Giovanni Lancioni

Energy-based non-local plasticity models for deformation patterning, localization and fracture

This paper analyses the effect of the form of the plastic energy potential on the (heterogeneous) distribution of the deformation field in a simple setting where the key physical aspects of the phenomenon could easily be extracted. This phenomenon is addressed through two different (rate-dependent and rate-independent) non-local plasticity models, by numerically solving two distinct one-dimensional problems, where the plastic energy potential has different non-convex contributions leading to patterning of the deformation field in a shear problem, and localization, resulting ultimately in fracture, in a tensile problem. Analytical and numerical solutions provided by the two models are analysed, and they are compared with experimental observations for certain cases.

Forced Nonlinear Oscillations of a Semi-Infinite Beam Resting on a Unilateral Elastic Soil: Analytical and Numerical Solutions

The dynamics of a semi-infinite Euler-Bernoulli beam on unilateral elastic springs is investigated. The mechanical model is governed by a moving-boundary hyperbolic problem, which cannot be solved in closed form. Therefore, we look for approximated solutions following two different approaches. From the one side, approximate analytical solutions are obtained by means of perturbation techniques. On the other side, numerical solutions are determined by a self-made finite element algorithm. The analytical and numerical solutions are compared with each other, and the effects of the problem nonlinearity on the beam motion are analyzed. In particular, the superharmonics oscillations and the resonances are investigated in depth.

Rate-independent deformation patterning in crystal plasticity

Metal forming processes involve continuous strain path changes inducing plastic anisotropywhich could result in the failure of the material. It has been often observed that the formation andevolution of meso-scale dislocation microstructures under monotonic and non-proportional loading have substantial effect on the induced anisotropy. It is therefore quite crucial to study the microstructureevolution to understand the underlying physics of the macroscopic transient plastic behavior. In thiscontext the deformation patterning induced by the non-convex plastic energies is investigated in amulti-slip crystal plasticity framework. An incremental variational approach is followed, which resultsin a rate-independent model exhibiting a number of similarities to the rate-dependent formulationproposed in [Yalcinkaya, Brekelmans, Geers, Int. J. of Solids and Structures, 49, 2625-2636, 2012].However there is a pronounced difference in the dissipative character of the models. The influenceof the plastic potential on the evolution of dislocation microstructures is studied through a Landau-Devonshire double-well plastic potential. Numerical simulations are performed and the results arediscussed with respect to the observed microstructure evolution in metals.

Effects of Underground Cavities on the Frequency Spectrum of Seismic Shear Waves

A numerical method is proposed to study the scattering of seismic shear waves induced by the presence of underground cavities in homogeneous soils. The method is based on the superposition of two solutions: the solution of the free-wave propagation problem in a uniform half-space, easily determined analytically, and the solution of the wave scattering problem due to the cave presence, evaluated numerically by means of an ad hoc code implemented by using the ANSYS Parametric Design Language. In the two-dimensional setting, this technique is applied to the case of a single cave, placed at a certain depth from the ground level. The frequency spectrum of the seismic shear oscillation on the ground surface is determined for different dimensions and depths of the cave and compared with the spectrum registered without caves. The influence of the cave dimensions and depth on the spectrum amplification is analyzed and discussed.

Plastic Slip Patterns through Rate-Independent and Rate-Dependent Plasticity

Plastic deformation induces various types of dislocation microstructures at different length scales, which eventually results in a heterogeneous deformation field in metallic materials. Development of such structures manifests themselves as macroscopic hardening/softening response and plastic anisotropy during strain path changes, which is often observed during forming processes. In this paper we present two different non-local plasticity models based on non-convex potentials to simulate the intrinsic rate-dependent and rate-independent development of plastic slip patterns, which is the simplified mechanism for the intrinsic microstructure development. For the sake of mechanistic understanding, the formulation and the simulations will be conducted in one-dimension which does not exclude its extension to multi-dimensions resulting in a crystal plasticity framework.

The NSCD method to analyze the dynamics of ancient masonry churches under seismic loadings

The dynamics of a medieval church, the S. Maria in Portunos church, subjected to seismic loadings has been analyzed by using LMGC90, a distinct element code which implements the Non-Smooth Contact dynamics method. Since the contact between blocks is governed by the Signorinis impenetrability condition and the dry-friction Coulombs law, the church exhibits a discontinuous dynamics. The sliding motions of blocks are non-smooth functions of time. Numerical simulations are performed with the aim of investigating the influence of the friction coefficient and of the type of connections between adjacent walls on the response.

On the Performances of High-Order Absorbing Boundary Conditions for Progressive and Standing Waves

The performances of three different high order absorbing boundary conditions (ABCs) are investigated in the case of progressive and standing waves in a dispersive one-dimensional medium. Their accuracy is first analyzed with respect to the frequency of a single incident wave. Then they are submitted to a wave train characterized by a wide frequency spectrum, resulting from an impulsive force. The influence of both the order and the parameters of the ABCs on the accuracy is analyzed in detail.Copyright

Bond Behavior of FRCM Carbon Yarns Embedded in a Cementitious Matrix: Experimental and Numerical Results

The use of inorganic cement based composite systems, known as Fiber Reinforced Cementitious Matrix (FRCM), is a very promising technique for retrofitting and strengthening the existing masonry or concrete structures. The effectiveness of FRCM systems is strongly related to the interface bond between inorganic matrix and fabric reinforcement, and, since the major weakness is often located on this interface, the study of stress-transfer mechanisms between fibers and matrix becomes of fundamental importance.FRCM are usually reinforced with uni-directional or bi-directional fabrics consisting of multifilament yarns made of carbon, glass, basalt or PBO fibers, disposed along two orthogonal directions. The difficulty of the mortar to penetrate within the filaments that constitute the fabric yarns and the consequent non-homogeneous stress distribution through the yarn cross section makes difficult to access the characterization of the composite material. The use of polymer coatings on the fibers surface showed to enhance the bond strength of the interface between fibers and mortar and, as a consequence, to improve the mechanical performance of the composite. The coating does not allow the mortar to penetrate within the filaments while is able to improve the bond between the two materials and to increase the shear stress transfer capacity at the interface.An experimental session of several pull out tests on carbon yarns embedded in a cementitious matrix was carried out. Different embedded lengths have been analyzed, equal to 20, 30 and 50 mm. The carbon yarns object of this study were pre-impregnated with a flexible epoxy resin enhanced with a thin layer of quartz sand applied on the surface.A variational model was proposed to evaluate the pull-out behaviour and failure mechanisms of the system and to compare numerical results to the experimental outcomes. Evolution of fracture in the yarn-matrix system is determined by solving an incremental energy minimization problem, acting on an energy functional which account for brittle failure of matrix and yarn, and for debonding at the yarn-matrix interface. The model was able to accurately describe the three phases of the pull-out mechanism, depending on the embedded length.

Localized versus diffuse damage: A variational approach

A variational model based on incremental energy minimization is proposed to describe the evolution of damage in elastic materials. The model accounts for an elastic energy, depending on the damage variable, and for a damage energy, which has a local and a non-local term. The evolution of the displacement and damage fields, representing the problem unknowns, is determined by an incremental energy minimization problem, which is analytically solved in a special one-dimensional case, and numerically in a two-dimensional setting. By properly assigning the shapes of the elastic and damage energies, two different damage modes are reproduced: localized damage, consisting in a stress-softening process, in which damage forms in thin body portions and coalesces in fracture surfaces, and diffuse damage, which is characterized by a stress-hardening response, with damage spreading in large zones of the body. The former mechanism is typical of quasi-brittle materials, while the latter one is proper for ductile materials...

The variational theory of fracture: diffuse cohesive energy and elastic-plastic rupture

This communication anticipates some results of a work in progress [1], addressed to explore the efficiency of the diffuse cohesive energy model for describing the phenomena of fracture and yielding. A first local model is partially successful, but fails to reproduce the strain softening regime. A more robust non-local model, obtained by adding an energy term depending on the deformation gradient, describes many typical features of the inelastic response observed in experiments, including strain localization and necking. Fracture occurs as the result of extreme strain localization. The model predicts different fracture modes, brittle and ductile, depending on the analytical form of the cohesive energy function.