3.1. Elements

PyFEM provides a comprehensive library of finite element formulations for structural and solid mechanics analysis. Elements define the kinematic assumptions, interpolation functions, and integration schemes that transform continuum mechanics equations into discrete algebraic systems.

3.1.1. Overview

Element types in PyFEM include:

Continuum elements: 2D, 3D, and axisymmetric solids for bulk materials
Structural elements: Beams, trusses, plates, and shells for slender members
Interface elements: Cohesive zone models for fracture and delamination
Special elements: Springs and other connectors

Each element type is implemented as a Python class that computes element stiffness matrices, internal forces, and output quantities. Elements are configured in the .pro input file and associated with specific element groups from the mesh.

3.1.2. Configuration in Input Files

Elements are defined by creating named element groups in the .pro file. Each group specifies the element type and its material properties:

input = "model.dat";

ContElem =
{
  type = "SmallStrainContinuum";

  material =
  {
    type = "PlaneStress";
    E    = 210.0e3;
    nu   = 0.3;
  };
};

solver =
{
  type = "NonlinearSolver";
  maxCycle = 50;
};

In this example:

ContElem is the element group name (must match a group in model.dat)
type specifies the element formulation
material defines the constitutive behavior
The mesh file model.dat assigns elements to groups

3.1.2.1. Multiple Element Groups

Complex models can combine different element types:

Solid =
{
  type = "SmallStrainContinuum";
  material = { type = "PlaneStress"; E = 210.0e3; nu = 0.3; };
};

Beam =
{
  type = "Beam";
  material = { type = "Isotropic"; E = 210.0e3; nu = 0.3; };
  A = 0.01;  # Cross-sectional area
  I = 8.33e-6;  # Moment of inertia
};

Interface =
{
  type = "Interface";
  material = { type = "XuNeedleman"; Tult = 10.0; Gc = 1.0; };
};

3.1.3. Element Categories

3.1.3.1. Continuum Elements

Solid continuum elements for bulk materials under small or finite strains. These elements use displacement-based formulations with material behavior defined by constitutive laws. Suitable for 2D plane stress/strain, 3D solids, and axisymmetric problems.

3.1.3.2. Shell and Plate Elements

Elements for thin-walled structures based on Kirchhoff or Reissner-Mindlin plate theory. These elements include shear-locking suppression (SLS) variants for improved performance with thin structures.

3.1.3.3. Beam and Rod Elements

One-dimensional structural elements for frames, trusses, and skeletal structures. Includes linear and geometrically nonlinear beam formulations (Timoshenko, Kirchhoff), truss elements, and spring connectors.

3.1.3.4. Other Elements

Special-purpose elements including interface elements for cohesive zone modeling, fracture mechanics, and delamination analysis. These elements use traction-separation laws to model progressive failure.

3.1.3.4.1. Interface