled in tension and uncoupled in compression. But there is
no discontinuity between tension and compression. In compression only fiber bending
generates global stresses. Figure 4 illustrates the mechanical behavior of
the structure.Figure 4. Local Frame Definition
A local micro model describes the material behavior (Figure 5). This model represents just ¼ of a
warp fiber wave length and ¼ of the weft one. Each fiber is described as a nonlinear beam
and the two fibers are connected with a contacting spring. These local nonlinear equations
are solved with Newton iterations at membrane integration point.Figure 5. Local Frame Definition