Analysis of Shape Memory Alloy Components Using Beam, Shell, and Continuum Finite Elements

This work discusses the increased capabilities of a three-dimensional analysis tool for shape memory alloy engineering components. As the number and complexity of proposed SMA applications increases, engineers and designers must seek out or develop more capable predictive methods. Three-dimensional models implemented in a continuum finite element analysis (FEA) framework can be applied to most SMA component geometries. However, such methods may require fine meshes in 3-D space, resulting in many degrees of freedom and potentially long analysis times. On the other hand, constitutive models implemented in one dimension can be simple and fast, but are restricted to a limited class of problems for which such reductions are appropriate (e.g., rods and beams). More recently, engineers have begun investigating more complex SMA bending components for which 2-D shell elements might provide a computationally efficient FEA discretization. Here we consider a single modeling tool (a material subroutine) that combines 1-D, 2-D, and 3-D implementations for use in a general FEA framework. As an example analysis case, we consider an SMA bending element that has been adhesively bonded to a carbon fiber-reinforced polymer (CFRP) laminate and is subjected to thermally-induced actuation. The active SMA and passive composite components are bonded in a pre-stressed configuration such that the elastic laminate provides a variable restoring force to the SMA during transformation, resulting in repeatable actuation cycles. This two-part bonded configuration is analyzed using different types of finite elements (1-D beam, 2-D shell, and full 3-D continuum elements). The constitutive behavior of the shape memory alloy is defined using an established three-dimensional model based on continuum thermodynamics and motivated by the methods of classical plasticity. A user material subroutine (UMAT) in an Abaqus Unified FEA framework is used to implement the model. The methodology for capturing 1-D, 2-D, and 3-D thermomechanical response in a single such UMAT is described. The run times of the various analyses are compared, and the relative accuracies of the results are discussed.