Computational micro to macro transitions for shape memory alloy composites using periodic homogenization

Abstract

In the current manuscript, a homogenization framework is proposed for periodic composites with shape memory alloy (SMA) constituents under quasi-static thermomechanical conditions. The methodology is based on the step-by-step periodic homogenization, in which the macroscopic and the microscopic problems of the composite are solved simultaneously. The implementation of the framework is examined with numerical examples on SMA composite laminates. Complexity of the composite nonlinear response and non-proportional stress state in the SMA appears, even in the case of uniaxial macroscopic boundary conditions. Moreover, under certain conditions, the composite laminate can exhibit a non-convex transformation surface. Additionally, the transformation temperatures at various stress levels under isobaric thermal cycling can be quite different between the composite and the pure SMA.

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

“…Based on the individual behaviour of each single layer, the non-linear response of such multi-layered composite is simulated through a homogenisation scheme. Although the non-linear extension of the classical laminate theory is commonly used for this purpose (Berthelot, 1999;Perreux and Lazuardi, 2001), it is convenient to consider instead a scheme based on periodic homogenization (Chatzigeorgiou et al, 2015) It is proposed to identify, at first, the parameters related to the microcracks density evolution (21) and the anelasticity (26) in the transverse tension, namely, R 22 , S, β, γ ∞ c and a 22 . These parameters can be assessed through an incremental load/unload tensile test performed on a [90 o ] 16 laminated specimen (Figure 8a).…”

“…Such approach can be achieved using the concept of periodic homogenization (Chatzigeorgiou et al, 2015(Chatzigeorgiou et al, , 2016. …”

Three-dimensional FE2 method for the simulation of non-linear, rate-dependent response of composite structures

“…It has been demonstrated that the use of an incremental linearized temporal integration approach, there exist a semi-analytical solution for this problem [40]. This test case is utilized as a validation of the implementation of the FE 2 framework.…”

“…A last advantage of this approach is that it can be extended to predict the overall fully coupled thermomechanical response of 3D composite structures [45,40] with more complex mechanisms between fibres-matrix as interfacial damage mechanisms. Such fully-coupled analyses on multiscale structures should be of a high interest for industrial applications that are usually computed with commercial finite element analyses packages.…”

Deformation Mechanisms in NiTi-Al Composites Fabricated by Ultrasonic Additive Manufacturing

“…These embedding techniques are therefore above the A f temperature of SMAs and therefore do not permit the control of oriented martensite that is possible in the present work. A corresponding outcome is that few of the many modeling frameworks for the stress-temperature coupled response of SMA-reinforced composites [20][21][22][23][24] are applicable to capture the preprocessing of NiTi fibers as to reorient martensite, prior to insertion into the matrix. Figure 2 provides a qualitative description of the stresstemperature (r-T) response within the embedded fiber during heating/cooling of the composite.…”