Stabilized Finite Element Method for Solids With Large Gradient Mechanical Properties

Many polymers exhibit mechanical properties that vary greatly with temperature. The stress-strain relationships may include a tensile modulus that for certain temperature ranges decreases drastically. For instance, linear amorphous polymers have glassy-transition-rubbery-flow regions where the Young’s modulus is nearly constant in the glassy and rubbery plateau, but decreases rapidly with temperature in the transition and flow regions. To predict displacement of solids the finite element method (FEM) is often used. However, for structural problem with large variations of material properties the stability of the solution is affected negatively. In this work we formulate a sub-scale finite element formulation for thermal plasticity problems based on differential inclusions of elliptic and parabolic type.