Theocharis Baxevanis

A macro-constitutive model for the deformation response of periodic rotating bistable auxetic surfaces is developed. Focus is placed on isotropic surfaces made of bistable hexagonal cells composed of six triangular units with two stable equilibrium states. Adopting a variational formulation, the effective stress–strain response is derived from a free-energy function expressed in terms of the invariants of the logarithmic strain. To address the mathematical ill-posedness and numerical artefacts—such as mesh sensitivity—arising from the double-well nature of the free energy, two regularization approaches are introduced: (i) a gradient-enhanced first invariant of the logarithmic strain and (ii) an artificial material rate dependency. Although neither regularization guarantees solution uniqueness, the former mitigates mesh sensitivity, while the latter improves the convergence behaviour of the nonlinear numerical scheme by promoting smooth temporal evolution of transition localization and enabling the system to overcome snap-backs induced by local non-proportional loading near transition fronts. The model is implemented using membrane/shell structural elements and plane stress continuum ones within the ABAQUS finite-element suite. Numerical simulations demonstrate the efficacy of the proposed formulation and its implementation.

An approach to infer mechanical properties of shape memory alloys (SMAs) from instrumented spherical indentation records of indenter tip loading force, P, versus the resultant indentation depth, h, during indentation loading and unloading is proposed. The approach is based on (i) a finite element (FE) model for describing the forward problem of determining the indentation response, i.e., the P−h curve, for a given set of SMA mechanical properties, (ii) a computationally efficient Gaussian process surrogate model to replace the costly FE one, and (iii) an iterative solution strategy, which approximates the unknown model parameters from an experimentally determined P−h record and their corresponding probability densities via a Bayesian inference framework and a Markov Chain Monte Carlo sampling strategy. The efficacy of the proposed approach is demonstrated using numerical experiments, i.e., indentation curves generated by evaluating the FE model at points in the parameter space.

Thermal expansion (TE) is inherent material property and a critical design parameter in applications in which dimensional stability and/or thermal fatigue resistance over a wide range of temperatures are required. Examples include high precision instruments, satellite antennas, and optical instruments. Metallic materials that undergo martensitic transformation have been recently shown to exhibit tailorable bulk TE due to the TE anisotropy of the low-crystallographic-symmetry martensite lattice. In these materials, the TE anisotropy of bulk polycrystals can be exploited through martensite variant "orientation" upon deformation processing. This work proposes a constitutive model for tailoring the anisotropic CTE in shape memory alloys (SMAs) during martensite variant texturing, which is validated against experimental data from NiTiPd. A description of the evolution of the anisotropic macroscopic thermal expansion (TE) tensor of bulk shape memory alloys (SMAs) during phase transformation and martensite (re)orientation is proposed. Given that the tailorability of the TE of SMAs originates from the crystallographic TE anisotropy of the low-crystallographic-symmetry martensite, the TE tensor is approximated by a function of the oriented martensite volume fraction and the orientation direction unitary tensor. The proposed model is validated against recent experiments on tailoring TE through martensite orientation in a NiTiPd high temperature SMA. In those experiments, the TE tensor component in the loading direction of NiTiPd in the martensite state was shown to decrease with increasing inelastic strain induced by uniaxial tensile loading. According to the model, the TE tensor components in the transverse to the loading directions decrease with increasing tensile inelastic strain.