# Constitutive Models in FLAC3D and 3DEC

The basic mechanical constitutive models provided in FLAC3D and 3DEC are arranged into null, elastic, and plastic model groups:

A null material model is used to represent material that is removed or excavated.

The elastic, isotropic model provides the simplest representation of material behavior. This model is valid for homogeneous, isotropic, continuous materials that exhibit linear stress-strain behavior with no hysteresis on unloading.The elastic, orthotropic model represents material with three mutually perpendicular planes of elastic symmetry. For example, this model may simulate columnar basalt loaded below its strength limit.The elastic, transversely isotropic model gives the ability to simulate layered elastic media in which there are distinctly different elastic moduli in directions normal and parallel to the layers.

The Drucker-Prager plasticity model may be useful to model soft clays with low friction angles. However, this model is not generally recommended for application to geologic materials. It is included here mainly to permit comparison with other numerical program results.The Mohr-Coulomb model is the conventional model used to represent shear failure in soils and rocks. Vermeer and de Borst (1984), for example, report laboratory test results for sand and concrete that match well with the Mohr-Coulomb criterion.The ubiquitous-joint model is an anisotropic plasticity model that includes weak planes of specific orientation embedded in a Mohr-Coulomb solid.The ubiquitous-joint model is a model with a plane of weakness and with anisotropic elasticity.The strain-softening/hardening model allows representation of nonlinear material softening and hardening behavior based on prescribed variations of the Mohr-Coulomb model properties (i.e., cohesion, friction, dilation and tensile strength) as functions of the deviatoric plastic strain.The bilinear strain-softening/hardening ubiquitous-joint model allows representation of material softening and hardening behavior for the matrix and the weak plane based on prescribed variations of the ubiquitous-joint model properties (i.e., cohesion, friction, dilation, and tensile strength) as functions of deviatoric and tensile plastic strain. The variation of material strength properties with mean stress can also be taken into account by using the bilinear option.The double-yield model is intended to represent materials in which there may be significant irreversible compaction in addition to shear yielding, such as hydraulically placed backfill or lightly cemented granular material.The modified Cam-Clay model may be used to represent materials when the influence of volume change on bulk property and resistance to shear need to be taken into consideration, as in the case of soft clay.A Hoek-Brown model provides an alternative to the Hoek-Brown-PAC model with a stress-dependent plastic flow rule, described above. The model characterizes post-failure plastic flow by simple flow rule choices given in terms of a user-specified dilation angle. This model also contains a tensile strength limit similar to that used by the Mohr-Coulomb model. In addition, a factor-of-safety calculation based on the strength reduction method can be run with the Hoek-Brown model.The Hoek-Brown failure criterion characterizes the stress conditions that lead to failure in intact rock and rock masses. The failure surface is nonlinear and is based on the relation between the major and minor principal stresses. The model incorporates a plasticity flow rule that varies as a function of the confining stress level.

- Cap-Yield (CYSoil) model (FLAC3D only)
The cap-yield (CY) soil model provides a comprehensive representation of the nonlinear behavior of soils. The model includes frictional strain-hardening and softening shear behavior, an elliptic volumetric cap with strain-hardening behavior, and an elastic modulus function of plastic volumetric strain. The model allows a more realistic representation of the loading/unloading response of soils.

- Simplified CYSoil (CHSoil) model (FLAC3D only)
A simplified version of the CYSoil model, called the CHSoil model, offers built-in features including a friction-hardening law that uses hyperbolic model parameters as direct input, and a Mohr-Coulomb failure envelope with two built-in dilation laws.

- Plastic-Hardening (PH) model (FLAC3D only)
An elasto-plasticity model with shear and volumetric hardening.

- Swell model (FLAC3D only)
A Mohr-Coulomb elasto-plasticity model considering wetting-induced deformation.

- Mohr-Coulomb-Tension (MohrT) model (FLAC3D only)
A Mohr-Coulomb elasto-plasticity model with tensile strain crack tracking.

- Soft-Soil model (FLAC3D only)
A elasto-plastic model for soft soils with high compressibility.

- NorSand model (FLAC3D only)
A critical state model applicable to soils in which particle to particle interactions are controlled by contact forces and slips rather than bonds.

Other mechanical material models are provided with the optional features in FLAC3D: There are ten time-dependent creep constitutive models available in the creep model option for FLAC3D. Nine of these models are included with 3DEC.

In addition, there are several pore-pressure generation material models available in the dynamic analysis option in FLAC3D. The models are described in Dynamic Analysis.

There is also a modified version of the Drucker-Prager model that is provided to simulate the mechanical behavior associated with thermal hydration, called Hydration-Ducker-Prager model (FLAC3D only).

The source codes of most of the models are included in the “\pluginfiles\cmodels” sub-directory. Users can modify these models or create their own constitutive models as DLLs by following the procedures given in Writing New Constitutive Models. The list of user-defined models (UDMs) is at Itasca UDM Website.

Fluid and thermal constitutive models are also included in FLAC3D. Three fluid constitutive models are available. These models are described in Fluid-Mechanical Interaction. Four basic thermal constitutive models are provided. These models are described in Thermal Analysis. A thermal hydration model is also included.

The formulation of the basic mechanical models is addressed in general terms first in the section of Incremental Formulation. Separate discussions of the theoretical background and specific implementation for each model are then presented.

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