Investigation of the role of Ti oxide layer in the size-dependent superelasticity of NiTi pillars: Modeling and simulation

Recent compression tests of NiTi pillars of a wide range of diameters have shown significant size dependency in the strain recovered upon unloading. In this paper, we propose a numerical model supporting the previously proposed explanation that the external Ti oxide layer may be responsible for the loss of superelasticity in the small pillars. The shape memory alloy at the center of the pillar is described using a nonlocal superelastic model, whereas the Ti oxide layer is modeled as elastoplastic. Voigt average analysis and finite element calculations are compared to experiments for the available range of pillar sizes. The simulation results also suggest a size-dependent strain hardening due to the constraint on the phase transformation effected by the confining Ti oxide layer.United States. Army Research Office (DAAD-19–02-D-0002

Upscaling from Atomistic Models to Higher Order Gradient Continuum Models for Crystalline Solids

In this work a new upscaling scheme for the derivation of a continuum mechanical model from an atomistic model for crystalline solids is developed. The scheme, called the inner expansion technique, is based on a Taylor series expansion of the deformation function and leads to a continuum mechanical model which involves higher order derivatives. It provides an approximation of the atomistic model within the quasi-continuum regime and allows to capture the microscopic material properties and the discreteness effects of the underlying atomistic system up to an arbitrary order. The quality of approximation is investigated for the model problem of an atomic chain with different types of potentials, including many-body potentials. The outcome of the inner expansion technique is numerically compared to other upscaling techniques, namely the classical thermodynamic limit and the direct expansion technique. It is shown that our technique carries over certain properties such as convexity from the atomistic to the continuum mechanical level, which results in well-posed problems on the continuum mechanical level. Furthermore, macroscopic approximation techniques are discussed to reduce the complexity of the continuum model. The upscaling technique is applied to the Stillinger-Weber potential for crystalline silicon and to the potential given by the Embedded-Atom Method (EAM) for shape memory alloys (SMA). Numerical simulations of the dynamic response of a silicon crystal and of one-way and two-way SMA micro-actuators are performed

PDE and Materials

This workshop brought together mathematicians, physicists and material to discuss emerging applications of mathematics in materials science

Data driven problems in elasticity

We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of ap- proximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.Comment: Result now covers the two well problem in full generality. Proof simplified. New Figure 9 illustrates geometry of separatio

Review and Perspectives: Shape Memory Alloy Composite Systems

Following their discovery in the early 60's, there has been a continuous quest for ways to take advantage of the extraordinary properties of shape memory alloys (SMAs). These intermetallic alloys can be extremely compliant while retaining the strength of metals and can convert thermal energy to mechanical work. The unique properties of SMAs result from a reversible difussionless solid-to-solid phase transformation from austenite to martensite. The integration of SMAs into composite structures has resulted in many benefits, which include actuation, vibration control, damping, sensing, and self-healing. However, despite substantial research in this area, a comparable adoption of SMA composites by industry has not yet been realized. This discrepancy between academic research and commercial interest is largely associated with the material complexity that includes strong thermomechanical coupling, large inelastic deformations, and variable thermoelastic properties. Nonetheless, as SMAs are becoming increasingly accepted in engineering applications, a similar trend for SMA composites is expected in aerospace, automotive, and energy conversion and storage related applications. In an effort to aid in this endeavor, a comprehensive overview of advances with regard to SMA composites and devices utilizing them is pursued in this paper. Emphasis is placed on identifying the characteristic responses and properties of these material systems as well as on comparing the various modeling methodologies for describing their response. Furthermore, the paper concludes with a discussion of future research efforts that may have the greatest impact on promoting the development of SMA composites and their implementation in multifunctional structures