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Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The popular elastic law of Fung that describes the non-linear stress-
strain behavior of soft biological tissues is extended into a viscoelastic material
model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a
three-dimensional constitutive model that is suitable for general analysis.
The model is derived in a configuration that differs from the current, or
spatial,...
We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement...
We prove the conical differentiability of the solution to a bone
remodeling contact rod model, for given data (applied loads and
rigid obstacle), with respect to small perturbations of the cross
section of the rod. The proof is based on the special structure of
the model, composed of a variational inequality coupled with an
ordinary differential equation with respect to time. This
structure enables the verification of the two following
fundamental results: the polyhedricity of a modified displacement
constraint...
Some foundational aspects of the constitutive theory of finite elasticity are considered in the case, regarded here as general, when internal kinematical constraints are imposed. The emphasis is on the algebraic-geometric structure induced by constraints. In particular, old and new examples of internal constraints are reviewed, and the material symmetry issue in the presence of constraints is discussed.
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