Constitutive Models: Relations between
Stress and Strain
Hooke’s Law Elastic Materials with Large Rotations
tensile specimen with length L and
cross-sectional area A is idealized
with a constitutive law that relates the material stress to the Lagrange strain by
E and are elastic constants. The specimen is subjected to a uniaxial
force P which induces an extension . Calculate the relationship between and ,
and compare the results with the predictions of a linear elastic constitutive
3.4.2. A thin walled tube with length L, radius a and wall
thickness t is subjected to a torque Q .
The tube can be idealized using the constitutive equation described in
the preceding problem. Assume that
during deformation plane sections of the tube remain plane, and that cross
sections of the tube rotate through and angle .
expression for the Lagrange strain in the specimen
Hence deduce an
expression for the material stress in the tube
Cauchy stress distribution
Hence, deduce an
expression relating the torque Q
to the tube’s twist . Compare the result with the predictions of a
simple linear elastic constitutive equation.
Check whether the
constitutive equation given in problem 3.4.1 satisfies the test for objectivity
described in Section 3.1.