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(σ o ,σ c ) Preisach space. (Top) Preisach space with offdiagonal elements, σ c � σ o , used in the calculations leading to the results in Fig. 8 (left panels). (Bottom) Preisach space with diagonal elements only, σ c = σ o , used in the calculations leading to the results in Fig. 8 (middle, right panels). (Inset) Schematic of μ protocol used in all calculations.
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The behavior of hysteretic, coupled elastic and fluid systems is modeled. The emphasis is on quasistatic equilibrium in response to prescribed chemical potential (μ) protocols and prescribed stress (σ) protocols. Hysteresis arises in these models either from the presence of hysterons or from the presence of self-trapping internal fields. This latte...
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... probability density P (σ c ) is similarly distributed with σ c � σ o (Fig. 6). The system is driven by the applied stress caused by a uniform set of forces applied to the nodes on its right edge (Fig. 5). The applied stress protocol is shown in the inset in the lower right of Fig. 6. It starts at σ xx < min(σ o ). Thus, initially η = +1 for all elastic elements. We monitor the behavior of the system with the x ...
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... probability density P (σ c ) is similarly distributed with σ c � σ o (Fig. 6). The system is driven by the applied stress caused by a uniform set of forces applied to the nodes on its right edge (Fig. 5). The applied stress protocol is shown in the inset in the lower right of Fig. 6. It starts at σ xx < min(σ o ). Thus, initially η = +1 for all elastic elements. We monitor the behavior of the system with the x strain (the departure of the average position of the right edge of the system from its initial value) and the y strain (the change in the separation of the average position of the top edge form the average ...
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... Take the system through the stress protocol using the off-diagonal (σ c ,σ o ) distribution in Fig. 6 (top) and the applied stress version of the change of state rules, that is, the applied stress is used in place of the internal stress in the rules. See the − σ curves in Fig. 8 (left panels). (2) Take the system through the stress protocol using the diagonal (σ c ,σ o ) distribution in Fig. 6 (bottom) and the applied stress version of the ...
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... using the off-diagonal (σ c ,σ o ) distribution in Fig. 6 (top) and the applied stress version of the change of state rules, that is, the applied stress is used in place of the internal stress in the rules. See the − σ curves in Fig. 8 (left panels). (2) Take the system through the stress protocol using the diagonal (σ c ,σ o ) distribution in Fig. 6 (bottom) and the applied stress version of the change of state rules; that is, the applied stress is used in place of the internal stress in the rules. See the − σ curves in Fig. 8 (center panels). (3) Take the system through the stress protocol using the diagonal(σ c ,σ o ) distribution in Fig. 6 (bottom) and the internal stress version of the ...
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... using the diagonal (σ c ,σ o ) distribution in Fig. 6 (bottom) and the applied stress version of the change of state rules; that is, the applied stress is used in place of the internal stress in the rules. See the − σ curves in Fig. 8 (center panels). (3) Take the system through the stress protocol using the diagonal(σ c ,σ o ) distribution in Fig. 6 (bottom) and the internal stress version of the change of state rules, that is, the rules in the first paragraph of this section. See the − σ curves in Fig. 8 (right ...
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... the system is strained with an applied stress we expect the capacity for moisture uptake to change. In Fig. 16 Example with details. To illustrate the assembly of the ingredients required to carry through the recipe above we look at a particular problem in some detail. The elements are 328 triangles having 185 nodes, etc., as above. We work near the fiducial chemical potential μ = 0 with chemical potential scaled so that the values of the ...
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... Furthermore, hysteresis is the dependence of the system's response on its history (could be inelastic), which exists in rate-dependent and path-dependent problems such as plasticity, viscoelasticity and poroelasticity. In the latter case, this behaviour is due to the Fluid-Solid Interaction and the time/path-dependent nature of the problem due to fluid drainage or absorption [41]. The numerical examples performed in this section respond to the above-mentioned questions. ...
Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for finite strain and large deformation problems while it ensures infinitesimal strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy’s law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under uniaxial cyclic test is simulated and studied.
... The viscosity of the composite matrix is taken into account in the framework of the model of frequency-independent internal friction. According to this approach, the shear modulus has the form (1 ) N i + β , where the value of β is proportional to the loss coefficient of a viscoelastic material [17] and can be determined experimentally [18]. As a result of this, a small complex component is present in the coefficients of equation (1) , , , N A Q R [19]. ...
Based on the solution of the dynamic contact problem of vibration of a rigid punch on a heterogeneous half-space, taking into account friction in the contact area, the tribological properties of an oil-filled composite material with a microstructure are modeled. The microstructure of the base is taken into account in the framework of the Biot-Frenkel model. The boundary-value problem is reduced to the integral equation, its approximate solution is constructed, which describes contact stresses, tangential displacements. The dependencies of the friction forces on the microstructure of the composite, the viscosity of the fluid filling the pores, and the degree of phase interaction are investigated. Keywords: dynamic contact problem with friction, oil-filled composite 1. Introduction Currently, there is a considerable amount of concepts, hypotheses, and research on diverse friction and wear-related issues. Many attempts have been made to study the properties, structure, and state of the surface layers of tribological conjugations at the atomic and molecular levels. The core problem of surface engineering (for example, metal friction units) is the synthesis of coating technologies and materials with specified wear-resistant properties. The most remarkable result to emerge from our study [1] is that the methods of vacuum ion-plasma treatment (PVD-method) and atomic modifications of diamond-like coatings (DLC) are the most appropriate among the wide array of methods aimed at hardening surface and improving tribological properties. However, along with increasing the strength properties of the materials, such technologies contribute to the formation of a damping layer with residual compressive stresses inside and a large number of stress micro-concentrators at the boundary with the main material. The above-listed aspects predetermine the formulation and solution of the dynamic contact problem, taking into account the friction forces on tribocontact. This problem is attracting an increasing interest due to the widespread application of polymer composite materials [2]. Recently, oil-filled nanocomposites, whose components are characterized with viscoelastic properties and the properties of viscous-fluid filler, have become extensively used in units and parts of tribotechnical purposes [3-5]. Constructing new composite materials with given physical and mechanical properties poses an actual, yet practically unexplored task to study the influence of dynamic effects that are caused by vibration on the antifriction properties of these materials. We undertook this study to investigate the patterns of changes in the stress-strain state of a composite material depending on its composition and dynamic loading conditions by solving a dynamic contact problem. The latest takes into account friction in the contact area for a base with a microstructure. The
... The internal microstructure of the base consisting of a viscoelastic skeleton and a filler fluid is considered by using the equations of a heterogeneous two-phase Biot's medium as determining ones [6][7][8][9]. The determination of the mechanical moduli for Biot's medium is a separate and very important problem. ...
... The viscosity of the composite matrix is considered within the model of frequency-independent internal friction. According to this approach, the shear modulus has the form of , where the value of is proportional to the loss coefficient of the viscoelastic material [9] and can be determined experimentally [14]. As a result, there is no small complex component in the coefficients of equation (2.1) [8,9]. ...
... According to this approach, the shear modulus has the form of , where the value of is proportional to the loss coefficient of the viscoelastic material [9] and can be determined experimentally [14]. As a result, there is no small complex component in the coefficients of equation (2.1) [8,9]. Within contact domain Ω, normal and shear stresses are connected through the Amonton-Coulomb law, , where is the friction coefficient. ...
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INTRODUCTION Contact problems and the applications thereof to tribology are attracting the attention of many researchers for a long time [1-5]. The complications in the formulations and approaches that arise when solving contact problems are described in detail in a fundamental monograph [1]. The contact problems in a quasistatic formulation for homogeneous viscoelastic media are considered by the authors of [1-5]. It should be noted that the properties of the contacting surfaces significantly affect the friction force. The microgeometry influence of the contacting surfaces on the friction force has been investigated by the authors of [4, 5]. In this paper, we consider the contact problem in a quasistatic formulation for the motion of a rigid die under friction on the base considering the microstructure of the base. The internal microstructure of the base consisting of a viscoelastic skeleton and a filler fluid is considered by using the equations of a heterogeneous two-phase Biot's medium as determining ones [6-9]. The determination of the mechanical moduli for Biot's medium is a separate and very important problem. The bulk compression moduli of a saturated and drained medium have been determined experimentally, including by the nanoindentation method [10-12], as well as based on micromechanics and finite-element simulation methods. The cases of dies with flat and parabolic bases are considered. The problems of friction force determination are relevant in designing antifriction composites based on a viscoelastic matrix and a fluid filler [11-13].
... In the literature, phenomenological models that extend the PM model to the negative (P o , P c ) plane were applied to cracked materials. For quasi-static experiments, (Scalerandi et al., 2003) combined negative pressure with random transitions in HMEUs due to thermal activation to model residual strain that slowly disappears (slow dynamics effect), and Guyer et al. (2011) used negative pressure to model tensile internal forces in the case of coupled elastic and fluid systems. In the context of micropotential modeling, Aleshin & Van Den Abeele (2005) allowed negative opening strains in a variant of the PM model in which the HMEUs are characterized by a pair of opening and closing strains instead of a pair of opening and closing pressures. ...
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Hysteresis in the elasticity of a rock is when its elastic properties depend on its history. A classical model of hysteresis is the Preisach‐Mayergoyz model. According to this model, after a compression‐decompression cycle, the system comes back to its original state. However, granular media are subject not only to hysteresis but also to irreversible deformation. To model it, we propose a modification of the Preisach‐Mayergoyz model. In brief, we assume that some units in the rock remain shrunk after decompression. Mathematically, we obtain this result by imposing that these units have negative opening pressure. From a physical point of view, these units represent rearrangements in the grain network. We apply this model to laboratory measurements on beach samples, and we show that this model, given a small number of parameters, describes sufficiently well the volumetric deformation of the samples and the response of the sample to wave propagation. This is important because this modified model improves the classic hysteresis model, including plasticity in the same mathematical framework. Both the static and dynamic behavior of granular media, as well as the strain path, are better explained.
... Based on the coupling between sorption and deformation, the element can switch its own states upon the influence of its neighbors, which finally leads to hysteresis in both sorption and deformation. One can refer to References [116,117] for further details. Here we show briefly an upscaling model applied to amorphous cellulose. ...
... The DDM was adopted to account for the hysteresis. We implemented all the elements stated above into a Finite Element method [116] and built a continuum model based on molecular simulations which captures the non-linear coupling between sorption and deformation with hysteresis, with good agreement between atomistic and continuum modeling results as shown in Figure 8. Here we show briefly an upscaling model applied to amorphous cellulose. ...
... The DDM was adopted to account for the hysteresis. We implemented all the elements stated above into a Finite Element method [116] and built a continuum model based on molecular simulations which captures the non-linear coupling between sorption and deformation with hysteresis, with good agreement between atomistic and continuum modeling results as shown in Figure 8. ...
This paper aims at providing a methodological framework for investigating wood polymers using atomistic modeling, namely, molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulations. Atomistic simulations are used to mimic water adsorption and desorption in amorphous polymers, make observations on swelling, mechanical softening, and on hysteresis. This hygromechanical behavior, as observed in particular from the breaking and reforming of hydrogen bonds, is related to the behavior of more complex polymeric composites. Wood is a hierarchical material, where the origin of wood-moisture relationships lies at the nanoporous material scale. As water molecules are adsorbed into the hydrophilic matrix in the cell walls, the induced fluid–solid interaction forces result in swelling of these cell walls. The interaction of the composite polymeric material, that is the layer S2 of the wood cell wall, with water is known to rearrange its internal material structure, which makes it moisture sensitive, influencing its physical properties. In-depth studies of the coupled effects of water sorption on hygric and mechanical properties of different polymeric components can be performed with atomistic modeling. The paper covers the main components of knowledge and good practice for such simulations.
... Derome et al. [50] showed that the swelling/shrinkage hysteresis of wood tissue is strongly linked to the moisture sorption hysteresis. Guyer et al. [51] suggested that the difference of forces induced by swelling and shrinkage is reflected by the difference of chemical potential required for adsorption and desorption, which is actually the difference in relative humidity required to obtain the same moisture content in a sorption loop. Hence, after being stored at 98% and 50% RH until attainment of equilibrium, nonwoven composites are in a desorption state. ...
... These mechanisms can include adhesion, i.e. the formation and breakage of adhesive necks connecting asperities of contacting surfaces [16][17][18], collective movements of dislocations engendering a phenomenon called kinking [19], or friction between faces of the internal contacts [20,21]. There also exists an application of the Preisach formalism to poroelastic materials [22]. ...
The observation of a hysteretic stress-strain relationship is widespread for a large class of solids, such as rocks and other geomaterials, concretes, bones, etc. A common feature that unifies these materials is the presence of internal mechanical contacts in their structure, which can either be natural, or appear as the result of damage or fatigue in consolidated materials with an originally non-hysteretic mechanical response. Even though a number of physical mechanisms can be identified to account for mechanical hysteresis, at moderate and high strains, when typical internal contact displacements largely exceed the atomic size, a friction-based mechanism becomes of primary importance. As an alternative for a physics-based description, phenomenological approaches, ignoring the physical nature of hysteresis, are often used in numerical simulations. In this paper, we intend to bridge the physical mechanism of friction-based hysteresis with the phenomenological Preisach formalism, and derive the Preisach density in a compact analytical form for a model system that represents an elastic continuum with a large number of diversely oriented frictional cracks. We validate the physical crack friction model and its phenomenological Preisach counterpart with experimental data for Fontainebleau sandstone. The new formulations and the results could be of interest for materials scientists dealing with systems that show hysteretic elasticity and/or distributed damage, geomaterials or construction materials.
... ble to sorption. Further, the tensile strain on an element is considered to produce extra volume for additional sorption of water molecules, which has also been observed in the atomistic simulations. The behavior of a distribution of such interacting elastic elements is studied by finite elements. Our group in collaboration with R. Guyer from LANL (Guyer et. al 2011) developed such a dependent domain approach for an academic material. General results showing the model performance are reported here. Figure 4a gives an example of predictions of sorption and swelling isotherms using the elastic dependent domain model of non-hysteretic elements where the coupling between sorption and swelling has been s ...
... vior at macro-or structural scale. Final aim is to be able to adequately model sorption induced swelling and hysteresis. The models should be physically sound from one side, but also sufficiently simple to be used in engineering practice. Figure 5. Swelling strain versus moisture content as determined by dependent domain. No hysteresis is observed (Guyer et. al 2011). ...
... welling isotherm of moisture content and strain versus RH for non-coupled dependent domain approach. No hysteresis is observed. (b) Sorption and swelling isotherm of moisture content and strain versus RH for coupled dependent domain approach, with interaction between filling and swelling process. Hysteresis both in sorption and swelling is observed(Guyer et. al 2011). ...
... In reverse, desorption occurs only when sufficient shrinkage occurs around the sorption site to make it spatially untenable and make desorption desirable. The difference of forces induced by swelling and shrinkage is thus reflected by the difference of chemical potential required for adsorption and desorption, which is actually the difference in RH to obtain the same MC in a sorption loop [25]. ...
The swelling behavior is of interest as the locus of the nice interaction of moisture and mechanical behavior. We take wood as our model material. Although, moisture behavior is known to be hysteretic in terms of relative humidity, we demonstrate that it is not hysteresis in terms of moisture content and take this as an opportunity to look for a full description of this moisture/mechanical interaction. Investigations by phase contrast synchrotron X-ray microtomography and by hygro-elastic modeling allows to see the strong effects of porosity and cellular geometry on the anisotropy of swelling. We end with a few observations on moisture-induced shape memory.
... During adsorption, the collapsed pores will expand again, but they cannot reach their usual size [23]. The reason of shrinkage and swelling has been explained in more detail in the literature [47]. The existing hysteretic behaviour leads to the need of hysteresis models when performing modelling of moisture transport. ...
The durability of reinforced concrete structures and their service life are closely related to the simultaneous occurrence of many physical and chemical phenomena. These phenomena are diverse in nature, but in common they are dependent on the moisture properties of the material. Therefore, the prediction of the potential degradation of cementitious materials requires the study of the movement of liquid-water and gas-phase transport in the material which is considered as a porous medium. In natural environment, structures are always affected by periodic variations of external relative humidity (RH). However, most moisture transport models in the literature only focus on the drying process. There are few researches considering both drying and wetting, although these conditions represent natural RH variations. Even few studies take into account hysteresis in moisture transport. Thus, this work is devoted to better understand how the moisture behaviour within cementitious materials responds to the ambient RH changes through both experimental investigations and numerical modelling. In particular, hysteretic effects will be included in numerical modelling. In this thesis, we first recalled a complicate multi-phase continuum model. By theoretical analysis and experimental verification, a simplified model can be obtained for the case of that the intrinsic permeability to liquid-water is smaller than the intrinsic permeability to gas-phase. The review of commonly-used hysteresis models enabled to conclude a set of best models for the prediction of water vapour sorption isotherms and their hysteresis. After that, the simplified model was coupled with selected hysteresis models to simulate moisture transport under drying and wetting cycles. Compared with experimental data, numerical simulations revealed that modelling with hysteretic effects can provide much better results than non-hysteresis modelling. Among different hysteresis models, results showed that the use of the conceptual hysteresis model, which presents closed form scanning loops, can provide more accuracy predictions. Further simulations for different scenarios were also performed. All comparisons and investigations enhanced the necessity of considering hysteresis to model moisture transport for varying relative humidity at the boundary. The investigation of moisture penetration depth could provide a better understanding of how deep moisture as well as ions can move into the material. Furthermore, the analysis revealed that the consideration of Knudsen effects for diffusion of vapour can improve the prediction of the apparent diffusivity
