•Time-modulation enables novel wave phenomena on subwavelength scales.•The modulated band structure is asymptotically described through a system of Hill equations.•The Hill equations generalize the ...discrete asymptotic approximation of static systems.•Dirac- and exceptional point degeneracies can be achieved through modulation.
In the field of metamaterials, many intriguing phenomena arise from having a structure which is periodic in space. In time-dependent structures, conceptually similar properties can arise, which nevertheless have fundamentally different physical implications. In this work, we study time-dependent systems in the context of subwavelength metamaterials. The main result is a capacitance matrix characterization of the band structure, which generalizes previous recent work on static subwavelength metamaterials. This characterization provides both theoretical insight and efficient numerical methods to compute the dispersion relationship of time-dependent structures. We exemplify this in several structures exhibiting interesting wave manipulation properties.
A simple procedure for measuring two independent material properties of a viscoelastic material is proposed. Poisson's ratio is directly measured using digital image correlation during dynamic ...viscoelasticity test. Therefore, the complex Poisson's ratio as well as the complex modulus is simultaneously obtained from same specimen under same condition. The effectiveness of the proposed method is demonstrated by measuring the material properties of a soft epoxy resin. The measurement example shows that the master curves of the time‐dependent Poisson's ratio as well as other material properties for the wide range of the reduced time can be obtained by the proposed procedure.
•Efficient machine learning RBF surrogates for large-scale uncertainty quantification.•Surrogates trained to replace the time integral of the energy release rate.•Uncertainty of multivariate problems ...with geometric, loading, and material variables.•RBF generalization capability successfully tested with thousands of Monte Carlo simulations.•Proposed RBF surrogates were significantly more accurate than response surface methods.•RBF surrogates accurately predicted long-tail distributions with relatively small training sets.
This paper proposes a machine learning strategy using radial basis function (RBF) as surrogate models for uncertainty quantification of age and time-dependent fracture mechanics problems. The RBF surrogate models are trained to replace the time-consuming evaluations of the mapping integral of the time-dependent energy release rate. The probabilistic problem considers input random variables of geometry, loading, and material parameters for a concrete plate section with the presence of an initial surface crack. The performance of the RBF surrogates was evaluated through cross-validation and Monte Carlo reference solutions that expensively evaluated the integrals. The results of mean square errors and the Kolmogorov-Smirnov goodness-of-fit tests on the predicted probability and cumulative density functions show that, the RBF surrogates reached good accuracy even for a small training set size, rather than second-order polynomial models which could reasonably perform only for bigger training set sizes. The RBF surrogates accurately predict even long-tail distributions for farther prediction times with relatively small training sets. The proposed RBF surrogate models presented the generalization capabilities to predict thousands of unseen data points from Monte Carlo simulations and successfully assess the uncertainty quantification of the time-dependent energy release rate.
The parallel between non-equilibrium dynamics in time-dependent systems and ``the eagle and the rat'' problem is explained, justifying the use of this problem as a metaphor.
Instrumented indentation is used to measure the complex modulus of highly plasticized polyvinyl chloride (HP-PVC) and four kinds of polyethylene over the frequency range of 1–50Hz. Over this range, ...the loss factor for the HP-PVC increases from 0.3 to 1, making this an ideal material for damping out noise and vibration. The storage moduli for the four polyethylene samples are ordered according to density, with the lowest-density material have the lowest storage modulus. Results for both storage modulus and loss factor compare well with published results obtained by dynamic mechanical analysis for nominally similar materials.
The dynamics of heterogeneous materials, like rocks and concrete, is complex. It includes such features as nonlinear elasticity, hysteresis, and long-time relaxation. This dynamics is very sensitive ...to microstructural changes and damage. The goal of this paper is to propose a physical model describing the longitudinal vibrations in heterogeneous material, and to develop a numerical strategy to solve the evolution equations. The theory relies on the coupling of two processes with radically different time scales: a fast process at the frequency of the excitation, governed by nonlinear elasticity and viscoelasticity, and a slow process, governed by the evolution of defects. The evolution equations are written as a nonlinear hyperbolic system with relaxation. A time-domain numerical scheme is developed, based on a splitting strategy. The features observed by numerical simulations show qualitative agreement with the features observed experimentally by Dynamic Acousto-Elastic Testing.
•Physical model relating ultrasonic experimental observations in complex nonlinear media.•Sound mathematical properties, combining nonlinear hyperbolic systems and relaxation terms.•Robust numerical methods.•Qualitative agreement with experiments.
State-of-the-art Additive Manufacturing processes such as three-dimensional (3D) inkjet printing are capable of producing geometrically complex multi-material components with integrated elastomeric ...features. Researchers and engineers seeking to exploit these capabilities must handle the complex mechanical behavior of inkjet-printed elastomers and expect a lack of suitable design examples. We address these obstacles using a pneumatic actuator as an application case. First, an inkjet-printable actuator design with elastomeric bellows structures is presented. While soft robotics research has brought forward several examples of inkjet-printed linear and bending bellows actuators, the rotary actuator described here advances into the still unexplored field of additively manufactured pneumatic lightweight robots with articulated joints. Second, we demonstrate that the complex structural behavior of the actuator’s elastomeric bellows structure can be predicted by Finite Element (FE) simulation. To this end, a suitable hyperviscoelastic material model was calibrated and compared to recently published models in a multiaxial-state-of-stress relaxation experiment. To verify the material model, Finite Element simulations of the actuator’s deformation behavior were conducted, and the results compared to those of corresponding experiments. The simulations presented here advance the materials science of inkjet-printed elastomers by demonstrating use of a hyperviscoelastic material model for estimating the deformation behavior of a prototypic robotic component. The results obtained contribute to the long-term goal of additively manufactured and pneumatically actuated lightweight robots.
A recent elasto-viscoplastic thixotropic model proposed by (de Souza Mendes in J. Non-Newton. Fluid Mech. 164:66–75,
2009
; de Souza Mendes in Soft Matter 7:2471–2483,
2011
) is applied to five ...benchmark problems: the flow in a lid cavity, the flow through an expansion followed by a contraction, the flow over a flat plate, the channel entry flow, and the flow around a cylinder confined between parallel plates. One of the main advantages of this approach is its ability to recover a model for elasto-viscoplastic materials in a smooth fashion, i.e., in the limit where the characteristic thixotropic time tends to zero. These problems are numerically solved using the finite element method, with a four-field GLS-type formulation. While the simplified version is applied to the first three problems, the full model including thixotropy is applied to the channel entry flow and the flow around the cylinder. The elasto-viscoplastic problems analyzed show that, in general, elasticity tends to inhibit yielding and is more concentrated in unyielded regions. The thixotropic effects analyzed show that the delay in the microstructure response of the material significantly alters the problem when compared to the pure elasto-viscoplastic counterpart.
Background
Although structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally ...graded viscoelastic structures.
Methods
In the present paper, a 2D boundary element formulation capable of modeling time-dependent functionally graded materials (FGM) is presented. A numerical implementation of the Somigliana identity in terms of the displacements is developed to solve 2D problems of the exponentially graded viscoelasticity. The FGM concept can be applied to various materials, for structural and functional purposes. In this model, only Green functions of the nonhomogeneous elastostatic problems are needed with material properties that vary continuously along a given dimension.
Results and Conclusions
Results reveal that the boundary element approach can successfully be employed for the present complicated problem for arbitrary time histories of the applied loads and arbitrary boundary conditions, without the need to use relaxation functions or mathematical transformations.
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