Dissipation Potential Research Articles

Identification of dissipative emissions for improved assessment of metal resources in life cycle assessment

AbstractEnvironmental dissipation is a novel approach to account for impacts from mineral resources. In contrast to all other resource‐related life cycle impact assessment methods, which use data on extractions as input to calculation of indicator scores, environmental dissipation is characterized solely through emissions to the environment. Making environmental dissipation work as a viable resource use impact category in life cycle assessment requires, however, that truly dissipative emissions are differentiated from those anthropogenic releases which do not contribute to loss of accessibility of a given resource over the time frame considered. We present a new method that allows for this differentiation to be made for 65 metals and metalloids in a consistent way. It determines (1) whether an emission flow reported in a life cycle inventory actually contributes to loss of accessibility of a given element when environmental fate mechanisms are considered, and (2) whether the element comes from a source that would be considered as a mineral resource for any generation living between the present and the time frame of assessment. We apply the new method to four different emission inventories, and characterize the resulting list of truly dissipative emissions using recently proposed long‐term environmental dissipation potentials (EDP). This highlights the need to differentiate dissipative emissions from other anthropogenic, potentially nondissipative emission flows of elements in metal resource impact assessment.

A Thermodynamically Consistent Model of Quasibrittle Elastic Damaged Materials Based on a Novel Helmholtz Potential and Dissipation Function.

In the paper, a thermodynamically consistent model of elastic damaged material in the framework of small strain theory is formulated, describing the process of deterioration in quasibrittle materials, concrete in particular. The main goal is to appropriately depict the distinction between material responses in tension and compression. A novel Helmholtz energy and a dissipation potential including three damage parameters are introduced. The Helmholtz function has a continuous first derivative with respect to strain tensor. Based on the assumed functions, the strain–stress relationship, the damage condition, the evolution laws, and the tangent stiffness tensor are derived. The model’s predictions for uniaxial tension, uniaxial compression, uniaxial cyclic compression–tension, and pure shear tests are calculated using Wolfram Mathematica in order to identify the main features of the model and to grasp the physical meaning of an isotropic damage parameter, a tensile damage parameter, and a compressive damage parameter. Their values can be directly bound to changes of secant stiffness and generalized Poisson’s ratio. An interpretation of damage parameters in association with three mechanisms of damage is given. The considered dissipation potential allows a flexible choice of a damage condition. The influence of material parameters included in dissipation function on damage mode interaction is discussed.

A Lagrangian approach for the electromechanical model of single-stage spur gear with tooth root cracks

This paper presents a unified electromechanical modeling framework of a single-stage spur gear with cracks at tooth root. The model has been developed following modified Lagrangian approach with the consideration of Rayleigh dissipative potential. The coupled electromechanical equations of motion represent a non-autonomous system. Improved analytical model based time-varying mesh stiffness (IAM-TVMS) at different crack depths is incorporated in the developed model to examine the impact of cracks on the dynamic behavior of the system. The IAM-TVMS model considers the effect of misalignment between base and root circle, accurate transition curve, nonlinear Hertzian contact stiffness, revised fillet foundation stiffness with the structural coupling effect when nearby tooth is loaded and improved crack model which considers the straight line for crack path and parabolic curve for limiting line. The current and vibration responses are taken after solving the coupled equations of motion through fourth order Runge–Kutta method. In this study, the impact of crack depths are effectively visualized using stator current as a primary source of signal. Even when the crack depth is significantly small, the residual signal clearly depicts the presence of crack in the cepstrum analysis. The cepstrum analysis of residual stator current signal is also compared and verified with the residual vibration signal for different crack depths. The developed analytical model is one of the first attempt of its kind in modeling approach; the model successfully shows the impacts of crack on the system with motor current signal.

Determination of critical energy flux for filled elastomer based on global energy balance and J-Integral

In this work, the crack growth of carbon black-filled ethylene propylene diene monomer rubber was analysed by experimental investigations and numerical simulations. The investigated sample is loaded cyclically under displacement-controlled test condition. The sample had a defined initial crack length. Due to the cyclic loading, the crack grows further due to excess critical energy flux. A uniform pattern was drawn on the surface of the investigated specimen, therefore the crack propagation per cycle can be determined. The cyclic loads were recorded with a camera. The time of initiation of crack propagation was determined by analysing the recorded pictures and the energy flux was determined based on global evaluation of the dissipation potential and the local evaluation of J-Integral.At the virgin cycle, the energy flux has the largest value, which decreases with increasing number of cycles. This behaviour is due to the stress-softening effect of elastomers. The local energy flux was determined near the crack tip by using the J-Integral. The experimentally and numerically determined energy fluxes show similar decreasing tendencies and have different values. These differences are due to the fact that in the evaluation of the energy flux based on the global energy balance during crack growth, the separation potential and the dissipated potential in the whole sample cannot be separated from each other.

A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers

We study the approximation of quasistatic evolutions, formulated as abstract finite-dimensional rate-independent systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamical solutions to the quasistatic one, employing the concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.

Multiphase field modeling of grain boundary migration mediated by emergent disconnections

Knowledge about grain boundary migration is a prerequisite for understanding and ultimately modulating the properties of polycrystalline materials. Evidence from experiments and molecular dynamics (MD) simulations suggests that the formation and motion of disconnections is a mechanism for grain boundary migration. Here, grain boundary migration is modeled using a multiphase field model based on the principle of minimum dissipation potential with nonconvex boundary energy, along with a stochastic model for thermal nucleation of disconnection pairs. In this model, disconnections arise spontaneously in the presence of an elastic driving force, and that their motion mediates boundary migration. The effect is due to the fact that the formation of the disconnections pairs results in a stress concentration, causing the elastic driving force to exceed the threshold value and driving the propagation of the disconnection along the interface. The model is applied to study the propagation/annihilation of single disconnection pairs, the relaxation of a perturbed interface, and shear coupling at various temperatures. The results are consistent with the current understanding of disconnections, and capture the effect of thermal softening.

EDP-convergence for nonlinear fast–slow reaction systems with detailed balance* *Research partially supported by NWO grant 613.001.552, `Large Deviations andGradient Flows' and DFG via SFB 1114 (Project No. 235221301, subproject C05).

We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics.

Variational Methods for Evolution

Variational principles for evolutionary systems take advantage of the rich toolbox provided by the theory of the calculus of variations. Such principles are available for Hamiltonian systems in classical mechanics, gradient flows for dissipative systems, but also time-incremental minimization techniques for more general evolutionary problems. The new challenges arise via the interplay of two or more functionals (e.g. a free energy and a dissipation potential), new structures (systems with nonlocal transport, gradient flows on graphs, kinetic equations, systems of equations) thus encompassing a large variety of applications in the modeling of materials and fluids, in biology, in multi-agent systems, and in data science. This workshop brought together a broad spectrum of researchers from calculus of variations, partial differential equations, metric geometry, and stochastics, as well as applied and computational scientists to discuss and exchange ideas. It focused on variational tools such as minimizing movement schemes, optimal transport, gradient flows, and large-deviation principles for time-continuous Markov processes, \Gamma -convergence and homogenization.

Strain amplitude effects on the seismic performance of dampers utilizing shape memory alloy wires

Superelastic shape memory alloys (SMAs) are unique smart materials with a considerable energy dissipation potential for the vibration control of structures. The energy dissipation arises from the hysteretic phase transformation. Random vibration patterns, such as by earthquakes and wind, include not only changing strain rates but also different strain amplitudes. Previous studies revealed that the reverse phase transformation behavior of SMAs depend apart from the strain rate also on the strain amplitude. This study confirms these findings by experiments and proposes a modeling approach for an accurate representation of this effect. Both tensile cyclic and seismic responses of Nitinol wires are studied for this purpose. The modeling approach is validated by the experimental results. Finally, the proposed model is applied numerically to a seismically excited 20-story benchmark building incorporating multiple SMAs. An intermediate time stepping approach is employed, which improves both the computational efficiency and the accuracy of the simulation process.

Validated tensile characterization of the strain rate dependence in soft materials

A major obstacle in the accurate measurement of the dynamic tensile response of soft materials is the issue of obtaining material response under simultaneous stress equilibrium, stress uniaxiality and constant strain rate. To resolve this issue, a split-Hopkinson pressure bar (SHPB)-based dynamic tension experiment is developed in this study, which has sufficient fidelity to ensure temporal and spatial accuracy of the stress state, to investigate soft materials under large deformations and intermediate dynamic strain rates (100-102 s−1). Cross-linked polydimethylsiloxane (PDMS) elastomer is chosen as a model material. By examining the evolution of full-field strain and strain rate measured using digital image correlation (DIC) and employing analytical criteria for quantifying stress equilibrium and deformation uniaxiality, it is demonstrated that the proposed test method yields a true steady-state and inertia-free stress-strain material response when all three conditions of equilibrium, uniaxiality and strain rate constancy are satisfied. Quasi-static experiments at 10−3-10−1 s−1 strain rate are also conducted for comparison. By analyzing the quasi-static and dynamic stress-strain plots and the variation of uniaxial moduli in the investigated range of strain rates, it is shown that the tensile response of PDMS points to limiting chain extensibility and exhibits a weak nonlinear strain rate sensitivity. Finally, a visco-hyperelastic model based on the Gent strain energy density function and a recently proposed viscous dissipation potential is employed to capture the experimentally obtained response. It is shown that all the features of the rate-dependent stress-strain response are modeled with good fitting accuracy.

Coupling of the phase field approach to the Armstrong-Frederick model for the simulation of ductile damage under cyclic load

The present contribution proposes a thermodynamically consistent model for the simulation of the ductile damage. The model couples the phase field method of fracture to the Armstrong-Frederick plasticity model with kinematic hardening. The latter is particularly suitable for simulating the material behavior under a cyclic load. The model relies on the minimum principle of the dissipation potential. However, the application of this approach is challenging since potentials of coupled methods are defined in different spaces: The dissipation potential of the phase field model is expressed in terms of rates of internal variables, whereas the Armstrong-Frederick model proposes a formulation depending on thermodynamic forces. For this reason, a unique formulation requires the Legendre transformation of one of the potentials. The present work performs the transformation of the Armstrong-Frederick potential, such that final formulation is only expressed in the space of rates of internal variables. With the assumption for the free energy and the joint dissipation potential at hand, the derivation of evolution equations is straightforward. The application of the model is illustrated by selected numerical examples studying the material response for different load cases and sample geometries. The paper provides a comparison with the experimental results as well.

Contact interactions in complex fibrous metamaterials

In this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).

A geometrically exact continuum framework for light-matter interaction in photo-active polymers I. Variational setting

Molecular photo-switches as, e.g., azobenzene molecules allow, when embedded into a polymeric matrix, for photo-active polymer compounds responding mechanically when exposed to light of certain wavelength. Photo-mechanics, i.e. light-matter interaction in photo-active polymers holds great promise for, e.g., remote and contact-free activation of photo-driven actuators. In a series of earlier contributions, Oates et al. developed a successful continuum formulation for the coupled electric, electronic and mechanical problem capturing azobenzene polymer compounds, thereby mainly focussing on geometrically linearized kinematics [1, 2, 3]. Building on that formulation, we here explore the variational setting of a geometrically exact continuum framework based on Dirichlet’s and Hamilton’s principle as well as, noteworthy, Hamilton’s equations. Thereby, when treating the dissipative case, we resort to incremental versions of the various variational problems via suited incorporation of a dissipation potential. In particular, the Hamiltonian setting of geometrically exact photo-mechanics is up to now largely under-explored even for the energetic case, arguably since the corresponding Lagrangian is degenerate in Dirac’s sense. Moreover, in general, the Hamiltonian setting of dissipative dynamical systems is a matter of ongoing debate per se. In this contribution, by advocating a novel incremental version of the Hamiltonian setting exemplified for the dissipative case of photo-mechanics, we aim to also unify the variational approach to dissipative dynamical systems. Taken together, the variational setting of a geometrically exact continuum framework of photo-mechanics paves the way for forthcoming theoretical and numerical analyses.

Life cycle impact assessment methods for estimating the impacts of dissipative flows of metals

The dissipation of metals leads to potential environmental impacts, usually evaluated for product systems with life cycle assessment. Dissipative flows of metals become inaccessible for future users, going against the common goal of a more circular economy. Therefore, they should be addressed in life cycle impact assessment (LCIA) in the area of protection “Natural Resources.” However, life cycle inventory databases provide limited information on dissipation as they only track emissions to the environment as elementary flows. Therefore, we propose two LCIA methods capturing the expected dissipation patterns of metals after extraction, based on dynamic material flow analysis data. The methods are applied to resource elementary flows in life cycle inventories. The lost potential service time method provides precautionary indications on the lost service due to dissipation over different time horizons. The average dissipation rate method distinguishes between the conservation potentials of different metals. Metals that are relatively well conserved, including major metals such as iron and aluminum, have low characterization factors (CFs). Those with poor process yields, including many companion and high-tech metals such as gallium and tellurium, have high CFs. A comparative study between the developed CFs, along with those of the Abiotic Depletion Potential and Environmental Dissipation Potential methods, show that dissipation trends do not consistently match those of the depletion and environmental dissipation potentials. The proposed methods may thus be complementary to other methods when assessing the impacts of resource use on the area of protection Natural Resources when pursuing an increased material circularity. This article met the requirements for a gold-silver JIE data openness badge at http://jie.click/badges.

Anisotropic damage model for concrete and other quasi-brittle materials

A thermodynamically consistent formulation to model anisotropic damage for quasi-brittle materials is proposed. The model is based on proper expressions for the specific Gibbs free energy and the complementary form of the dissipation potential. Damaging of the material is described by a symmetric positive definite second order damage tensor. Especially, the failure surface is formulated in such a way that it will mimic the behaviour of the well known Ottosen’s four parameter failure surface. While testing the model against the experimental results found in literature, the results were in good agreement in uniaxial tensile and compressive loadings as well as in biaxial compression. Besides the correct failure stress states, the model predicts the correct failure modes of concrete: axial splitting along the direction of uniaxial compression and tensile damaging normal to the direction of tension.

Comparative Analysis of Heat Transfer and Fluid Flow in Circular and Rhombus Pin Fin Heat Sink Using Nanofluid

Abstract Numerical investigation has been carried out to compare the heat transfer performance and fluid flow behavior of microchannel heat sinks with circular and rhombus pin fins which are arranged in an in-line manner. Diameter and sides are 1 mm for circular and rhombus fins. Three-dimensional (3D) computational domain has been simulated using two types of cooling medium, i.e., water and Al2O3–H2O nanofluid. A comprehensive comparative analysis has been presented considering the coolants and pin fin profiles as variable parameters. Two operating variables, i.e., heat flux (q) and Reynolds number (Re), are varied in the range of q = 100–400 kW/m2 and Re = 100–400. A total of 64 cases have been simulated to identify the promising features of both the pin fins attributed to improved heat transfer and overall thermal performance. Comparison has also been made between the coolant medium to find out their heat dissipation potential and flow characteristics in the heat sink. Results obtained in terms of average bottom wall temperature, heat transfer coefficient, Nusselt number (Nu), and pressure drop demonstrate that heat sink with rhombus pin fins dissipates more heat compared to its counterpart. It is attributed to the shape and geometry of rhombus fins that facilitate distinct fluid flow behavior; nevertheless, the pressure drop is less in the circular fin heat sink. Moreover, for constant value of Re, nanofluid extracts more heat compared to water in both configurations of the heat sink.

On standard gradient plasticity and visco-plasticity

This paper is devoted to the standard theory of gradient plasticity and visco-plasticity, cf. Gudmundson (2004), Fleck and Willis (2009) and the quoted references. Within the framework of the generalized standard materials and the generalized principle of virtual work, our attention is focussed on the mathematical basis of the theory in order to underline the basic assumptions, general results and principal difficulties compared to the classical theory of plasticity. Gradient terms can be introduced in the expression of the energy potential or the dissipation potential. Various general results of the literature on the constitutive modeling and on the response of a solid under a given loading are revisited in this unified description. The quasi-static response is governed by a variational inequality which is an alternative form of Biot equation. A full discussion of this evolution equation is given in terms of the energy and dissipation potentials of the solid. The rate problem and the rate variational principle are considered and compared to the incremental problem and the incremental variational principle which result from an implicit discretization of the evolution equations. In particular, rate and incremental minimum principles are related to a stability condition.

On a mixed energetic–dissipative constitutive law for non-proportional loading, with focus on small-scale plasticity

We analyse the mixed energetic–dissipative potential (MP) recently proposed by our group to predict, within higher-order strain gradient plasticity (SGP), reliable size-dependent responses under general loading histories. Such an MP follows former proposals by Chaboche, Ohno and co-workers for nonlinear kinematic hardening in the context of size-independent metal plasticity. The MP is given by M quadratic addends that each transitions, at a different threshold value, into a linear dissipative contribution. Hence, the MP involves 2 M positive material parameters, given by the M threshold values and the M moduli weighing each quadratic recoverable term. We analytically demonstrate that, under proportional loading, the MP limit for M → ∞ converges to a less-than-quadratic potential with well-defined properties. This result is of crucial importance for identifying the material parameters of any model adopting the MP. Moreover, our analysis provides a formula for the characterization of the energetic and dissipative parts of any possible MP limit, showing that, regarding the capability to describe the effect of diminishing size within SGP, the MP can be selected such that its contribution to the strengthening (i.e. an increase in yield point) is mostly dissipative, whereas its contribution to the increase in strain hardening is mostly recoverable.

A Dissipative Green’s Function Approach to Modeling Gravity Waves behind Submerged Bodies

Potential flow-based methods are common in early design stages because of their associated speed and relative simplicity. By separating the resistance components of a ship into viscous and wave resistance, an inviscid method such as potential flow can be used for wave resistance determination. However, gravity waves are affected by viscosity and decay with time and distance. It has, therefore, long been assumed that the inclusion of a damping parameter in potential flow would better model the wave resistance. This article presents a Kelvin-Neumann dissipative potential flow model. A Rayleigh damping term is inserted into the Navier-Stokes equations to capture the decay of waves. A new 3D Green’s function based on the Havelock-Lunde formulation is derived by the use of a Fourier transform. An upper limit for the Rayleigh damping term is found by comparison with experiments and a possible improvement on conventional potential flow models for the wave making resistance prediction of a submerged ellipsoid is proposed.

Energetic upscaling strategy for grain growth. II: Probabilistic macroscopic model identified by Bayesian techniques

This paper is the second part of an energetic upscaling strategy to simulate grain growth at the macroscopic scale with state variables that contain statistical descriptors of the grain structure. The first part was dedicated to the derivation of a fast mesoscopic model of grain growth based on orientated tessellation updating method, which consists in a succession of Voronoi-Laguerre tessellations obtained by establishing an evolution law directly on the parameters defining the tessellations. In this contribution, the final step of the upscaling strategy is detailed by deriving macroscopic evolutions laws of the state variables representing statistical distributions of the grain structure. The approach relies on macroscopic free energy and dissipation potentials that are identified not axiomatically, but using a large database of mesoscopic computations. The macroscopic energy is found to be purely deterministic, although the dissipation necessitates to introduce a probabilistic framework. Indeed, an epistemic uncertainty arises due to the loss of information in the reduction of the amount of data between the detailed mesoscopic state and the statistical macroscopic state (i.e., several mesoscopic states can share the same macroscopic state). Classical Bayesian inference has been used to identify the probability density functions associated to the epistemic uncertainty. From the computational point of view, this work can be used to simulate grain growth at very large scale with short computation time, while processing rich statistical information about the grain structure, such as statistical indicators of the grain boundary character distribution. The resulting stochastic macroscopic model has been compared to several particular mesoscopic evolutions, and good agreement is observed. However, the macroscopic model still requires an experimental validation.