Abstract In this paper, the nonlinear response of indenter–foam dampers is characterized. Those dampers consist of indenters pressed on open-cell foams swollen with wetting liquids. Recently, the authors identified the dominant mechanism of damping in those dampers as poro-viscoelastic (PVE) relaxations as in articular cartilage, one of nature’s best solutions to vibration attenuation. Those previous works by the authors included dynamic mechanical analyses of the indenter–foam dampers under small vibrations, i.e., linear regime. The current study features the dynamic response of similar dampers under larger strains to investigate the nonlinear regime. In particular, the indenter–foam dampers tested in this paper consist of an open-cell polyurethane foam swollen with castor oil. Harmonic displacements are applied on the swollen and pre-compressed foam using a flat-ended cylindrical indenter. Measured forces and corresponding hysteresis (force–displacement) loops are then analyzed to quantify damping performance (via specific damping capacity) and nonlinearities (via harmonic ratio). The effects of strain and strain rates on the damping capacity and harmonic ratio are investigated experimentally. The dominant source of the nonlinearity is identified as peeling at the indenter–foam interface (and quantified via peeling index). A representative model consisting of a linear viscoelastic foam and rate-dependent adhesive interface (slider element with limiting adhesive strength) explains the observed trends in peeling and thus nonlinear dynamic response. Possible remedies to suppress those nonlinearities in future designs of indenter–foam dampers are also discussed.
more »
« less
Influence of Lateral Constraints on Wave Propagation in Finite Granular Crystals
Abstract In the presented work, wave dynamics of 2D finite granular crystals of polyurethane cylinders under low-velocity impact loading was investigated to gain better understanding of the influence of lateral constraints. The deformation of the individual grains in the granular crystals during the impact loading was recorded by a high-speed camera and digital image correlation (DIC) was used to calculate high fidelity kinematic and strain fields in each grain. These grain-scale kinematic and strain fields were utilized for the computation of the intergranular forces at each contact using a granular element method (GEM) based mathematical framework. Since the polyurethane were viscoelastic in nature, the viscoelasticity constitutive law was implemented in the GEM framework and it was shown that linear elasticity using the strain rate-dependent coefficient of elasticity is sufficient to use instead of a viscoelastic framework. These particle-scale kinematic and strain field measurements in conjunction with the interparticle forces also provided some interesting insight into the directional dependence of the wave scattering and attenuation in finite granular crystals. The directional nature of the wave propagation resulted in strong wave reflection from the walls. It was also noteworthy that the two reflected waves from the two opposite sidewalls result in destructive interference. These lateral constraints at different depths leads to significant differences in wave attenuation characteristics and the finite granular crystals can be divided into two regions: upper region, with exponential wave decay rate, and lower region, with higher decay rate.
more »
« less
- Award ID(s):
- 1845200
- NSF-PAR ID:
- 10157648
- Date Published:
- Journal Name:
- Journal of Applied Mechanics
- Volume:
- 87
- Issue:
- 7
- ISSN:
- 0021-8936
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)This paper is devoted to the development of a continuum theory for materials having granular microstructure and accounting for some dissipative phenomena like damage and plasticity. The continuum description is constructed by means of purely mechanical concepts, assuming expressions of elastic and dissipation energies as well as postulating a hemi-variational principle, without incorporating any additional postulate like flow rules. Granular micromechanics is connected kinematically to the continuum scale through Piola's ansatz. Mechanically meaningful objective kinematic descriptors aimed at accounting for grain-grain relative displacements in finite deformations are proposed. Karush-Kuhn-Tucker (KKT) type conditions, providing evolution equations for damage and plastic variables associated to grain-grain interactions, are derived solely from the fundamental postulates. Numerical experiments have been performed to investigate the applicability of the model. Cyclic loading-unloading histories have been considered to elucidate the material-hysteretic features of the continuum, which emerge from simple grain-grain interactions. We also assess the competition between damage and plasticity, each having an effect on the other. Further, the evolution of the load-free shape is shown not only to assess the plastic behavior, but also to make tangible the point that, in the proposed approach, plastic strain is found to be intrinsically compatible with the existence of a placement function.more » « less
-
more » « less
For many problems in science and engineering, it is necessary to describe the collective behavior of a very large number of grains. Complexity inherent in granular materials, whether due the variability of grain interactions or grain-scale morphological factors, requires modeling approaches that are both representative and tractable. In these cases, continuum modeling remains the most feasible approach; however, for such models to be representative, they must properly account for the granular nature of the material. The granular micromechanics approach has been shown to offer a way forward for linking the grain-scale behavior to the collective behavior of millions and billions of grains while keeping within the continuum framework. In this paper, an extended granular micromechanics approach is developed that leads to a micromorphic theory of degree n. This extended form aims at capturing the detailed grain-scale kinematics in disordered (mechanically or morphologically) granular media. To this end, additional continuum kinematic measures are introduced and related to the grain-pair relative motions. The need for enriched descriptions is justified through experimental measurements as well as results from simulations using discrete models. Stresses conjugate to the kinematic measures are then defined and related, through equivalence of deformation energy density, to forces conjugate to the measures of grain-pair relative motions. The kinetic energy density description for a continuum material point is also correspondingly enriched, and a variational approach is used to derive the governing equations of motion. By specifying a particular choice for degree n, abridged models of degrees 2 and 1 are derived, which are shown to further simplify to micro-polar or Cosserat-type and second-gradient models of granular materials.
-
null (Ed.)Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales — a nonlinear elastic length scale ℓ and a dissipation length scale ξ — that do not exist in Linear Elastic Fracture Mechanics (LEFM), the classical theory of cracks. In particular, it has been shown that at a propagation velocity v of about 90% of the shear wave-speed, cracks in 2D brittle materials undergo an oscillatory instability whose wavelength varies linearly with ℓ, and at larger loading levels (corresponding to yet higher propagation velocities), a tip-splitting instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the oscillatory instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit ℓ→0, with a wavelength determined by the dissipation length scale ξ. This result shows that the instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the phenomenological forms of the degradation functions assumed in the phase-field framework to describe the cohesive zone, and of the velocity-dependence of the fracture energy Γ(v) that is controlled by the dissipation time scale in the Ginzburg-Landau-type evolution equation for the phase-field. These results substantiate the universal nature of the oscillatory instability in 2D. In addition, we provide evidence indicating that the tip-splitting instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. The latter is sensitive to the wave-speed inside the dissipation zone, which can be systematically varied within the phase-field approach. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach, allowing its application in a broad range of materials failure problems.more » « less
-
ABSTRACT The work loop technique has provided key insights into in vivo muscle work and power during steady locomotion. However, for many animals and muscles, ex vivo experiments are not feasible. In addition, purely sinusoidal strain trajectories lack variations in strain rate that result from variable loading during locomotion. Therefore, it is useful to develop an ‘avatar’ approach in which in vivo strain and activation patterns from one muscle are replicated in ex vivo experiments on a readily available muscle from an established animal model. In the present study, we used mouse extensor digitorum longus (EDL) muscles in ex vivo experiments to investigate in vivo mechanics of the guinea fowl lateral gastrocnemius (LG) muscle during unsteady running on a treadmill with obstacle perturbations. In vivo strain trajectories from strides down from obstacle to treadmill, up from treadmill to obstacle, strides with no obstacle and sinusoidal strain trajectories at the same amplitude and frequency were used as inputs in work loop experiments. As expected, EDL forces produced with in vivo strain trajectories were more similar to in vivo LG forces (R2=0.58–0.94) than were forces produced with the sinusoidal trajectory (average R2=0.045). Given the same stimulation, in vivo strain trajectories produced work loops that showed a shift in function from more positive work during strides up from treadmill to obstacle to less positive work in strides down from obstacle to treadmill. Stimulation, strain trajectory and their interaction had significant effects on all work loop variables, with the interaction having the largest effect on peak force and work per cycle. These results support the theory that muscle is an active material whose viscoelastic properties are tuned by activation, and which produces forces in response to deformations of length associated with time-varying loads.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4047004
