Oliver, "Modelling strong discontinuities in solid mechanics via strain softening constitutive equations
. Part 1: fundamentals," International Journal for Numerical Methods in Engineering, vol.
The non-Newtonian effects of the second-order fluids on the lubrication characteristics of inclined slider bearings is analyzed by considering the constitutive equations
proposed by Coleman and Noll .
The main tasks in establishing the constitutive equations
for geomaterials are the determination of stress-strain relations in principal stress/strain space and the coordinate transformation of the relationship from principal stress/strain space to general coordinate space.
Looking in turn at principles, steel, and other metals, they discuss such topics as techniques for modeling microstructure in metal forming processes, recrystallization and grain growth in hot working, modeling phase transformations in steel, determining unified constitutive equations
for modeling the hot forming of steel, and aging behavior and microstructure evolution in the processing of aluminum alloys.
However, it is difficult to obtain the precise orientation distribution function and also to include the orientation distribution function into constitutive equations
. For this purpose the alignment tensor is a better alternative.
In this section, governing and constitutive equations
that describe elasto-plastic deformation of solids, as well as discretization procedures in the context of FV formulation are briefly outlined.
In this case, the constitutive equations
General topics include benchmarks, material flow and constitutive equations
, microstructures, optimization, dies and tools.
One purpose of rubber testing is to determine parameters (constants and functions) in constitutive equations
. Such equations are used to represent hyper- and viscoelastic behavior of rubber for arbitrary strains or loading histories.
Papanastasiou  proposed an exponential modification to the viscoplastic constitutive equations
by introducing a material parameter known as the stress growth exponent.
Thickness integration of plane stress constitutive equations
has proven to be the method of choice for elastoplastic shell modeling.