Ugo Galvanetto

NUMERICAL HOMOGENIZATION OF PERIODIC COMPOSITE MATERIALS WITH NON-LINEAR MATERIAL COMPONENTS

In this paper a numerically developed homogenized constitutive relation for the global behaviour of periodic composite materials with elasto-plastic components is derived. The algorithm presented is general and can be applied to any kind of non-linear material behaviour respecting the complementarity rule. The method, different from those presented in the literature, is currently restricted to small strains, plane problems and monotonic proportional loading conditions. Copyright

Crack propagation with adaptive grid refinement in 2D peridynamics

The most common technique for the numerical implementation of peridynamic theory is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon. As a consequence of that computational resources may not be used efficiently. The present work proposes adaptive refinement algorithms for 2D peridynamic grids. That is an essential component to generate a concurrent multiscale model within a unified approach. Adaptive grid refinement is here applied to the study of dynamic crack propagation in two dimensional brittle materials. Refinement is activated by using a new trigger concept based on the damage state of the material, coupled with the more traditional energy based trigger, already proposed in the literature. We present as well a method, to generate the nodes in the refined zone, which is suitable for an efficient numerical implementation. Moreover, strategies for the mitigation of spurious reflections and distortions of elastic waves due to the use of a non-uniform grid are presented. Finally several examples of crack propagation in planar problems are presented, they illustrate the potentialities of the proposed algorithms and the good agreement of the numerical results with experimental data.

Non-linear dynamics of multiple friction oscillators

This paper deals with the dynamics of multiple friction oscillators. In some particular cases, when the driving velocity is small, the dynamics of the systems can be described by low-dimensional discrete maps which allow all existing attractors and their basins of attraction to be detected. Moreover the maps allow the relevant Lyapunov exponents to be computed and the classical path following techniques to be applied. The complex dynamics of the systems is clearly illustrated.

Structural Damage Detection Based on Proper Orthogonal Decomposition : Experimental Verification

The present paper describes a new structural damage detection method based on the monitoring of vibrational properties of the structure. Sensors record the accelerations of several points of the structure. The recorded data are then used to compute the proper orthogonal modes. The comparison between the proper orthogonal modes of the undamaged structure and those of the damaged structure provides information on damage location. Experimental results are presented.

Computational techniques for nonlinear dynamics in multiple friction oscillators

This paper presents some numerical techniques used to investigate the nonlinear dynamics of a class of mechanical systems affected by dry friction forces. They allow for the exact detection of the points which separate slip phases from stick phases, in this way the correct dynamic equations are integrated during the different motion phases. Finally, a method is described to perform the numerical computation of the Lyapunov exponents in such non-smooth systems.

Effects of the presence of the body in helmet oblique impacts

The oblique impact methods of motorcycle helmet standards prescribe using an isolated headform. However, in accidents the presence of the body may influence impact responses of the head and helmet. In this study, the effects of the presence of the body, in helmet oblique impacts, are investigated. Using the Finite Element method, oblique impacts of a commercially available helmet, coupled with a model of the human body, are simulated. A comparison between full-body impacts and those performed with an isolated headform show that the presence of the body modifies the peak head rotational acceleration by up to 40%. In addition, it has a significant effect on head linear acceleration and the crushing distance of the helmets liner. To include the effect of the body on head rotational acceleration in headform impacts, modifying inertial properties of the headform is proposed. The modified inertial properties are determined for a severe and frequent impact configuration. The results of helmet impacts obtained by using the modified headform are in very good agreement with those of full-body impacts; this verifies the accuracy of the proposed method.

Stick-slip vibrations of a two degree-of-freedom geophysical fault model

This paper considers the behaviour of a two degree-of-freedom autonomous system with static and dynamic friction consisting of two blocks linked by springs on a moving belt. This system is the simplest model which has been used to simulate the dynamics of seismic faults. The friction force is assumed to be a decreasing function of the relative sliding velocity. The motion of the blocks is composed of a uniform stick motion, during which the divergence of the system is zero, and an accelerated slip motion, during which the divergence is positive. The mathematical model by definition concentrates the dissipation on the point where the slip motion ceases. It is assumed that slip occurs only in one direction. A three-dimensional Poincare map and a scalar single variable map are discussed which characterize the dynamics of the system in a simple way. The one-dimensional map can be used to diagnose the chaotic behaviour of the full system, and quantities, similar to Lyapunov exponents, can be easily calculated which provide information regarding the system-sensitive dependence on initial conditions. The system dynamics illustrate the idea of studying the earthquake generation mechanism as a chaotic phenomenon.

Examples of applications of the peridynamic theory to the solution of static equilibrium problems

Peridynamics is a recently proposed continuum theory based on a non local approach and formulated with integral equations. The theory is suitable for dealing with crack propagation in solid materials. The original peridynamic formulation regarded dynamic problems and was adapted to the static case mainly using a relaxation method by introducing a substantial amount of numerical damping in the time integration. In the present work the implementation of the theory within an implicit code for static crack propagation phenomena based on the Newton-Raphson method is presented and applied to several examples of static crack propagation equilibrium problems. Results obtained with the newly developed procedure are presented for various structural configurations, with different boundary and load conditions and quantitatively compared to published data.

Events Maps in a Stick-Slip System

This paper describes a one-dimensional map generated by a two degree-of-freedom mechanical system that undergoes self-sustained oscillations induced by dry friction. The iterated map allows a much simpler representation and a better understanding of some dynamic features of the system. Some applications of the map are illustrated and its behaviour is simulated by means of an analytically defined one-dimensional map. A method of reconstructing one-dimensional maps from experimental data from the system is introduced. The method uses cubic splines to approximate the iterated mappings. From a sequence of such time series the parameter dependent bifurcation behaviour is analysed by interpolating between the defined mappings. Similarities and differences between the bifurcation behaviour of the exact iterated mapping and the reconstructed mapping are discussed.

CORRECTORS IN A BEAM MODEL FOR UNIDIRECTIONAL COMPOSITES

Homogenization theory is applied to the elastic analysis of beams composed of many fibers parallel to the beam axis. We first analyze the microstructure of the beam to define the local perturbation of a global mean behavior, due to nonhomogeneity. We describe this perturbation using first- and second-order terms in the asymptotic expansion of displacements in the power series of the small parameter. As an example of application, we use this description in the derivation of a beam-type element for the analysis of beams with multiple parallelfibers. Independent shear rotations are included in the kinematics defining the global behavior of the beam. We quote the formula for the stiffness matrix of an equivalent homogeneous, Hermitian beam element, in which effective coefficients and local perturbations appear. The computational process is then illustrated on an example of a superconducting coil for a nuclear fusion device.