Material -- Element Frame

As already mentioned, in Fig. 2 the material-element frame is schematically shown. In this frame, the following base classes & objects are introduced:

• Class Element, which is an abstraction of a finite element. It declares common general services, provided by all elements. Derived classes are the base classes for specific analysis types (structural analysis, thermal analysis). They declare and implement necessary services for specific analysis.

• Integration point class & object: It is an abstraction for the integration point of the finite element. It maintains its coordinates and integration weight. Any integration point can generally contain any number of other integration points - called slaves. The Integration point containing slaves is called master. Slaves are, for example, introduced by a layered cross section model, where they represent integration points for each layer, or can be introduced at material model level, where they may represent, for example, micro-planes. Slave integration points are hidden from elements. The Integration point also contains associated material status (the reasons for introducing this feature will be explained later).

• Cross section class is an abstraction for cross section. Its main role is to hide from an element all details concerning the cross section description and implementation. By cross section description is meant, for example, an integral cross section model, layered cross section model or fibered model. Elements do not communicate directly with material, instead they always use a Cross Section interface, which performs all necessary integration over its volume and invokes necessary material class services². The Cross section interface, defined in terms of general functions, allows the use of any cross section model, even that added in the future, without modification of any code, because all cross section models implement the same interface.

• Material class is shown here. It represents base class for all constitutive models. Derived classes should be the base analysis-specific classes, which declare required analysis specific services (for example structural material class declares services for the stiffness computation and services for the real stress evaluation). Again, the material analysis specific interface, defined in terms of general services, allows the use of any material model, even that added in the future, without modifying any code, because all material models implement the same interface.

One of the most important goals, which have been formulated, is extensibility. In the case of extension of the material library, the analyst is facing a key problem. Every material model must store its unique history parameters for every related integration point. The amount, type, and meaning of these history variables vary for each material model. Therefore, it is not possible to efficiently match all needs and to reflect them in the integration point data structure. The suggested remedy is the following:

The Integration point class is equipped with the possibility to have associated a Material status class. When a new material model is implemented, the analyst has also to declare and implement a related material status derived from the base Material status class to this material model. This status contains all necessary history variables and data access and modification services. The Integration point provides services for inserting and accessing its related status. For every Integration point, the corresponding material creates unique copy of its related material status and associates it with that integration point. Because the Integration point is a compulsory parameter of all messages sent to any material model, the particular material model can access its related material status from the given Integration point, and therefore can access its history variables.

Figure 4: Element-material frame structure.

In Fig. 4, the material - element frame is depicted in more detail, although it is still simplified. A simple cross section model class hierarchy is shown there. There are two derived classes from the parent Cross Section class: Simple cross section class representing an integral cross section model and Layered cross section model class, representing a layered cross section model implementation. At the bottom, the hierarchies of the material model and the associated material status representations are indicated. The program flow for an element, requesting the computation of its real nodal forces is also indicated in Fig. 4. This is generally done by integrating real stresses at its integration points. For each Integration point it asks the Cross section model to compute real stresses at the given integration point. In this example, the Layered cross section uses the master-slave integration point principle. Each element integration point, here called master, contains its slaves, each representing one layer. These slave integration points are introduced by the cross section model, and are hidden to the element. For a given master integration point, the cross section model performs integration over cross section volume using slaves. Therefore each slave integration point, which is requested by the master, uses material model class services to compute real stresses for each corresponding layer, passing the slave integration point as a parameter. Then for each slave, the material model asks the given integration point for its associated status. Having obtained reference to it, the material model can access all its history variables through status services, and computes results.