The External Stress–Strain Relation is a special type of material model where the computation of stress is delegated to external code which has been compiled into a shared library. External libraries must first be imported into an External Material feature under Global Definitions > Materials.

The External Stress–Strain Relation node is only available with some COMSOL products (see www.comsol.com/products/specifications/).

The Global coordinate system is selected by default. The Coordinate system list contains all applicable coordinate systems in the component. The coordinate system is used for interpreting directions of orthotropic and anisotropic material data and when stresses or strains are presented in a local system. The coordinate system must have orthonormal coordinate axes, and be defined in the material frame. Many of the possible subnodes inherit the coordinate system settings.

Select an External material from the list of compatible external materials added under Global Definitions > Materials. For a material to be compatible with this External Material model node, its Interface type must be set to a type whose required input quantities are all defined by this external material. Allowed required inputs include strain, the deformation gradient, as well as all standard model inputs.

Select a Formulation — From study step, Total Lagrangian, or Geometrically linear to set the kinematics of the deformation and the definition of strain. When From study step is selected, the study step controls the kinematics and the strain definition.

When From study step is selected, a total Lagrangian formulation for large strains is used when the Include geometric nonlinearity checkbox is selected in the study step. If the checkbox is not selected, the formulation is geometrically linear, with a small strain formulation.

To have full control of the formulation, select either Total Lagrangian, or Geometrically linear. When Total Lagrangian is selected, the physics will force the Include geometric nonlinearity checkbox in all study steps.

Select a Strain decomposition — Automatic, Additive, Logarithmic, or Multiplicative to decide how the inelastic deformations are treated. This option is not available when the formulation is set to Geometrically linear.

The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of the deformation gradient.

As a default, it is assumed that the transverse shear strains are zero. For a state of plane stress, this is true for an isotropic material, and for nonisotropic materials where the normal to the surface is a principal direction. If this is not the case, select the Transverse shear strains checkbox to store state variables also for the two transverse shear strains.

Select the Reduced integration checkbox to reduce the number of integration points used for the weak contribution in the material. Reduced integration give faster computations at the element level and help mitigate locking issues. However, reduced integration may also introduce numerical instabilities, which then require an additional stabilization term.

By default, the Reduced integration checkbox is cleared, except in interfaces designed for explicit dynamic analysis, where it is always selected.

Select a method for Hourglass stabilization — Automatic, Energy sampling, Hessian, Flanagan–Belytschko, Manual, or None to be used in combination with the reduced integration scheme.

The Automatic option selects the stabilization method and its properties based on the physics interface, space dimension, shape function type and order of the displacement field, and the study type.

For the Energy sampling, Hessian, and Flanagan–Belytschko methods, the hourglass stiffness can be scaled by specifying a stiffness multiplier fstb. This multiplier can be an expression of any parameter or variable in the model. This multiplier can be expressed as any parameter or variable in the model. However, to maintain computational efficiency, avoid expensive definitions such as nonlocal coupling operators.

For the hourglass stabilization methods, the stiffness is automatically adjusted during the solution process using an internal multiplier. This accounts for the effect of inelastic deformations, such as damage and plasticity. This correction can be disabled by setting Inelastic deformations to Ignore. Ignoring inelastic deformations may be necessary for scenarios like cyclic loading, where the hourglass stiffness could become too small during unloading. Alternatively, adjust the value for the Minimum stiffness multiplier., which acts as a lower bound for the hourglass stiffness, which is applied in addition to any expression entered for fstb.

For the Energy sampling method, the default stabilization uses an isotropic linear elastic potential. Set the Energy Sampling Potential to Hyperelastic for large deformations. When selected, a neo-Hookean potential is used for nonlinear strains, while linear strains use the linear elastic potential.

The Hessian method evaluates a weak contribution using the reduced integration order. For hexahedral mesh elements, this approach may not suppress all hourglass modes. In most cases, non-stabilized modes are suppressed by constraints adjacent to the domain, but if they are not, select Use full integration to increase the integration order of the stabilization equations to suppress all modes. The higher integration order will increase the computational cost of the stabilization method.

Select how to define Equivalent elastic constants — Automatic, or User defined. When Automatic is selected, the equivalent elastic constants are computed from the output of the external material. In some cases this may lead to unexpected results or expensive evaluations when used in for example contact conditions. It is possible to instead manually define the equivalent elastic constants by selecting the User defined option. When selected enter values for the equivalent bulk modulus Keq and the equivalent shear modulus Geq.

Physics tab with Solid Mechanics selected:

Physics tab with Membrane selected: