Sonia Marfia

Modelling of SMA materials: Training and two way memory effects

Abstract The present work addresses a simple and effective one-dimensional model able to reproduce the superelastic behaviour as well as the shape memory effect. In particular, it considers the transformations from austenite to single variant martensite and from single variant martensite to austenite, taking into account the influence of the temperature. Moreover, the training and the two way memory effects are modelled considering the evolutions of the phase-transformation stress thresholds as well as of the residual “permanent” deformation. The time integration of the evolutive equations is performed adopting a backward Euler scheme and the finite time step is solved through a modified return-map algorithm. The proposed SMA constitutive law and numerical procedure are adopted to develop numerical applications. Finally, the ability of the model to reproduce experimental data is assessed.

Modeling of reinforced masonry elements

In this paper, a micromechanical investigation for the evaluation of the overall response of the masonry material reinforced by innovative composite materials is developed. The masonry is regarded as a heterogeneous medium realized by a regular arrangement of blocks into a matrix of mortar. A homogenization procedure is developed for a one-dimensional reinforced masonry problem, considering the progressive damage and plasticity of the mortar and the block. Moreover, the brittle failure of the fiber reinforced plastic reinforcement is accounted for. The delamination effect of the composite sheets from the masonry element is also modeled. A numerical procedure, based on the arc-length method with a backward-Euler integration of the evolutive equations, is developed to study the behavior of the reinforced masonry. Numerical applications regarding the axial and the bending response of the material are presented.

Superelastic and Shape Memory Effects in Laminated Shape-Memory-Alloy Beams

A simple shape-memory-alloy (SMA) model to simulate the superelastic behavior as well as the shape memory effect is proposed. It considers only the transformations from austenite to single-variant martensite and from single-variant martensite to austenite, taking into account the ine uence of the temperature in the constitutive relationship. The proposed SMA constitutive model is employed in a novel layerwise beam theory to develop new SMA beam e nite element models with suitable interpolation of the e eld variables involved. The e nite element models developed herein account for the time evolution SMA constitutive equations. In particular, the developed e nite elements treat the SMA material as reinforcement of elastic beams. Several applications are presented to assess the validity of the constitutive model and the proposed numerical procedure.

Micromechanics and homogenization of SMA-wire reinforced materials

The aim of the paper is to develop a micromechanical model for the evaluation of the overall constitutive behavior of a composite material obtained embedding SMA wires into an elastic matrix. A simplified thermomechanical model for the SMA inclusion, able to reproduce the superelastic as well as the shape memory effect, is proposed. It is based on two assumptions: the martensite volume fraction depends on the wire temperature and on only the normal stress acting in the fiber direction; the inelastic strain due to the phase transformations occurs along the fiber direction. The two introduced hypotheses can be justified by the fact that the normal stress in the fiber direction represents the main stress in the composite. The overall nonlinear behavior of long-fiber SMA composites is determined developing two homogenization procedures: one is based on the Eshelby dilute distribution theory, the other considers the periodicity conditions. Numerical applications are developed in order to study the thermomechanical behavior of the composite, influenced by the superelastic and shape memory effects occurring in the SMA wires. Comparisons of the results obtained adopting the two homogenization procedures are reported. The influence of the matrix stiffness and of a prestrain in the SMA wires on the overall behavior of the composites is investigated.

Numerical Procedure for Elasto-Plastic No-Tension Model

In the present work a generalization of the classical elastic no-tension model accounting for irreversible crushing strains is proposed. The model considers limited tensile and compressive strength; in particular, fracture strain arises when the tensile strength is reached, while plastic strain can be developed because of the limited compressive strength. As a consequence, inelastic strains are partitioned into the sum of a positive semi-definite fracture strain and a plastic (crushing) strain, which are both assumed to fulfill a normality rule. A numerical procedure, based on the backward Euler time-integration scheme, is proposed; the time step is solved adopting a strain driven predictor-corrector scheme. The consistent no-tension elastoplastic tangent is computed. Then, the model is implemented in a finite element code. Numerical applications, concerning the study of the behavior of some significative masonry structures, are presented.

Stress Analysis of Reinforced Masonry Arches

The paper deals with the modeling and the analysis of masonry arches reinforced with FRP materials. A nonlinear elastic model for the masonry material, characterized by no tensile capacity and limited strength in compression, is proposed; the FRP is modeled as a linear elastic material with brittle failure, considering a perfect adhesion between the masonry and the FRP reinforcement. A novel numerical procedure based on the stress approach of the structural problem, i.e. on the minimization of the complementary energy, is developed within a dual formulation of the arc-length continuation method. The proposed model and the developed numerical procedure are implemented in a computer code. Moreover, a new post-computation technique of the stresses at the FRP-masonry interface, based on a micromechanical analysis that takes into account the heterogeneity of the masonry material, is proposed. Numerical applications are developed to assess the model effectiveness and the efficiency of the numerical procedure. The results obtained using the proposed model and implemented procedure are put in comparison with the ones carried out considering an elasto-plastic masonry model implemented in a finite element procedure; finally, a comparison between numerical and experimental results is provided.

Modeling approaches for masonry structures

Different scale approaches, micromechanical, multiscale and macromechanical or phenomenological, are presented to study the structural response of masonry elements. First, a micromechanical model is introduced and the masonry is considered to be a heterogeneous material, made of mortar and bricks joined by interfaces, where the mortarbrick decohesion mechanisms occur. To this end, a special interface model combining damage and friction is proposed. Then, two multiscale procedures are presented, that consider regular arrangements of bricks and mortar, modeled by nonlinear constitutive laws which account for damage and friction effects. A homogenization technique is developed to derive two different equivalent continuum models at the macro-level, a micropolar Cosserat continuum and a nonlocal Cauchy model. Finally, a macromechanical model, based on the adoption of a classical No-Tension Material (NTM) model, and on the presence of irreversible crushing strains, is proposed. A zero tensile strength is assumed, thus fracture strains arise when the stress is zero. Moreover, an elastoplastic model is considered for the material response in compression. Numerical applications are performed on a masonry arch and two masonry panels, by adopting the three approaches presented. Comparisons with experimental outcomes, published elsewhere, are performed.

A fracture evolution procedure for cohesive materials

The present paper deals with the problem of the evaluation of the softening mechanical response of cohesive materials under tensile loading. A nonlinear fracture mechanics approach is adopted. A new numerical procedure is developed to study the evolution of the crack processes for 2D solids. The proposed algorithm is based on the derivation and use of the fracture resistance curve, i.e., the R-curve, and it takes into account the presence of the process zone at the crack tip. In fact, assuming a nonlinear constitutive law for the cohesive interface, the procedure is able to determine the R-curve, the process zone length and hence the mechanical response of any material and structure. Numerical applications are developed for studying the damage behavior of a infinite solid with a periodic crack distribution. Size effects are investigated and the ductile-brittle transition behavior for materials characterized by the same crack density is studied. The results obtained adopting the proposed procedure are in good accordance with the results recovered through nonlinear step by step finite element analyses. Moreover, the developed computations demonstrate that the procedure is simple and efficient.

Micromechanical analysis of porous SMA

The present paper deals with computational micromechanical analyses of porous shape memory alloy (SMA). Porous SMAs are considered composite materials made of a dense SMA matrix including voids. A three-dimensional constitutive law is presented for the dense SMA able to reproduce the pseudo-elastic as well as the shape memory effects and, moreover, to account for the different elastic properties of the austenite and martensite phases. Furthermore, a numerical procedure is developed and the overall behavior of the porous SMA is recovered studying a representative volume element. Comparisons between the numerical results, recovered using the proposed modeling, and experimental data available in the literature are presented. The case of closed and open porosity is investigated. Parametric studies have been conducted in order to investigate the influence of the porosity, the shape and orientation of the pores on the overall mechanical response and, mainly, on the energy absorption dissipation capability.

Response of porous SMA: a micromechanical study

Lately porous shape memory alloys (SMA) have attracted great interest as low weight materials characterized by high energy dissipation capability. In the present contribution a micromechanical study of porous SMA is proposed, introducing the simplifying hypothesis of periodic distribution of voids. The mechanical response of the heterogeneous porous medium is derived by performing nonlinear finite element micromechanical analyses considering a typical repetitive unit cell made of a circular hole in a dense SMA matrix and prescribing suitable periodicity and continuity conditions. The constitutive behavior and the dissipation energy capability of the porous Nitinol are examined for several porosity levels. Numerical applications are performed in order to test the ability of the proposed procedure to well capture the overall behavior and the key features of the special heterogeneous material.