A nonlinear theory for fibre-reinforced magneto-elastic rods

We derive a model for the finite motion of a magneto-elastic rod reinforced with isotropic (spherical) or anisotropic (ellipsoidal) inclusions. The particles are assumed weakly and uniformly magnetised, rigid and firmly embedded into the elastomeric matrix. We deduce closed form expressions of the quasi-static motion of the rod in terms of the external magnetic field and of the body forces. The dependences of the motion on the shape of the inclusions, their orientation, their anisotropic magnetic properties and the Young modulus of the matrix are analysed and discussed. Two case studies are presented in which the rod is used as an actuator suspended in a cantilever configuration. This work can foster new applications in the field of soft-actuators

Experimental testing and nonlinear viscoelastic modeling of filled rubber

Owing to its unique physical properties, rubber plays a keyrole in countless industrial applications. Tires, vibration absorbers and shoe soles are only but a few of the myriad uses of natural and synthetic rubber in an industry which in 2009 had an estimated market value of 2 billion euro. Despite a peculiar internal structure, the macroscopic behavior of filled-rubber is reminiscent of several biological soft tissues. While rubber is internally constituted by flexible long chain molecules that intertwine with each other, a similar role is played, in soft-tissues, by collagen fiber bundles. As a consequence, both classes of materials are able to sustain large strains and exhibit the characteristics of a viscous fluid and an elastic solid. In industry, the requirement to model complex geometrical structures made of materials exhibiting a nonlinear constitutive behavior is a compelling reason to use Finite Element Analysis (FEA) software. The predictive capabilities of these numerical tools strongly rely upon the capabilities of the underlying model to describe the material’s rheological properties. The possibility of simulating accurately the material behavior over the entire working range avoids the use of excessive number of prototypes, thereby reducing the need for expensive and difficult experimental tests; consequently, development costs can be drastically reduced. The theory of viscoelasticity is crucial in describing materials, such as filled rubber, which exhibit time dependent stress-strain behavior. In many engineering applications, such as the estimate of the rolling resistance of tires and hysteretic losses in soft biological tissues, the energy dissipation is a primary feature to be predicted. In addition, in the usual operative range, tires, shock absorbers and other rubber components bear finite dynamic deformations. Therefore, a reliable constitutive equation must be assessed within the theory of nonlinear viscoelasticity. A review of the literature revealed significantly more well-established studies dealing with hyperelastic constitutive models, than those dealing with finite viscoelasticity. Over the years, many hyperelastic models able to describe all the relevant aspects of the quasi-static response have been introduced. Furthermore, the American norms (ASTM D412, ASTM D575, ASTM D945, ASTM D6147, ASTM D1456) establish all the experimental techniques to identify the material constitutive parameters. In this context, many authors have recently addressed the problem of finite amplitude wave propagation or focused their interest upon particular boundary value problems. On the other hand, there is a lack of well-established nonlinear viscoelastic models capable of describing all the relevant effects in the material response. Moreover, a standardization similar to that concerning the static norms is yet to be achieved. The usual methodology provides for small harmonic deformations superimposed on a large static displacement. However, such a prescription does not allow the capture of many of the relevant nonlinear phenomena. In the literature, experimental evidence concerning finite dynamic deformations is rarely reported

Effective filtering of modal curvatures for damage identification in beams

In this work, we investigate the effectiveness of a damage identification technique recently proposed in [1] and assess how it is affected by the number and position of the sensors used. Mode shapes and curvatures have been claimed to contain local information on damage and to be less sensitive to environmental variables than natural frequencies. It is known that notch-type damage produces a localized and sharp change in the curvature that unfortunately could be difficult to detect experimentally without the use of an adequate number of sensors. However, we have recently shown that even a coarse description of the modal curvature can still be employed to identify the damage, provided that it is used in combination with other modal quantities. Here, by exploiting the perturbative solution of the Euler-Bernoulli equation, we consider the inverse problem of damage localisation based on modal curvatures only and we ascertain the feasibility of their sole use for recostructing the damage shape. To do so, we set up a filtering procedure acting on modal curvatures which are expressed in a discrete form enabling further investigation on the effect of using a reduced number of measurement points. The sensitivity of the procedure to damage extension is further assessed

Torque-induced reorientation in active fibre-reinforced materials

We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli. The model is formulated in the framework of large strain hyperelasticity and the kinematics of the continuum is described by both a position vector and by a remodelling tensor which, in the present context, is an orthogonal tensor representing the fibre reorientation process. By imposing suitable thermodynamical restrictions on the constitutive equation, we obtain an evolution equation of the remodelling tensor governed by the Eshelby torque, whose stationary solutions are studied in absence of any external source terms. It is shown that the fibres reorient themselves in a configuration that minimises the elastic energy and get aligned along a direction that may or may not be of principal strain. The explicit analysis of the Hessian of the strain energy density allows us to discriminate among the stationary solutions, which ones are stable. Examples are given for passive reorientation processes driven by applied strains or external boundary tractions. % Applications of the proposed theory to biological tissues, nematic or magneto-electro active elastomers are foreseen.Comment: 23 pages, 4 figure

Non-affine fiber reorientation in finite inelasticity

This paper introduces a model for the mechanical response of anisotropic soft materials undergoing large inelastic deformations. The composite is constituted by a soft isotropic matrix reinforced with stiff fibres, that can evolve independently from each other. The constitutive equations are provided in terms of the free energy density and the dissipation density which are both required to be thermodynamically consistent and structurally frame-indifferent, i.e., they must be independent of a rotation overimposed on the natural state. This is in contrast to many of the currently used inelastic models for soft fiber-reinforced materials which do not deal with the lack of uniqueness of the natural state. A constraint between the inelastic spin of the matrix and the rotation spin of the fibre is introduced to fully determined the natural state. The resulting flow rules of the inelastic processes incorporate some typical scenarios including viscoelasticity and growth

A structurally frame-indifferent model for anisotropic visco-hyperelastic materials

One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed thoroughly and addressed by introducing a novel anisotropic remodelling equation compatible with the principle of structural frame indifference, a requirement that every inelastic theory based on the multiplicative decomposition of the deformation gradient must obey to. The evolution laws of the dissipative process are %obtained by introducing a novel (remodelling) balance equation which is completely determined by two scalar functions, the elastic strain energy and the dissipation densities. The proper choice of the dissipation function allows us to reduce the proposed model to the Ericksen anisotropic fluid, when deformation is sufficiently slow, or to the anisotropic hyperelastic solid for fast deformations. Finally, a few prototype examples are discussed to highlight the role of the relaxation times in the constitutive response.Comment: 43 pages,, 9 figure

Damage evolution and debonding in hybrid laminates with a cohesive interfacial law

The hybridisation of fibres reinforced laminates, i.e., the combined use of two or more families of fibres, is an effective technique to achieve a pseudo-ductile response and overcome the inherent brittleness which limits the wider use of composite materials. In this paper, a one-dimensional analytical model for unidirectional hybrid laminates is derived. The model considers two elastic–brittle layers bonded together by a cohesive elasto–plastic–brittle interface. This formulation is applied to the study of the debonding and fracture of laminates under uniaxial loading and the results compared to experiments available from the open literature. This study shows that the proposed model provides a close fit to the experimental data and it is able to match accurately the crack patterns seen in the experiments. The model predicts four different failure mechanisms and is able to discriminate among them according to the geometrical and mechanical properties of the layers

Fabrication and characterisation of short fibre reinforced elastomer composites for bending and twisting magnetic actuation

Polydimethylsiloxane (PDMS) films reinforced with short Nickel-coated Carbon Fibres (NiCF) were successfully fabricated, with the fibres aligned along different directions using an external magnetic field. The fibres were dispersed in the host matrix using sonication and mechanical mixing before being cured for 48 h in the magnetic field; thanks to the nickel functionalisation, the fibre orientation was achieved by a low intensity field (<0.2 T) which required an inexpensive experimental set-up. The main focus of this study was looking at the actuation potential of this magnetic composite material; successful actuation was achieved, showing its large displacement capability. The results confirm the presence of an instability controlled by the magnetic torque, as predicted by the introduced model. The composite films undergo a transition from a bending-only deformed configuration for the 0° fibre specimen, to a twisting-only configuration, achieved for fibres at 90°, whereas all the intermediate angles show both bending and twisting. This behaviour mirrors that which is used to propel a selection of marine mammals