Christian Licht

Thermomechanical couplings and pseudoelasticity of shape memory alloys

Abstract Energy balances of a polycrystalline CuZnAl Shape Memory Alloy are performed using infrared and calorimetric techniques. The experiments underline the main role of temperature variations induced by deformation process on the stress–strain curves. A thermodynamic analysis shows variations essentially due to the latent heat of phase change and indicates a very small intrinsic dissipated energy compared with deformation work or latent heat. On the basis of these results, a behaviour model that takes account of thermomechanical couplings is proposed. Implemented in a finite elements code, this model is used to verify the consistency and the potentialities of such an approach by means of numerical experiments.

Phenomenological Constitutive Equations for Numerical Simulations of SMA's Structures. Effects of Thermomechanical Couplings

Tension-compression tests at different room temperatures and at different strain rates have been performed on Shape Memory Alloys (CuZnAl, NiTi) using a thermomechanical device. The experiments underline the main role of the temperature variations induced by the deformation process on the stress-strain curves. These variations are essentially due to the latent heat of phase change and the analysis of the associated energy balances shows that the intrinsic dissipated energy remains very small compared to deformation work or latent heat of phase change. On the basis of these results, a behavioral model is proposed that assumes an intrinsic dissipation identically equal to zero and that considers anisothermal deformation processes. This model, written under the formalism of Generalized Standard Materials takes into account the thermoelastic couplings and considers two self-accommodating martensite variants. It is implemented in a finite element code realized to predict the effects of thermomechanical couplings. An implicit integration scheme is used to derive at each step in time the fields stress, strain, temperature, and volume proportions of phases. At each step and due to the thermomechanical coupling, we have to solve non-symmetric linear systems. Numerical simulations are shown first to verify the coherence with the experimental results obtained under uniaxial loading, and secondly to underline the practical interest of such an approach to design SMAs structures.

Variational limit of a one-dimensional discrete and statistically homogeneous system of material points

Abstract The energy of a discrete system of material points situated at random on a line and subjected to nearest-neighbor interactions, almost surely converges in a variational sense to a deterministic energy defined on spaces of functions with bounded variation.

Characterization of composite material properties using eigenstrain method

A technique to solve the periodic homogenization problem is described systematically in this work. The method is to solve the cell problems by imposing eigenstrains in terms of thermal or piezoelectric strain to the representative volume element. Homogenized coefficients are then calculated from stress solutions of those cell problems. Benefit of the proposed technique is that it is readily applicable for common finite element softwares regardless of using user subroutines. Several numerical examples are examined. The obtained results show good agreements with the published data.

A MATHEMATICAL MODEL FOR A PSEUDO-PLASTIC WELDING JOINT

An elementary situation in welding involves the perfect assembly of two adherents and a strong adhesive occupying a thin layer. The bulk energy density of the hyperelastic adherents grows superlinearly while that of the pseudo-plastic adhesive grows linearly with a stiffness of the order of the inverse of its thickness e. We propose a simplified but accurate model by studying the asymptotic behavior, when e goes to zero, through variational convergence methods: at the limit, the intermediate layer is replaced by a pseudo-plastic interface which allows cracks to appear.

Quinze Ans Après...

We aim to present mathematical models of smart devices and smart structures. Smart devices are made of materials which present significant multiphysical couplings. They are integrated in smart structures which take technological advantages of some multiphysical effects. We first propose simplified but accurate models of thin plates or slender rods made of piezoelectric or electromagneto-elastic materials in both static and dynamic cases. Then we focus on smart structures such as piezoelectric patches bonded on a linearly elastic body and piezoelectric junctions between two linearly piezoelectric or elastic bodies.

Mathematical Modelings of Some Smart Materials and Structures

Models of smart materials and structures are derived through rigorous mathematical methods. We establish a classification of piezoelectric and piezomagnetic crystalline materials and propose simplified but accurate models of thin structures made of piezoelectric or electromagneto-elastic materials.

Homogenization of Flat and Thin Linearly Elastic Masonries

Though rigorous mathematical arguments of variational convergence we identify the macroscopic behaviour of a flat wall made of a periodic distribution of blocks linked by a mortar of small stiffness. This asymptotic behaviour depends strongly on the relative behaviour of the parameters describing the masonry. We confine to a two-dimensional analysis in the framework of linearized elasticity.

Asymptotic Modelling of Linearly Piezoelectric Plates

Here, we rigorously derive a theory of linearly piezoelectric plates by studying the limit behaviour of a three-dimensional flat body as its thickness tends to zero. In the static case, two limit models appear depending essentially on the nature and the magnitude of the electromechanical loading. In the dynamic case, under the realistic quasi-electrostatic approximation, the limit behaviour depends further more on the relative magnitudes of the density and of the thickness of the plate. The transient problems can be formulated in term of evolution equation in Hilbert spaces of possible states with finite electromechanical energy, so that the studies of these transient problems are easily deduced from the static case trough the Trotter theory of convergence of semi-groups of operators acting on variable spaces.

Mathematical Modeling of Thin Multiphysical Structures

Smart materials, which present significant multiphysical couplings, are now widely used for the conception of smart structures whose mathematical modelings are here presented in the case of thin plates or slender rods made of piezoelectric or electromagneto-elastic materials.