In this study, a framework for the multi-objective materials discovery based on Bayesian approaches is developed. The capabilities of the framework are demonstrated on an example case related to the discovery of precipitation strengthened NiTi shape memory alloys with up to three desired properties. In the presented case the framework is used to carry out an efficient search of the shape memory alloys with desired properties while minimizing the required number of computational experiments. The developed scheme features a Bayesian optimal experimental design process that operates in a closed loop. A Gaussian process regression model is utilized in the framework to emulate the response and uncertainty of the physical/computational data while the sequential exploration of the materials design space is carried out by using an optimal policy based on the expected hyper-volume improvement acquisition function. This scalar metric provides a measure of the utility of querying the materials design space at different locations, irrespective of the number of objectives in the performed task. The framework is deployed for the determination of the composition and microstructure of precipitation-strengthened NiTi shape memory alloys with desired properties, while the materials response as a function of microstructure is determined through a thermodynamically-consistent micromechanical model.

This work presents a three-dimensional constitutive model for shape memory alloys considering the TRansformation-Induced Plasticity (TRIP) as well as the Two-Way Shape Memory Effect (TWSME) through a large deformation framework. The presented logarithmic strain based model is able to capture the large strains and rotations exhibited by SMAs under general thermomechanical cycling. By using the martensitic volume fraction, transformation strain, internal stress, and TRIP strain tensors as internal state variables, the model is capable to capture the stress-dependent TRIP generation when SMAs are subjected to a multiaxial stress state, as well as the TWSME for thermomechanically trained SMAs under load-free conditions. A detailed implementation procedure of the proposed model is presented through a user-defined material subroutine within a finite element framework allowing for solving different Boundary Value Problems (BVPs). Comprehensive instruction on calibrating the model parameters as well as the derivation of continuum tangent stiffness matrix are also provided. In the end, the simulated cyclic pseudoelastic and actuation responses by the presented model for a wide range of SMA material systems under both uniaxial and multiaxial stress states are compared against experimental results to validate the proposed modeling capabilities.

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A thermo-mechanically coupled finite element (FE) for the simulation of multi-layered shape memory alloy (SMA) beams admitting large displacements and rotations (LDRs) is developed to capture the geometrically nonlinear effects which are present in many SMA applications. A generalized multi-field beam theory implementing a SMA constitutive model based on small strain theory, thermo-mechanically coupled governing equations and multi-field kinematic hypotheses combining first order shear deformation assumptions with a sixth order polynomial temperature field through the thickness of the beam section are extended to admit LDRs. The co-rotational formulation is adopted, where the motion of the beam is decomposed to rigid body motion and relative small deformation in the local frame. A new generalized multi-layered SMA FE is formulated. The nonlinear transient spatial discretized equations of motion of the SMA structure are synthesized and solved using the Newton–Raphson method combined with an implicit time integration scheme. Correlations of models incorporating the present beam FE with respective results of models incorporating plane stress SMA FEs, demonstrate excellent agreement of the predicted LDRs response, temperature and phase transformation fields, as well as, significant gains in computational time.

The proposed article describes the development of a new beam finite element for the coupled thermomechanical analysis of shape memory alloy actuators. The element is formulated, assuming coupled equilibrium equations for the thermoelastic stresses and thermal loads. Displacements and temperature are treated as internal degrees of freedom giving the ability to predict the coupled thermal–displacement response of a shape memory alloy beam. The constitutive shape memory alloy model of Lagoudas and coworkers is implemented in the formulation. A generalized beam theory is formulated assuming shear deformation with a cubic temperature field through the thickness. The new element is capable to simulate heat transfer phenomena, electric Joule heating as direct input, and heat convection effects. The coupling between mechanical and thermal equilibrium equations due to endothermic/exothermic martensitic transformation procedures is also included. Numerical results and evaluations of the developed beam element are presented for the thermomechanical response of shape memory alloy wire actuators and an adaptive strip subject to various types of applied thermal loading and heat convection conditions. The effect of coupling terms on the prediction of shape memory alloy actuator response is also evaluated.