The hardening behaviour of metals is generally described in terms of a stress‐strain curve derived from experiments. In this paper, a linear method to identify the stress‐strain curve starting from full‐field measurement data is presented. This method can be applied to any stress state using a generic yield function, the only requirement is that the full‐field measurement is extended up to the border of the specimen. The method is presented and validated using a finite element model of a notched specimen. Moreover, experiments were performed on specimens cut from a BH340 steel sheet to illustrate the viability to actual cases. Two geometries were considered, a standard uniaxial test, where the method was used to evaluate the post‐necking behaviour, and a notched specimen with a heterogeneous strain field. The proposed method, named linear stress‐strain curve identification (LSSCI), can be a useful tool in combination with inverse methods to identify the constitutive behaviour of metals in large strain plasticity.

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The Virtual Fields Method (VFM) is a well established inverse technique used to identify the constitutive parameters of material models using heterogeneous full-field strain data. When VFM is employed to retrieve the coefficients of advanced plasticity models, including non linear hardening and anisotropy, however, the procedure may become computationally intensive.

Stereo-DIC allows to track with a high accuracy the shape change and the surface displacement field of objects during deformation processes. When multiple camera arrangements are used, the shape and deformation measurement can be performed over the whole surface of the object. We submit that, in the case of intact specimens, with no internal defects and/or discontinuities, such boundary information can be used to estimate the internal displacement field by using proper interpolation functions. This calculation could serve, for instance, to evaluate the strain localization that occurs in metal specimens subjected to plastic deformation, hence allowing to get a better insight in the necking initiation and fracture propagation processes.In this paper, an interpolation method based on Bézier curves is developed and tested using simulated and real experiments on specimens with flat and cylindrical geometries. In particular, the deformation behaviour in the necking zone was investigated in the case of highly ductile and anisotropic materials. Numerical models were used to validate the method while the application to two real experiments demonstrated its feasibility in practi-

This article describes a numerical method to reconstruct the stress field starting from strain data in elastoplasticity. Usually, this reconstruction is performed using the radial return algorithm, commonly implemented also in finite element codes. However, that method requires iterations to converge and can bring to errors if applied to experimental strain data affected by noise. A different solution is proposed here, where an approximated numerical method is used to derive the stress from the strain data with no iterations. The method is general and can be applied to any plasticity model with a convex surface of the yield locus in nonproportional loading. The theoretical basis of the method is described and then it is implemented on two constitutive models of anisotropic plasticity, namely, Hill48 and Yld2000-2D. The accuracy of the proposed method and the advantage in terms of computational time with respect to the classical radial-return algorithm are discussed. The possibility of using such method to reconstruct the stress field in case of few temporal data and noisy strain fields is also investigated. K E Y W O R D Sintegration, large deformation, plasticity, solids INTRODUCTIONThe computation of stress from strain is a well-known problem in elastoplasticity. According to the adopted constitutive model, the stress depends on the strain history in a nonlinear way and, in general, a closed-form solution to obtain directly the stress from the strain does not exist. Since the integration of such elastoplastic constitutive equations is required, for instance, to implement plasticity models in finite element analysis (FEA), many numerical methods have been proposed during the years to solve efficaciously the problem. Most of the integration algorithms were developed during the 1980s although the first approach was already described by Wilkins 1 in 1964 who introduced the radial return algorithm. This method was further developed by other authors 2-4 and then extensively used in finite element applications. 5,6 The procedure is also referred to as the closest point projection method (CPPM) because it finds the closest point projection of the elastic predictor or trial stress to the yield surface. Several variations of the CPPM were developed 7,8 and extended to finite plasticity. 9 Another numerical method often used to integrate the stress is known as cutting-plane algorithm. 10 It does not require the evaluation of the second derivative of the plastic potential and is convenient when such derivation becomes complicated. 11 An in-depth description of various integration methods can be found in several books. [12][13][14] The above-mentioned algorithms are nowadays implemented in most commercial FE software. 3048

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Numerical simulations have become essential in engineering and manufacturing processes involving plasticity. The reliability and effectiveness of the simulations depend strongly on the accuracy of the adopted constitutive model. Accordingly, in recent years, an increasing interest is pointed towards experimental procedures and characterization methods that can be used to identify the constitutive parameters of advanced plasticity models, which allow to simulate properly the plastic behaviour of complex materials like, for instance, high strength steel. This paper provides a thorough review of the current stateof-the-art, looking at both academia and industry. The available methodologies can be subdivided in two main areas: quasi-homogeneous material tests with analytical or numerical post-treatment of the experimental data and heterogeneous tests coupled with inverse methods for parameter identification. For each method, a brief description and references to norms and articles is provided, illustrating the advantages and the disadvantages.

Shape Memory Polymers (SMPs) are materials capable of changing their primary shape to a secondary shape thanks to the so called Shape Memory Effect (SME) phenomenon. The shape-shifting is achieved through the action of an external stimulus, such as heat, electricity, pH, etc. In this paper, experiments on a thermally actuated thin film of a Shape Memory Thermoplastic Polyurethane (SMPU) were performed to calibrate the parameters of a constitutive model which accounts the rubbery/glassy phase transition mechanism behind the shape memory behaviour. In particular, thermomechanical uniaxial tensile tests have been carried out in order to the Young modulus and Poisson’s ratio above/under glass transition temperature and the fixity/recovery ratio. Additionally, the hydraulic bulge test (HBT) in a thermally controlled loading/unloading cycle was used to study the behaviour of the SME at large strains under equi-biaxial stress state. The corresponding outcomes were, therefore, employed to validate the results of the initial calibration by means of a Finite Element (FE) simulation of the HBT.