Elastic Models

Three elastic models are available in PISA: the linear elastic model, cross isotropic elastic model and non-linear hyperbolic model. The characteristic of an elastic model is that no yielding is considered in the model although non-linear elastic models can have limited strength and softening of modulus.

Linear Elastic Model
The linear elastic model is based on Hooke's law. The loading modulus and unloading modulus are the same for the model. For isotropic model, the behaviour of the material is governed by two material parameters. There are four material parameters for an elastic model, the elastic modulus E, Poisson's ratio n, bulk modulus K and shear modulus G; and only two are required to fully specify the material. In PISA, the elastic modulus and Poisson's Ratio are used.

Cross Isotropic Elastic Model
The cross isotropic elastic model is designed to model materials with different stiffnesses and strengths in different directions. It can model material with preferred direction of shearing, defined by a bedding angle q, in which the shearing resistance on the plane is drastically different than that in any other directions. For example, a clay shale material has weaker resistance on the bedding plane than in other directions across the bedding planes.

The model is basically an elastic model with different elastic moduli governing the deformation in the direction normal and tangent to the bedding plane. The model has limited strength on the bedding plane which is governed by the Mohr-Coulomb failure criterion.

Nonlinear Hyperbolic Elastic Model
The hyperbolic model was proposed by Duncan and Chang to analyze dam deformation. The parameters of the model can be determined from triaxial test results.