Elements

Materials are attributes of any element, and are therefore independently applied. There is no concept therefore of a linear elastic element, or a plastic one.

Most importantly here is the definition of the element itself - only variational statement or formulation of the internal reaction. Such a distinct factorization of tasks ensures compatibility and robustness of implementation. Some examples are given below.

Mechanical elements

• Small deformation elements are available using either the initial configuration or in an updated form which integrates over the current time step volume (at the end of an increment). This element is available for all geometries, and all material behaviors with the "primal" variable of eto (symmetric small strain tensor), and "dual" variable sig (Cauchy stress).
• Plane stress Plane stress elements have an additional degree of freedom at each Gauss point for the eto33 strain component, which will be solved such that sig33=0. This increases the number of solution variables, but does not enlarge the front size appreciably so it is still computationally efficient. For single element solutions the cost is approximately 1.2, and diminishes as the problem size increases. the eps33 variable can also be set to a uniform value throughout a mesh to give generalized plane strain. This method furthermore allows very complex material laws to run in plane stress without modification.
• 2.5 D The 2.5 dimension elements in Zebulon have 6 degrees of freedom per node. These include 3 rotations. The material law is evaluated using 6 components of stress and strain.
• Total Lagrangian are available in a classical formulation.
• Total Lagrangian Incompressible elements are available with either penalty or mixed formulations, and have reduced interpolation for the volumetric dof.
• Updated Lagrangian Updated Lagrangian formulations are available. Material behaviors must be "modified" with a transformation layer which implements the transformation from a F-sig primal-duel variable to a E-S local material primal-dual couple. Integrated rotation (Jaumann) or polar decomposition based (Green-Naghdi) corotational formulations are available.

• Mindlin shell formulations in Zebulon are designed especially in the interest of being able to handle arbitrary material behaviors. For anisotropic behavior such as the single crystal, full 3D tensors (6 component) are required because even simple tension creates 3D strain (the graphic at right for example). The element employs a similar philosophy as the plane stress element to enforce the shell normal stress equal to zero. The shell also has a generalized section property, where any number of "elements" with any number of integration points can be assigned through the thickness.
  
• Springs Several spring formulations are available, with various "spring behaviors." One node springs are available which can apply a force against any displacement. with very low modulus, these "springs" are useful to stabilize free bodies before contact occurs.
• Periodic elements Periodic elements are available to apply mean states of mixed uniform strain or stress through a periodic geometry.
• Cosserat continuum The cosserat continuum is a higher order continuum where "micropolar" rotations exist and are correlated to alignment of material microstructures. Because the stress and strain tensors are not symmetric, special material behaviors are required. Currently elastic and classical plasticity is available, while a much broader class of materials are under development.
• Representative volume elements are special element formulations with the full strain tensor as degrees of freedom. The element is used in 1-element meshes as a means to simulate material behavior under mixed stress/strain state loading. Its functionality is similar to the simulation module, except it uses iterations to solve the system.

Other elements

• Thermal continuum Thermal elements are available with either stationary or transient solutions. The thermal heat flux and capacity term are determined from the thermal behavior selected, which can include anisotropic terms, phase change (latent heat), etc.
• Diffusion continuum is a classical diffusion element.
• Diffusion multi-variable with phase change is an element specially formulated for problems with phase change, and multiple diffusing variables. Diffusion DOFs are divided by solubility to allow discontinuities in C for phase boundaries.
• Viscous fluid (under development)