"3 Constitutive Behavior (p. 27-28)
3.1 The Materials Point of View
The description of any material behavior within a ?nite element simulation requires a clearly structured interface within an element formulation. As stated before in (2.36), in Sec. 2.6.4 and in (2.53), the (local) material behavior is respected and needed for at the integration points while the integration loop on element level. According to the presented modular structure of DAEdalon, we intend to de?ne any constitutive model by the function MATMOD, where the deformation gradient F and the history database is given as input and the material response is given out in terms of the stress tensor and the material (tangent) modulus.
In that sense, linear or nonlinear material behavior is treated in the same way. So, the user has all possibilities in de?ning any deformation measure as function of the deformation gradient F and the history and take care for the conjugated stress tensor and its derivative. Please note, that the overall convergence behavior of a ?nite element solution procedure depends dramatically on the right formulation of the stress response and its derivative in form of the material modulus.
3.1.1 Stress Response
Basically, one has the free choice in formulating the material behavior with respect to any con?guration. There are many discussions on that topic, each with advances and each with negative aspects, but the overlaying element formulation has to be respected to take care on the energy turn over expressed by the tensors given by the material model, see Sec. 2.4.
3.1.2 The Material Modulus
The crucial task in the formulation and assembly of Kmat in (2.53) is the representation of the derivative of the stress response with respect to the applied deformation measure in the algorithmic setting. We illustrate here the results of that procedure for two typical material behaviors, namely hyperelasticity in its simplest form and ?nite plasticity, in the following. Generally, we have a look on the structure and the implementation of typical representations of forth order tensors like."
|