## Solid property definition

@SOLID_PROPERTY_DEFINITION {
@SOLID_PROPERTY_NAME {SolPropName} {
@IS_DEFINED_IN_FRAME {BasisFlag}
@LAYER_ORIENTATION {LayOriFlag}
@LAYUP_NAME {LayUpName}
}
}

### Introduction

This section defines the material properties for the solid element. The face of the solid element is associated with a surface, which defines a local basis, called the solid local basis, U = (i1, u, v).

Within each solid element, it is assumed that the material is arranged in parallel heterogeneous layers, as would be the case if the structure is made of layered composite materials. Figure 1 illustrates the configuration of the layered material. If the material is homogeneous, it is sufficient to define a single layer that covers the entire solid element.

##### Figure 1. Stacks of layers defining solid properties. In the left portion of the figure, the layers all run parallel to the u axis: LayOriFlag = ALONG_U. In the right portion of the figure, the layers all run parallel to the v axis: LayOriFlag = ALONG_V.

Material properties are defined with the help of the lay-up definition. The physical characteristics of a typical layer, called layer i in fig. 1, are specified through (1) a thickness, ti, (2) material properties, and (3) orientation angles, βi, γi.

### Notes

1. The basis flag, BasisFlag, plays an important role in the definition of the material axes orientation as discussed below. Two options are available, BasisFlag = LOCAL or GLOBAL.
2. Similarly, the layer orientation flag, LayOriFlag, defines the orientation of the layers with respect to the solid local basis.
• If LayOriFlag = ALONG_U, the layers all run parallel to axis u of the solid local basis, as illustrated in the left portion of fig. 1.
• If LayOriFlag = ALONG_V, the layers all run parallel to axis v of the solid local basis, as illustrated in the right portion of fig. 1.
3. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.

### Layer orientation angles

Because the materials can present anisotropic stiffness and strength properties, it is important to define the orientation of each layer accurately. Within each layer, the lay-up definition provides two angles, called βi and γi, which are used to determine the orientation of the material basis with respect to the global reference basis. The procedure by which the orientation of the material basis is determined based on two orientation angles, βi and γi, depends on flag BasisFlag, which can take two values. To simplify the writing, the subscript (.)i will be dropped: orientation angles βi and γi are simply referred to as angles β and γ.

#### BasisFlag = LOCAL

##### Figure 2. Orientation of the material basis using the local axes option (BasisFlag = LOCAL).

When BasisFlag = LOCAL, three bases are involved in the determination of the orientation of the material basis.

1. The global reference basis, I = (i1, i2, i3).
2. The solid local basis, U = (i1, u, v), which is determined by the surface associated with the solid element to which the present properties refer.
3. The material basis, E = (e1, e2, e3), which is defined by the material properties, MatPropName, assigned to the layer.

The orientation of the solid local basis, U, and of the two orientation angles, β and γ, are used to define the orientation of the material basis, E. A sequence of three planar rotations brings the global reference basis, I, to the material basis, E, as illustrated in fig. 2.

1. The first planar rotation is of magnitude α about unit vector i1 and brings the reference basis, I, to solid local basis U. Angle α is determined by the local geometry of the surface.
2. The second planar rotation is of magnitude β about unit vector i1 and brings the solid local basis, U, to basis B = (i1, b2, b3). Angle β is defined in the layer list. Because these first two planar rotations take place about the same unit vector, i1, they can be combined into a single planar rotation of magnitude (α + β) about unit vector i1.
3. The third planar rotation is of magnitude γ about unit vector b3 and brings basis B to the material basis E. Angle γ is defined in the layer list.

Note that positive angles β and γ correspond to positive rotations about axes i1 and b3, respectively, following the right-hand rule. If the layer is a transversely isotropic material such as a unidirectional layer of composite, angle β = 0 and angle γ corresponds to the fiber orientation angle.

#### BasisFlag = GLOBAL

##### Figure 3. Orientation of the material basis using the global axes option (BasisFlag = GLOBAL).

When BasisFlag = GLOBAL, two bases are involved in the determination of the orientation of the material basis.

1. The global reference basis, I = (i1, i2, i3).
2. The material basis, E = (e1, e2, e3), which is defined by the material properties, MatPropName, assigned to the layer.

The two orientation angles, β and γ define the orientation of the material basis, E. A sequence of two planar rotations brings the global reference basis, I, to the material basis, E, as illustrated in fig. 3.

1. The first planar rotation is of magnitude β about unit vector i1 and brings the reference basis,I, to basis B = (i1, b2, b3). Angle β is defined in the layer list.
2. The second planar rotation is of magnitude γ about unit vector b3 and brings basis B, to the material basis, E.

Note that positive angles β and γ correspond to positive rotations about axes i1 and b3, respectively, following the right-hand rule. It is important to note that in this scheme, the orientation of the material basis depends on angles β and γ only. The determination of the material basis orientation is independent of that of the solid local basis.