Dissipation Potential Research Articles

Conceptualization, proposed design and theoretical investigations of an active adaptive cutting device with enhanced energy dissipation potential

Active adaptive energy dissipation systems can receive and interpret data from onboard vehicle sensors to respond to external stimuli by modifying their geometries and corresponding load bearing capacities. This is a highly promising subfield in structural crashworthiness since these devices possess multiple potential configurations, thus allowing them to achieve the preferred balance between high-capacity energy absorption and mitigation of human injury for a broad and disparate range of loading conditions. A novel cutting-based active adaptive energy absorber was conceptualized, design and theoretically assessed in this investigation with guidance from previous experimental observations and extensively validated modeling approaches. The proposed, hydraulically-driven active adaptive cutter (HAAC) was capable of transitioning between 4, 6, 8 and 12-bladed cutting deformation modes in either direction (e.g., from 6 to 12-bladed cutting or vice versa) and in a nondestructive manner. The steady-state force capacity could be varied by an average factor of 2.6, quantifying the significant range available to the HAAC regardless of extrusion material or geometry. A broad scale analytical study revealed that the proposed HAAC could eclipse the energy absorbing performance of the traditional axial crushing deformation mode for AA6061-T6 extrusions with 50.80 mm to 76.20 mm diameters and 1.59 mm to 3.18 mm wall thicknesses, with an average enhancement of 73 % calculated for the 12-bladed cutting mode. The newly proposed active adaptive capabilities allow the system to carefully balance energy absorption requirements and mitigation of occupant/pedestrian injury in a manner which the current state-of-the-art cannot achieve.

Cosh gradient systems and tilting

We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type. We show how such dissipation potentials emerge in large deviations of jump processes, multi-scale limits of diffusion processes, and more. We show how the exponential nature of the cosh derives from the exponential scaling of large deviations and arises implicitly in cell problems in multi-scale limits.We discuss in-depth the role of tilting of gradient systems. Certain classes of gradient systems are tilt-independent, which means that changing the driving functional does not lead to changes of the dissipation potential. Such tilt-independence separates the driving functional from the dissipation potential, guarantees a clear modelling interpretation, and gives rise to strong notions of gradient-system convergence.We show that although in general many gradient systems are tilt-independent, certain cosh-type systems are not. We also show that this is inevitable, by studying in detail the classical example of the Kramers high-activation-energy limit, in which a diffusion converges to a jump process and the Wasserstein gradient system converges to a cosh-type system. We show and explain how the tilt-independence of the pre-limit system is lost in the limit system. This same lack of independence can be recognized in classical theories of chemical reaction rates in the chemical-engineering literature.We illustrate a similar lack of tilt-independence in a discrete setting. For a class of ‘two-terminal’ fast subnetworks, we give a complete characterization of the dependence on the tilting, which strongly resembles the classical theory of equivalent electrical networks.

Experimental and analytical investigations of steel shear buckling-inhibited energy dissipation devices

This study presents the development and cyclic performance assessment of steel buckling-inhibited shear yielding devices (St-BISYDs). These devices consisted of thin steel plates as the main energy dissipating elements and modular built-up restrainers as the buckling inhibition mechanism. St-BISYDs are designed to achieve a shear strain of at least 20% without buckling to maximize the energy dissipation potential by minimizing the heat-affected zone (HAZ) and using the bolted connections. Ten specimens with two geometric configurations, namely, hourglass and rectangular, steel plates were experimentally tested under quasi-static displacement-controlled cyclic loading. The proposed restrainers greatly enhanced the cyclic performance of St-BISYDs and helped the St-BISYDs to reach the target shear strain level without significant strength and stiffness degradation under cyclic loading. An analytical study is conducted to predict the force-deformation characteristics of St-BISYDs. Experimental results of the tested specimens are also compared with other similar energy dissipation devices. Further, nonlinear modeling parameters are proposed for the force-deformation response of St-BISYDs which can be directly used in the design practices.

A thermomechanical finite strain shape memory alloy model and its application to bistable actuators

This work presents a thermomechanical finite strain shape memory alloy model that utilizes a projection method to deal with the incompressibility constraint on inelastic strains. Due to its finite strain formulation, it is able to accurately predict the behavior of shape memory alloys with high transformation strains. The key feature of this model is the thermomechanical modeling of the shape memory effect and superelastic behavior by optimizing a global, incremental mixed thermomechanical potential, the variation of which yields the linear momentum balance, the energy balance, the evolution equations of the internal variables as well as boundary conditions of Neumann- and Robin-type. The proposed thermal strain model allows to properly capture transformation induced volume changes, which occur in some shape memory alloys. A finite strain dissipation potential is formulated, which incorporates the disappearance of inelastic strains upon austenite transformation. This important property is consistently transferred to the time-discrete potential using a logarithmic strain formulation. Yield and transformation criteria are derived from the dual dissipation potential. The implementation based on an active set search and the algorithmically consistent linearization are discussed in detail. The model is applied in three-dimensional simulations of a bistable actuator design to explore its capabilities.

Plasticity damage self-consistent model incorporating stress triaxiality and shear controlled fracture mechanisms – Model formulation

A model for plasticity and damage, developed in the context of continuum damage mechanics and consistent with micromechanisms of void nucleation, growth, and coalescence, is presented. The damage dissipation potential has been formulated specifically to account for different damage contributions due to intervoid necking, shearing, and sheeting under arbitrary stress states. The existence of a cut-off for the negative stress triaxiality was questioned and unilateral conditions for ductile damage have been reformulated accordingly, considering the combination of stress triaxiality and Lode parameter. The model allows the derivation, although in implicit form, of the fracture locus for the whole range of stress triaxiality. An example application to Al2024-T351 and Al6061-T6 is presented. The proposed formulation represents an attempt to reconcile CDM theoretical framework with the ductile fracture specific mechanisms and their sequential progression under general loading conditions, making advantages of micromechanical modeling to establish correlations between void evolution and continuum scale physical quantities. Finite element model implementation and plasticity model formulation will be discussed in a forthcoming companion paper.

Morphological controls on surface runoff: an interpretation of steady-state energy patterns, maximum power states and dissipation regimes within a thermodynamic framework

Abstract. Recent research explored an alternative energy-centred perspective on hydrological processes, extending beyond the classical analysis of the catchment's water balance. Particularly, streamflow and the structure of river networks have been analysed in an energy-centred framework, which allows for the incorporation of two additional physical laws: (1) energy is conserved and (2) entropy of an isolated system cannot decrease (first and second law of thermodynamics). This is helpful for understanding the self-organized geometry of river networks and open-catchment systems in general. Here we expand this perspective, by exploring how hillslope topography and the presence of rill networks control the free-energy balance of surface runoff at the hillslope scale. Special emphasis is on the transitions between laminar-, mixed- and turbulent-flow conditions of surface runoff, as they are associated with kinetic energy dissipation as well as with energy transfer to eroded sediments. Starting with a general thermodynamic framework, in a first step we analyse how typical topographic shapes of hillslopes, representing different morphological stages, control the spatial patterns of potential and kinetic energy of surface runoff and energy dissipation along the flow path during steady states. Interestingly, we find that a distinct maximum in potential energy of surface runoff emerges along the flow path, which separates upslope areas of downslope potential energy growth from downslope areas where potential energy declines. A comparison with associated erosion processes indicates that the location of this maximum depends on the relative influence of diffusive and advective flow and erosion processes. In a next step, we use this framework to analyse the energy balance of surface runoff observed during hillslope-scale rainfall simulation experiments, which provide separate measurements of flow velocities for rill and for sheet flow. To this end, we calibrate the physically based hydrological model Catflow, which distributes total surface runoff between a rill and a sheet flow domain, to these experiments and analyse the spatial patterns of potential energy, kinetic energy and dissipation. This reveals again the existence of a maximum of potential energy in surface runoff as well as a connection to the relative contribution of advective and diffusive processes. In the case of a strong rill flow component, the potential energy maximum is located close to the transition zone, where turbulence or at least mixed flow may emerge. Furthermore, the simulations indicate an almost equal partitioning of kinetic energy into the sheet and the rill flow component. When drawing the analogy to an electric circuit, this distribution of power and erosive forces to erode and transport sediment corresponds to a maximum power configuration.

Plasticity damage self-consistent model incorporating stress triaxiality and shear controlled fracture mechanisms – Model verification and validation

The plasticity damage self-consistent (PDSC) model is a damage model developed in the context of continuum damage mechanics in which the damage dissipation potential is formulated to account for damage contributions due to intervoid necking, shearing, and sheeting for an arbitrary stress state. The synergic action of different micromechanisms contributing to ductile fracture is accounted for by their dependence on the plastic deformation, stress triaxiality, third invariant of the deviatoric of the stress tensor, and unilateral conditions. In this work, the PDSC has been implemented in the commercial finite element code MSC MARC via user subroutines and used to predict ductile failure response under different stress state conditions. Firstly, the model implementation has been verified by comparing calculated damage evolution as a function of plastic strain, for prescribed combinations of stress triaxiality and Lode parameter under proportional loading, with an analytical solution. Successively, the model has been validated in predicting ductile fracture for Al6061-T6 in different specimen geometries and comparing with experiment results. Model capability to anticipate fracture initiation conditions, together with specimen global response, and ductile crack propagation also for complex load paths, is demonstrated.

Demonstration of high-stable self-mode-locking pulses based on self-focusing in fiber lasers

Passive ultrafast photoelectric devices based on the self-focusing effect have been deeply studied in ultrashort pulse formation, and great progress has been made in solid-state oscillators known as Kerr-lens mode-locking (KLM). The intensity-dependent change of refractive index and the 1–2 fs electronic response time of materials are the basics of KLM. Recently, the advantages of fiber lasers such as compact structure, outstanding environmental stability, excellent heat dissipation potential, and low cost have stimulated great interest among researchers to explore stable and reliable fiber lasers. Based on the feasibility of KML in fiber lasers that have been reported, we demonstrate a high-stable self-mode-locking Er-doped fiber laser in this work. Diverse stable self-mode-locking pulses phenomena can be obtained through adjusting the polarization state of the cavity, including the output pulses with a fundamental frequency of 3.93 MHz, dark-bright soliton pulses, the 3rd harmonic operation, the 81st harmonic operation with the repetition rate of 318.4 MHz and the signal-to-noise ratio of 80 dB, and dual-wavelength output.

A non incremental variational principle for brittle fracture

The aim of the paper is to propose a paradigm shift for the variational approach to brittle fracture. Both dynamics and the limit case of statics are treated in a same framework. By contrast with the usual incremental approach, we use a space–time principle covering the whole loading and crack evolution. The emphasis is given on the modelling of the crack extension by the internal variable formalism and a dissipation potential as in plasticity, rather than Griffith’s original approach based on the surface area. The new formulation appears to be more fruitful for generalization than the standard theory.

Evolving structural tensor approach to model the damage induced anisotropy in viscoelastic solids

A three-dimensional anisotropic damage model, based on continuum damage mechanics, is presented capturing the damage induced anisotropy in the initially isotropic, viscoelastic (VE) solid. The second order tensor damage variable, conceived as an evolving structural tensor, is coupled with linear VE model at the finite as well as infinitesimal strains. A dissipation potential, based on a novel damage interaction tensor (fourth order tensor), is proposed from which the damage tensor evolution happens in an associative manner. The newly proposed model is numerically implemented as an implicit stress update algorithm, and the infinitesimal part of the formulation is validated against the available experimental results in the literature. A parametric study of the newly developed finite strain formulation is presented employing three different deformation histories demonstrating further the utility of the proposed anisotropic damage model. The successful experimental validation of the proposed model demonstrates its applicability and utility in the existing finite element codes.

Experimental Cyclic Response of a Novel Friction Connection for Seismic Retrofitting of RC Buildings with CLT Panels

The seismic vulnerability of existing RC framed buildings in seismic-prone areas requires affordable and practice-oriented solutions for their retrofitting. In this paper, the authors present a retrofitting solution for RC buildings based on the combined use of cross-laminated timber (CLT) panels and asymmetric friction connections (AFCs). The AFC connection is activated when the force level reaches the design threshold. The energy dissipation of the AFC increases the structural dissipation capacity and reduces the displacement demand. This research presents the outcomes of an experimental campaign on selected prototypes of these AFC connectors. The authors assess their dissipative capacity from cyclic load tests in four different connector arrangements and examine the contribution of aluminum shim layers. The first results highlight the significant dissipation potential of the AFC, although they also provide evidence of the notable sensitivity on the design and constructive details. The authors present a modeling approach to simulate the experimental results.

Constitutive and damage model for the whole-life uniaxial ratcheting behavior of SAC305

With the wide application of SAC305 solders in electronic packaging, it is important to examine their reliability. In this study, uniaxial ratcheting experiments were carried out on SAC305 solders with varying loading rates, mean stresses, and stress amplitudes at room temperature. Based on the unified creep–plasticity constitutive model applicable to SAC305 solders, a nonlinear continuum damage mechanics model was established to simulate the whole-life ratcheting behavior. The damage variable was extracted from the elastic modulus decline of the unloading section during the cyclic loading process, and its evolution was based on the damage dissipation potential, which was derived from the theory of continuum damage mechanics. In addition, the normalized life was used to correct the evolution of the damage variable. For a more accurate description of their evolution, the energy method was used to modify the damage evolution parameters under different loading conditions. Finally, the uniaxial ratcheting behavior of SAC305 solder could be accurately described by the modified damage-coupled constitutive model under different loading conditions.

Variational modeling of temperature induced and cooling-rate dependent phase transformations in polycrystalline steel

Phase transformations in steel have a high impact on the material properties. The material is modified by a changed stiffness as well as residual stresses which are a result of transformation strains and plastic deformations during the phase transition. In the current work, we propose a variational material model which is able to display the phase transformations which occur during thermal processes like induction hardening and grinding. Depending on the cooling rate, the material model is able to show the transformation between austenite and martensite, austenite and ferrite as well as a mixture of both. The polycrystalline structure of the steel is taken into account by use of different oriented grains which are considered by a combined Voigt–Reuss bound for the energy of the phase and grain mixture. The material model is derived using the principle of the minimum of the dissipation potential for non-isothermal problems. Compared to classical approaches in material science, the model is thermomechanically coupled. Thus, the phase transformation is also influenced by the stress state and individual martensitic variants are favored during the transformation process, which is an important property for applications to process chains. The model’s ability to show the complex material behavior is proven by calculations on the material point level as well as by finite element simulations.

Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager’s variational principle, which allows us to write such PDEs in terms of two potentials: the free energy and the dissipation potential. Specifically, these two potentials are learned from spatio-temporal measurements of macroscopic observables via proposed neural network architectures that strongly enforce the satisfaction of the second law of thermodynamics. The method is applied to three distinct physical processes aimed at highlighting the robustness and versatility of the proposed approach. These include (i) the phase transformation of a coiled-coil protein, characterized by a non-convex free-energy density; (ii) the one-dimensional dynamic response of a three-dimensional viscoelastic solid, which leverages the variational formulation as a tool for obtaining reduced order models; and (iii) linear and nonlinear diffusion models, characterized by a lack of uniqueness of the free energy and dissipation potentials. These illustrative examples showcase the possibility of learning partial differential equations through their variational action density (i.e., a function instead), by leveraging the thermodynamic structure intrinsic to mechanical and multiphysics problems.

How dynamic is the Brahmaputra? Understanding the process–form–vegetation interactions for hierarchies of energy dissipation

AbstractThe spatio‐temporal heterogeneity in process–form–vegetation interactions has enabled the Brahmaputra river system to dissipate the fluvial energy at hierarchical scales. The present review article synthesizes the knowledge on braided rivers and an extensive review of the bio‐morphological processes in the Brahmaputra River. In addition, field investigated datasets along with geo‐spatial imageries and Google Earth Engine computed fluvial information are integrated to conceptualize and understand the complex underlying processes in the river. The review can be further used to propose rejuvenation frameworks and research directions concerning the implication of hierarchical energy dissipation potential in the Brahmaputra River.

On nonlinear Onsager symmetry and mass-action kinetics

ABSTRACT This brief paper is a continuation of previous work (J.D. Goddard, “Dissipation potentials for reaction-diffusion systems.” I&EC Res.,54.16,4078–4083, 2015) dealing with the application of Edelen’s dissipation potentials to the irreversible thermodynamics of chemical-reaction networks. It is shown that one can achieve non-linear Onsager symmetry by means of constraints on a certain combination of Gibbs free energies dubbed reactivity, from which it follows that reaction rates are given simply as gradients of a dissipation potential. This may open the door to the application of thermodynamics and variational methods to combustion and biochemical reaction networks, including the possibility of enhanced derivation of reduced kinetic mechanisms. A graph-theoretical description of reaction networks is presented, which is based on stoichiometric hypergraphs and encompasses several past treatments in a more economical fashion. It may also suggest hypergraph optimization techniques to enhance the selection of reduced mechanisms.

A constitutive framework for steady-state creep in coarse-grained zirconium alloys under irradiation

ABSTRACT A constitutive framework for steady-state creep in polycrystalline zirconium alloys under neutron irradiation is elaborated. The framework combines a two-scale description with internal variables. The structure of the local constitutive laws within individual grains follows from a thermodynamical formulation accounting for freely migrating defects nucleated by radiation and for deformation produced by dislocation glide and climb, while the structure of the overall constitutive relations for the polycrystalline aggregate follows from homogenisation. The resulting description is thermodynamically consistent and conforms to the generalised standard material model. A special class of constitutive laws is generated using convex dissipation potentials reproducing the mean-field reaction rate theory. The relations are nonlinear and reflect an inherent coupling between irradiation creep and growth; however, they admit partial linearisation even for moderate stress levels. Some implications for mechanistic creep models of common use are discussed.

Numerical Modeling of Energy Dissipation during Fatigue Crack Propagation in Metals

It is well-known that mechanical work spent on inelastic deformation of metal converts into the heat. However, experimental studies have shown that process of plastic deformation is accompanied not only by extensive heat dissipation but also by energy storage. Therefore, precise calculation of the dissipated energy value should take into account the portion of energy which is accumulated in the material. In this work, we applied thermodynamic constitutive theory based on multiple dissipation potentials to obtain constitutive equations for structural parameter responsible for the stored energy and plastic strain causing plastic dissipation. Evolution equation for structural parameter is derived from phenomenological form of free energy function. Combined hardening model is used for plastic strain calculation. Value of the dissipated energy is calculated as difference between plastic work and stored energy. We have applied this model to calculate dependence of dissipated energy per cycle on crack length for two titanium alloys (Ti-5Al-2V and Grade-2). Simulation was carried out in finite-element package Comsol Multiphysics in plane stress formulation. A stationary crack approach was used for energy balance calculation at the crack tip. Results of the simulation were compared with experimental data on heat dissipation obtained by original heat flux sensor.

Experimental modal analysis of glass and laminated glass large panels with EVA or PVB interlayer at room temperature

Laminated glass is used for fail-safe structures in many fields of engineering. It contains a polymeric interlayer that improves the brittle glass behavior after fracture, provides damping, increases impact resistance, and at the same time maintains transparency. This paper examines the effect of the type of the interlayer on laminated glass oscillation using a roving hammer test. It also compares the modal response of the laminated glass before and after the low-velocity impact. The experimental modal analysis is validated by numerical modal analysis and using a different experimental methodology. This contribution discusses natural frequencies and damping ratios affecting the impact response and the reduction of noise and vibrations. It is found that the inserted polymer foils increased the damping and the impact resistance of the transparent plate. The interlayer with a higher ratio between loss and storage modulus showed higher damping and thus energy dissipation potential. No significant difference was measured in the natural frequencies of laminated glass before and after low-velocity impact. Inferences drawn from this study can be used by engineers, architects, and contractors when selecting suitable panels for applications such as windshields or curtain walls.

Observations on the fourth-power scaling of high-pressure shock waves in solids

This paper is concerned with the bounds and approximations that are found in the original derivation of the fourth-power scaling of shock waves in solids [D. Grady, Appl. Phys. Lett. 38, 825 (1981)]. The analysis is focused on the framework of the derivation and is independent of constitutive assumption, such as visco-plastic behavior. Results include an upper bound for the shock pressure and a restriction on the range of power coefficient for materials having a power-type function for the shock velocity–particle velocity relation. Relaxation of this restriction is proposed based on the idea that the rise time along the Rayleigh line is strain dependent. The idea led to the application of the Onsager relation to strain rate calculation that in turn resulted in a quadratic function for the strain rate–shock pressure relation. The fourth-power relation is obtained by generalizing the Onsager relation through the introduction of a quadratic dissipative potential in analogy to Rayleigh's dissipative potential.