Biomedical Engineering Reference
In-Depth Information
6.5
Conclusions
Continuummechanical approaches are an important tool to model the mechanical
behavior of trabecular bone. The first part of this chapter summarized the common
approaches based on generalized Hooke's law in its different forms under sym-
metry considerations. The second part of the continuum mechanical approaches
introduced basic ideas for yield and failure surfaces. The major intention of this
part was to collect some kind of basic understanding, which can be extended
to more complex approaches, for example, in the form of anisotropic yield or
failure criteria. The derived and applied constitutive equations can be used in the
scope of the finite element method or any other numerical approximation method
to simulate the macroscopic behavior. However, it may turn out that a derived
constitutive equation is not available in a commercial code. Thus, such laws must
be implemented based on user-subroutines. Respective approaches for the imple-
mentation, that is, integration of the constitutive equations, may be found in the
textbooks on nonlinear finite element analysis by Simo and Hughes [12], Crisfield
[59, 60], and Belytschko
et al
. [61]. In the second part of this chapter, classical model
approaches were introduced. Despite more and more powerful numerical tools and
computer hardware, these simple models still remain attractive. Such models allow
the derivation of the basic structure of constitutive equations without given exact
predictions of the involved material constants. However, such material constants
may be obtained from basic mechanical tests such as the uniaxial tensile or pure
shear test.
References
1.
Chen, W.F. (1982)
Plasticity in Reinforced
Concrete
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2.
Chen, W.F. and Saleeb, A.F. (1982)
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,
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Chen, W.F. and Baladi, G.Y. (1985)
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Hayes, W.C. and Carter, D.R. (1976)
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Reilly, D.T. and Burstein, A.H. (1974)
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Simo, J.C. and Hughes, T.J.R.
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Chen, W.F. and Han, D.J. (1988)
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William, K.J. (2001) Constitutive models
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Betten, J. (2001)
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