Constrained and Shear Moduli for Finite Elements

The stress-strain matrix used in finite element analyses has been reformulated in terms of constrained and shear moduli. The new formulation partially uncouples shear and compression and is relatively independent of the relationships of elasticity. Simple hyperbolic functions have been proposed to define equivalent elastic compression and shear moduli for modeling nonlinear soil behavior. Straightforward procedures are provided to determine the parameters for the hyperbolic equations from conventional one-dimensional compression and simple shear tests. In some cases, compression and shear wave propagation velocities measured in situ may also be used. For compatibility with many existing nonlinear finite element programs, either secant or tangent moduli may be developed. Several examples are given for the determination of the hyperbolic parameters from actual soil test data.