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This paper studies the dynamic deployment of cylindrical thin-shell structures with open cross section, attached to a rigid base. The structures are elastically folded and then released. Previous experiments have shown that the total energy decreases while a fold moves back and forth along the structure, which was explained in terms of energy losses related to the fold "bouncing" against the boundary. This paper uses a rigorous numerical simulation, based on an in-house isogeometric shell finite element code that simultaneously eliminates shear locking and hourglassing without any intrinsic energy dissipation, to show that the total energy of the system is conserved during deployment. The discrepancy with the previous results is explained by showing that energy transfers from low-frequency, "rigid body" modes, to higher frequency modes. [ABSTRACT FROM AUTHOR]

This paper has revisited the roof deformation and collapse of stamps with isolated grooves based on a contact mechanics approach, with emphasis on establishing the nonadhesive and adhesive contact solutions for surfaces containing a shallow rectangular groove with the effects of applied load and interfacial adhesion taken into account. By solving singular integral equations and using the energy release rate approach, closed-form solutions are derived analytically for the deformed groove shapes, interfacial stress distributions, and equilibrium relations between load and contact size, which reduce to the previously proposed solutions without adhesion or without applied load. Finite element (FE) analysis is performed to validate the nonadhesion solutions, while experiment results of stamp collapse reported in the literature are adopted to examine the adhesion solutions. By introducing the Johnson parameter a to represent a competition between surface energy and elastic strain energy of the groove, four kinds of contact behaviors of the groove roof can be characterized appropriately: nonadhesion, weak adhesion, intermediate adhesion, and strong adhesion. Hysteresis loop and energy loss due to distinct load/unloading paths are revealed in the cases of intermediate and strong adhesion. We have also provided the critical applied pressure to achieve roof collapse and the corresponding equilibrium contact size for full range of a. [ABSTRACT FROM AUTHOR]

Dielectric elastomers (DEs) are a class of highly deformable electroactive polymers (EAPs) employed for electromechanical transduction technology. When electrostatically actuated dielectric elastomer actuators (DEAs) are subjected to an input signal comprising multiple Heaviside voltage steps, the emerging inherent residual vibrations may limit their motion accuracy in practical applications. In this paper, the systematic development of a command-shaping scheme is proposed for controlling residual vibrations in an electrically driven planar DEA. The proposed scheme relies on invoking the force balance at the point of maximum lateral stretch in an oscillation cycle to bring the actuator to a stagnation state followed by the application of an additional electric input signal of predetermined magnitude at a specific time. The underlying concept of the proposed control scheme is articulated for a single Heaviside step input-driven actuator and further extended to the actuator subjected to the multistep input signal. The equation governing the dynamic motion of the actuator is derived using the principle of virtual work. The devised dynamic model of the actuator incorporates the effects of strain stiffening of elastomer and viscous energy dissipation. The nonlinear dynamic governing equation is solved using matlab ode solver for extracting the dynamic response of the actuator. The applicability of the devised command-shaping control scheme is illustrated by taking a wide range of parameters including variations in the extent of equilibrium state sequences, damping, and polymer chain extensibility. The proposed scheme is found to be adaptable in controlling the vibrations of the actuator for any desired equilibrium state. The results presented in this paper can find its potential application in the design of an open-loop control system for DEAs. [ABSTRACT FROM AUTHOR]

Capture of a prey by spider orb webs is a dynamic process with energy dissipation. The dynamic response of spider orb webs under prey impact requires a multi-scale modeling by considering the material microstructures and the assembly of spider silks in the macro-scale. To better understand the prey capture process, this paper addresses a multi-scale approach to uncover the underlying energy dissipation mechanisms. Simulation results show that the microstructures of spider dragline silk play a significant role on energy absorption during prey capture. The alteration of the microstructures, material internal friction, and plastic deformation lead to energy dissipation, which is called material damping. In addition to the material damping in the micro-scale modeling, the energy dissipation due to drag force on the prey is also taken into consideration in the macro-scale modeling. The results indicate that aerodynamic drag, i.e., aero-damping, plays a significant role when the prey size is larger than a critical size. [ABSTRACT FROM AUTHOR]

Fracture of polymer gels is often time- and rate-dependent. Subject to a constant load, a gel specimen may fracture immediately or after a delay (time-dependent, delayed fracture). When a crack grows in a gel, the fracture energy may depend on the crack speed (rate-dependent). The underlying mechanisms for the time- and rate-dependent fracture of gels could include local molecular processes, polymer viscoelasticity, and solvent diffusion coupled with deformation (poroelasticity). This paper focuses on the effects of poroelasticity. A path-independent, modified J-integral approach is adopted to define the crack-tip energy release rate as the energetic driving force for crack growth in gels, taking into account the energy dissipation by solvent diffusion. For a stationary crack, the energy release rate is time-dependent, with which delayed fracture can be predicted based on a Griffith-like fracture criterion. For steady-state crack growth in a long-strip specimen, the energy release rate is a function of the crack speed, with rate-dependent poroelastic toughening. With a poroelastic cohesive zone model, solvent diffusion within the cohesive zone leads to significantly enhanced poroelastic toughening as the crack speed increases, rendering a rate-dependent traction-separation relation. While most of the results are based on a linear poroelastic formulation, future studies may extend to nonlinear theories with large deformation. In addition to the poroelastic effects, other mechanisms such as viscoelasticity and local fracture processes should be studied to further understand the time and rate-dependent fracture of polymer gels. [ABSTRACT FROM AUTHOR]

This paper presents a new energy dissipation system composed of multistable cosine-curved domes (CCD) connected in series. The system exhibits multiple consecutive snap-through and snap-back buckling behavior with a hysteretic response. The response of the CCDs is within the elastic regime and hence the system's original configuration is fully recoverable. Numerical studies and experimental tests were conducted on the geometric properties of the individual CCD units and their number in the system to examine the force-displacement and energy dissipation characteristics. Finite element analysis (FEA) was performed to simulate the response of the system to develop a multilinear analytical model for the hysteretic response that considers the nonlinear behavior of the system. The model was used to study the energy dissipation characteristics of the system. Experimental tests on 3D printed specimens were conducted to analyze the system and validate numerical results. Results show that the energy dissipation mainly depends on the number and the apex height-to-thickness ratio of the CCD units. The developed multilinear analytical model yields conservative yet accurate values for the dissipated energy of the system. The proposed system offered reliable high energy dissipation with a maximum loss factor value of 0.14 for a monostable (self-recoverable) system and higher for a bistable system. [ABSTRACT FROM AUTHOR]

This paper presents a method to achieve high deformability levels in dielectric elastomer actuators (DEAs) by applying a modulated voltage waveform. The method relies on supplying the electrostatic energy during the specific phase of the oscillation cycle, resulting in the enhanced travel range at a relatively low driving voltage. We consider a standard sandwich configuration of the DE actuator with neo-Hookean material model and outline an energy-based approach for delineating the underlying principles of the proposed method. A comparison of the deformability levels achieved using the quasi-static, Heaviside step, and the modulated input waveforms is presented. Significant reduction in instability voltages together with a considerable increase in the stable actuation limit is observed in the case of the modulated voltage input. The estimates of the stability thresholds are validated by integrating the equation of motion obtained using Hamilton's principle. The effect of energy dissipation is assessed by considering variations in the quality factor. Further, a qualitative comparison with experimental observations is presented highlighting the practical feasibility of the method. This investigation can find its potential use in the design and development of DEAs subjected to a time-dependent motion. [ABSTRACT FROM AUTHOR]

In this paper, an acoustomechanical constitutive model is developed to describe the heating effect of a tissue-mimicking gel by cavitation in exposure to high-intensity focused ultrasound (HIFU). An internal variable, representing the evolution of cavitation process, is introduced into the Helmholtz free energy under the framework of thermodynamics that combines the acoustic radiation stress theory and the nonlinear elasticity theory together. Thus, the internal variable is related to the cavitation process and the mechanical energy dissipation of a tissue-mimicking gel from a macroscopic viewpoint. Since the temperature rise of cavitation phenomenon is more remarkable than that of heating waves, the temperature inside the tissue-mimicking gel rises rapidly mainly due to large amounts of cavitation bubbles. This phenomenon can be quantitatively described by the present model, which fits the existing experimental data well. [ABSTRACT FROM AUTHOR]

Geomaterials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores with different hydromechanical properties. Moreover, these pore-networks are connected through fissures and conduits. Although some models are available in the literature to describe flows in such media, they lack a strong theoretical basis. This paper aims to fill this gap in knowledge by providing the theoretical foundation for the flow of incompressible single-phase fluids in rigid porous media that exhibit double porosity/permeability. We first obtain a mathematical model by combining the theory of interacting continua and the maximization of rate of dissipation (MRD) hypothesis, and thereby provide a firm thermodynamic underpinning. The governing equations of the model are a system of elliptic partial differential equations (PDEs) under a steady-state response and a system of parabolic PDEs under a transient response. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the model satisfy. We also present several canonical problems with analytical solutions which are used to gain insights into the velocity and pressure profiles, and the mass transfer across the two pore-networks. In particular, we highlight how the solutions under the double porosity/permeability differ from the corresponding ones under Darcy equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the interlayer slidable friction structures on soft-substrate as the hardcover book-like-laminated-plates with internal friction on the Winkler foundation. For a quasi-static problem, a detailed analysis of the bending response and energy dissipation is carried out for a three-point-supported layered plate on the Winker foundation. Our numerical investigations show that the hardcover, friction, and substrate have a great influence on bending response, and in particular, the friction can cause a considerable amount of energy dissipation within per loading-unloading cycle. The study is not only to predict the mechanical interactions behavior in-between of geometry, friction, elasticity, and substrate but also as a representative case to help finding some clue on the universal behaviors of interlayer slidable friction structures on soft-substrate. [ABSTRACT FROM AUTHOR]

Compliant contact force modeling has become a popular approach for contact and impact dynamics simulation of multibody systems. In this area, the nonlinear viscoelastic contact force model developed by Hunt and Crossley (1975, "Coefficient of Restitution Interpreted as Damping in Vibroimpact," ASME J. AppI. Mech., 42, pp. 440-445) over 2 decades ago has become a trademark with applications of the model ranging from intermittent dynamics of mechanisms to engagement dynamics of helicopter rotors and implementations in commercial multibody dynamics simulators. The distinguishing feature of this model is that it employs a nonlinear damping term to model the energy dissipation during contact, where the damping coefficient is related to the coefficient of restitution. Since its conception, the model prompted several investigations on how to evaluate the damping coefficient, in turn resulting in several variations on the original Hunt-Crossley model. In this paper the authors aim to experimentally validate the Hunt-Crossley type of contact force models and furthermore to compare the experimental results to the model predictions obtained with different values of the damping coefficient. This paper reports our findings from the sphere to flat impact experiments, conducted for a range of initial impacting velocities using a pendulum test rig. The unique features of this investigation are that the impact forces are deduced from the acceleration measurements of the impacting body, and the experiments are conducted with specimens of different yield strengths. The experimental forces are compared with those predicted from the contact dynamics simulation of the experimental scenario. The experiments, in addition to generating novel impact measurements, provide a number of insights into both the study of impact and the impact response. [ABSTRACT FROM AUTHOR]

Enriched by the nonlinear Onsager reciprocal relations and thermodynamic equilibrium points (Onsager, Phys. Rev., 37, pp. 405-406; 38, pp. 2265-2279), an extended normality structure by Rice (1971, J. Mech. Phys. Solids, 19, pp. 433-455) is established in this paper as a unified nonlinear thermodynamic theory of solids. It is revealed that the normality structure stems from the microscale irrotational thermodynamic fluxes. Within the extended normality structure, this paper focuses on the microscale thermodynamic mechanisms and significance of the convexity of flow potentials and yield surfaces. It is shown that the flow potential is convex if the conjugate force increment cannot not oppose the increment of the rates of local internal variables. For the Rice fluxes, the convexity condition reduces to the local rates being monotonic increasing functions with respect to their conjugate forces. The convexity of the flow potential provides the thermodynamic system a capability against the disturbance of the thermodynamic equilibrium point. It is proposed for time-independent behavior that the set of plastically admissible stresses determined by yield conditions corresponds to the set of thermodynamic equilibrium points. Based on that viewpoint, the intrinsic dissipation inequality is just the thermodynamic counterpart of the principle of maximum plastic dissipation and requires the convexity of the yield surfaces. [ABSTRACT FROM AUTHOR]

This paper presents a novel asymptotic framework to obtain detailed solutions describing the propagation of hydraulic fractures in an elastic material. The problem consists of a system of nonlinear integro-differential equations and a free boundary problem. This combination of local and nonlocal effects leads to transitions on a small scale near the crack tip, which control the behavior across the whole fracture profile. These transitions depend upon the dominant physical process(es) and are identified by simultaneously scaling the associated parameters with the distance from the tip. A smooth analytic solution incorporating several physical processes in the crucial tip region can be constructed using this new framework. In order to clarify the exposition of the new methodology, this paper is confined to considering the impermeable case in which only the two physical processes of viscous dissipation and structure energy release compete. [ABSTRACT FROM AUTHOR]

Nonviscously damped vibrating systems are characterized by dissipative mechanisms depending on the time-history of the response velocity, introduced in the physical models using convolution integrals involving hereditary kernel functions. One of the most used damping viscoelastic models is the Biot's model, whose hereditary functions are assumed to be exponential kernels. The free-motion equations of these types of nonviscous systems lead to a nonlinear eigenvalue problem enclosing certain number of the so-called nonviscous modes with nonoscillatory nature. Traditionally, the nonviscous modes (eigenvalues and eigenvectors) for nonproportional systems have been computed using the state-space approach, computationally expensive. In this paper, we address this problem developing a new method, computationally more efficient than that based on the state-space approach. It will be shown that real eigenvalues and eigenvectors of viscoelastically damped system can be obtained from a linear eigenvalue problem with the same size as the physical system. The numerical approach can even be enhanced to solve highly damped problems. The theoretical results are validated using a numerical example. [ABSTRACT FROM AUTHOR]

Hydrodynamic phase field models for multiphase fluids formulated using volume fractions of incompressible fluid components do not normally conserve mass. In this paper, we formulate phase field theories for mixtures of multiple incompressible fluids, using volume fractions, to ensure conservation of mass and momentum for the fluid mixture as well as the total volume for each fluid phase. In this formulation, the mass-average velocity is nonsolenoidal when the densities of incompressible fluid components in the mixture are not equal, making it a bona fide compressible model subject to an internal constraint. Derivation of mass conservation and energy dissipation in phase field models based on both Allen-Cahn dynamics and Cahn-Hilliard dynamics are presented. One salient feature of the phase field models is that the hydrostatic pressure is coupled with the transport of the volume fractions making the momentum transport and the volume fraction transport fully coupled in light of the mass conservation. Near equilibrium dynamics are explored using a linear analysis. In the case of binary fluid mixtures, one potential growth mode is identified in all the models for a class of free energy, which has been adopted for multiphase fluids. The growth is either absent for all waves or of a longwave feature. [ABSTRACT FROM AUTHOR]

The subdetonative propulsion mode using thermal choking has been studied with a one-dimensional (1D) real gas model that included projectile acceleration. Numerical results from a control volume analysis that accounted for unsteady flow effects established that the thrust coefficient versus Mach number profile was lower than that obtained with a quasi-steady model. This deviation correlates with experimental results obtained in a 38-mm-bore ram accelerator at 5.15 MPa fill pressure. Theoretical calculations were initially carried out with the assumption that the combustion process thermally choked the flow about one projectile length behind the projectile base. Thus the control volume length used in this 1D modeling was twice the projectile length, which is consistent with experimental observations at velocities corresponding to Mach number less than 3.5. Yet the choice of the length of the combustion zone and thus the control volume length remains a key issue in the unsteady modeling of the ram accelerator. The present paper provides a refinement of the unsteady one-dimensional model in which the effect of control volume length on the thrust coefficient and the projectile acceleration were investigated. For this purpose the control volume length determined from computational fluid dynamics (CFD) as a function of projectile Mach number was applied. The CFD modeling utilized the Reynolds-averaged Navier-Stokes (RANS) equations to numerically simulate the reacting flow in the ram accelerator. The shear-stress transport turbulence and the eddy dissipation combustion models were used along with a detailed chemical kinetic mechanism with six species and five-step reactions to account for the influence of turbulence and rate of heat release on the length of the combustion zone. These CFD computational results provided Mach number dependent estimates for the control volume length that were implemented in the 1D modeling. Results from the proposed improved 1D unsteady modeling were compared and validated with ram accelerator experimental data with significant improvements in terms of the predicted thrust dependence on Mach number. [ABSTRACT FROM AUTHOR]

Elastoplastic deformation occurs widely in engineering impact. Although many empirical solutions of elastoplastic impact between two spheres have been obtained, the analytical solution, verified by means of other methods, to the impact model has not been put forward. This paper proposes a dynamic pattern of elastoplastic impact for two spheres with low relative velocity, in which three stages are introduced and elastic and plastic regions are both considered. Finite element analyses with various parameters are carried out to validate the above model. The numerical results prove to agree with the theoretical predictions very well. Based on this model, the dissipation nature of elastoplastic impact are then analyzed, and the conclusion can be drawn that materials with lower yield strength, higher elastic modulus, and higher mass density have better attenuation and dissipation effects. The study provides a basis to predict the particle impact damping containing plastic deformation and to model the impact damped vibration system enrolling microparticles as a damping agent. [ABSTRACT FROM AUTHOR]

This paper presents a robust computational model for the response of composite laminates to high intensity transverse dynamic loading emanating from local impact by a projectile and distributed pressure pulse due to a blast. Delaminations are modeled using a cohesive type tie-break interface introduced between sublaminates while intralaminar damage mechanisms within the sublaminates are captured in a smeared manner using a strain-softening plastic-damage model. In the latter case, a nonlocal regularization scheme is used to address the spurious mesh dependency and mesh-orientation problems that occur with all local strain-softening type constitutive models. The results for the predicted damage patterns using the nonlocal approach are encouraging and qualitatively agree with the experimental observations. The predictive performance of the proposed numerical model is assessed through comparisons with available instrumented impact test results on a class of carbon-fiber reinforced polymer (CFRP) composite laminates. Force-time histories and other derived cross-plots such as the force versus projectile displacement and progression of projectile energy loss as a function of time are compared with available experimental results to demonstrate the efficacy of the model in capturing the details of the dynamic response. Another case study involving the blast loading of CFRP composite laminates is used to further highlight the capability of the proposed model in simulating the global structural response of composite laminates subjected to distributed pressure pulses. [ABSTRACT FROM AUTHOR]

This paper deals with the dissipation associated with quasistatic microcracking of brittle materials exhibiting softening behavior. For this purpose an elastodamaging cohesive zone model is used, in which cohesive tractions decrease (during crack propagation) with increasing displacement discontinuities. Constant cohesive tractions are included in the model as a limiting special case. Considering a representative volume element containing a dilute distribution of many parallel microcracks, we quantify energy dissipation associated with mode I microcrack propagation. This is done in the framework of thermodynamics, without restricting assumptions on the size of the cohesive zones. Model predictions are compared with exact solutions, which are accessible for constant cohesive tractions. The proposed model reliably predicts both onset of crack propagation and the dissipation during microcracking. It is shown that the energy release rate is virtually equal to the area under the softening curve, if the microscopic tensile strength is at least twice as large as the macroscopic tensile strength. This result justifies approaches relying on the concept of constant energy release rate, such as those frequently used in the engineering practice. [ABSTRACT FROM AUTHOR]

Rayleigh quotients in the context of linear nonconservative vibrating systems with vis- cous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and non- viscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix. [ABSTRACT FROM AUTHOR]

In this paper, we present a fracture-mechanics based model, the so-called bridged crack model (Carpinteri, A., 1981, "A Fracture Mechanics Model for Reinforced Concrete Collapse," Proc. of IABSE Colloquium on Advanced Mechanics of Reinforced Concrete, Delft, I.A.B.S.E., Zürich, pp. 17-30; Carpinteri, A., 1984, "Stability of Fracturing Process in R.C. Beams," J. Struct. Engng. (A.S.C.E.), 110, pp. 544-558) for the analysis of brittle matrix composites with discontinuous ductile reinforcements under the condition of repeated bending loading. In particular, we address the case of composites with very high number of reinforcements (i.e., fiber-reinforced composites, rather than conventionally reinforced concrete). With this aim, we propose a new iterative procedure and compare it to the algorithm recently proposed by Carpinteri, Spagnoli, and Vantadori (2004, "A Fracture Mechanics Model for a Composite Beam with Multiple Reinforcements Under Cyclic Bending," Int. J. Solids Struct., 41, pp. 5499-5515), showing the advantages in terms of computational efficiency. Furthermore, we analyze the combined effects of crack length, brittleness number, and fiber number on the cyclic behavior of the composite beam, showing the conditions enhancing the energy dissipation in the composite system. Eventually, we analyze crack propagation and propose, consistently with the model premises, a fracture-mechanics-based crack propagation criterion that allows one to simulate cyclic bending tests under the fixed grip condition. [ABSTRACT FROM AUTHOR]

The Principle of Maximum Dissipation Rate (PMD) can be exploited to derive homogeneous kinetic rate laws for the internal variables. A "normality structure" expressing the rates of the internal variables as normal to convex functions (entropy production rate, dissipation function as flow potentials) in the space of the conjugate thermodynamic forces is a direct consequence of the PMD. This paper can be considered as a note to Yang et al., 2005, ASME J. Appl. Mech., 72, pp. 322-329. [ABSTRACT FROM AUTHOR]

This paper discusses an exact decomposition of the kinetic energy to determine the energy content that influences the dynamics of unilateral contacts in multibody systems. This decomposition essentially divides the kinetic energy of the whole multibody system into two completely decoupled parts associated with the constrained and admissible directions of unilateral contacts. This will provide a picture of how the energy absorption/dissipation during impacts is related to the variation of the generalized velocities and the configuration of multibody systems. Potential applications of such a decoupling are highlighted. [ABSTRACT FROM AUTHOR]