Continuum models of shape memory alloys for simulations

Shape memory alloys can be used in a wide variety of applications that exploit their complex material behaviors. Computer simulations of complete structures using continuum material models are extremely valuable in design and applications, however due to the complexity of SMA behavior, few truly robust SMA continuum models have been developed and used in simulations. This dissertation analyzes a composite reinforced with SMA wires using a numerically implemented one-dimensional SMA model and also explores the development of a three-dimensional continuum SMA model.; A self-healing, metal matrix composite reinforced by shape memory alloy wires is simulated using finite element analysis. A one-dimensional constitutive model for SMA behavior is implemented as a user-defined truss element in ABAQUS. Loading causes a crack to propagate through the specimen as the SMA wires bridge the crack. Applied heat "heals" the crack by causing reverse transformation in the wires which shrink and bring the crack faces back together at a temperature where controlled partial melting can reweld the matrix.; A micromechanics based multivariant model is used as an aid in developing three-dimensional continuum SMA models that can model general reorientation. The multivariant model is shown to produce results that correspond closely to experimental data for reorientation tests. It is then used to create benchmark test cases for testing the continuum models and for motivating the form of the new models.; The continuum models developed here use the existing framework of a previously developed multi-dimensional model for phase transformation, but then determine the reorientation of martensite variants from a response that depends on the applied stress and the existing orientation strain. The "two-component" model shows the correct response for the basic test case, but proves inadequate for other load cases. An alternative formulation, the "strain exchange" model, is developed which also depends on the current stress. This model is able to simulate the response for the basic test case and calculate the correct directions for the strain changes of more complex cases.