 By Dettmar J.

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Extra resources for A Finite Element Implementation of Mooney-Rivlin's Strain Energy Function In Abaqus

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For example, in Figure 29, this is the case of the operators acting in SU' and SG2, which satisfy + + For generic cochains this property corresponds to and is expressed in terms of incidence matrices by Eq. (89). The corresponding property for differential operators is the (formal) adjointness of -grad and div, and of curl and -curl. The nondegenerate bilinear forms which put in duality the cochain spaces in Eq. (130) are, in the natural basis representation, G2) = ' j + j (where we have as(U', Q') = C~LT" -.

As anticipated in the Introduction, this in turn suggests the adoption of a discretization strategy in which what is intrinsically discrete is included as such in the model, and the discretization effort is focused on what remains. It must be said, however, that once the discretization error is brought into by the presence of the constitutive terms, it is the joint contribution of the approximation implied by the discretization of these terms and of our enforcing only a finite number of topological relations in place of the infinitely many that are implied by the corresponding physical law that shapes the actual discretization error.

FIGURE 24. Two adjacent cells have compatible orientation if they induce on the common face opposite orientations. The concept of induced orientation can be used to propagate the orientation of a p-cell to neighboring p-cells. 190 CLAUD10 MATTIUSSI 4. Chains Now that we know how to represent algebraically the cell complex, which discretizes the domain, we want to construct a machinery to represent generic parts of it. This means that we want to represent an assembly of cells, each with a given orientation and weight of our choice.