We numerically investigate the stress distribution of a paste when an external oscillation is applied. The paste memorizes the oscillation as plastic deformation. Due to the plastic deformation, the residual stress remains after the oscillation, where the residual stress distribution depends on the number of cycles in the oscillation. As this number increases, the symmetry of the stress distribution is enhanced, which is consistent with the crack patterns observed in the experiments using a drying paste.
Yield stress of aerated cement paste is studied. Samples are prepared by mixing aqueous foam with cement paste, which allows controlling bubble size, gas volume fraction and yield stress of the cement paste. Two distinct behaviors are observed depending on the surfactant used to prepare the precursor aqueous foam: (i) For a surfactant with low adsorption ability with respect to cement grains, bubbles tend to decrease the yield stress of the paste with magnitude governed by the Bingham capillary number, which accounts for bubble deformability. (ii) For a surfactant with high adsorption ability,…
We study the rheological behavior of mixtures of foams and pastes, which can be described as suspensions of bubbles in yield stress fluids. Model systems are designed by mixing monodisperse aqueous foams and concentrated emulsions. The elastic modulus of the suspensions decreases with the bubble volume fraction. This decrease is all the sharper as the elastic capillary number (defined as the ratio of the paste elastic modulus to the bubble capillary pressure) is high, which accounts for the softening of the bubbles as compared to the paste. By contrast, the yield stress of most studied materia…
Production of morphology-controlled cement foams remains challenging, mainly due to bubble stability issues during cement setting. The use of cement paste with high yield stress is expected to promote stability by damping intrinsic bubble kinetics. Here we show however that for given W/C ratio, fresh foam stability can be achieved instead by decreasing the yield stress of the cement paste. Indeed, in this low apparent yield stress regime, van der Waals attraction between cement grains is reduced and grains are allowed to be efficiently packed by bubbles, providing enhanced mechanical propertie…
Metakaolin is a broadly used industrial raw material, with applications in the production of ceramics and geopolymers, and the partial replacement of Portland cement. The early stages of the manufacturing of some of these materials require the preparation and processing of a foamed metakaolin-based slurry. In this study, we propose to investigate the rheology of a foamed metakaolin-based fresh paste by performing well-controlled experiments. We work with a non-reactive metakaolin paste containing surfactant, in which we disperse bubbles of known radius at a chosen volume fraction. We perform r…
A possible clarification of memory effect observed in crack patterns of drying pastes [A. Nakahara and Y. Matsuo, J. Phys. Soc. Japan 74, 1362 (2005)] is presented in terms of a macroscopic elastoplastic model of isotropic pastes. We study flows driven by steady gravitational force instead of external oscillation. The model predicts creation of residual tension in favor of cracks perpendicular to the flow direction, thus causing the same type of memory effect as that reported by Nakahara and Matsuo for oscillated CaCO_3 pastes.
Capillary effects such as imbibition-drying cycles impact the mechanics of granular systems over time. A multiscale poromechanics framework was applied to cement paste, that is the most common building material, experiencing broad humidity variations over the lifetime of infrastructure. First, the liquid density distribution at intermediate to high relative humidities is obtained using a lattice gas density functional method together with a realistic nano-granular model of cement hydrates. The calculated adsorption/desorption isotherms and pore size distributions are discussed and compare well…
Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growth-induced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters. This modelling provides promising avenues for designing and directing some ap…
Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the loca…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic remodelling processes aiming at optimizing the overall structural response to environmental physical forces. From a mechanical viewpoint, residual stresses are classically modelled through the introduction of a virtual incompatible state that collects the local relaxed states around each material point. In this work, we instead employ an alternative approach…
In soft amorphous materials, shear cessation after large shear deformation leads to structures having residual shear stress. The origin of these states and the distribution of the local shear stresses within the material is not well understood, despite its importance for the change in material properties and consequent applications. In this work, we use molecular dynamics simulations of a model dense non-Brownian soft amorphous material to probe the non-trivial relaxation process towards a residual stress state. We find that, similar to thermal glasses, an increase in shear rate prior to the s…
Initial residual stress is omnipresent in biological tissues and soft matter, and can affect growth-induced pattern selection significantly. Here we demonstrate this effect experimentally by letting soft tubes grow in the presence or absence of initial residual stress and by observing different growth pattern evolutions. These experiments motivate us to model the mechanisms at play when a growing bilayer tubular organ spontaneously displays buckling patterns on its inner surface. We demonstrate that not only differential growth, geometry and elasticity, but also initial residual stress distrib…
In this paper the inelastic features of stress relaxation, hysteresis and residual strain are combined with the Arruda-Boyce eight-chain model of elasticity, in order to develop a model that is capable of describing the Mullins effect for cyclic stress-softening of an incompressible hyperelastic material, in particular a carbon-filled rubber vulcanizate. We have been unable to identify in the literature any other model that takes into consideration all the above inelastic features of the cyclic stress-softening of carbon-filled rubber. Our model compares favourably with experimental data and g…
We report on the interplay between creep and residual stresses in a carbopol microgel. When a constant shear stress $σ$ is applied below the yield stress $σ_\text{y}$, the strain is shown to increase as a power law of time, $γ(t)=γ_0 + (t/τ)^α$, with an exponent $α=0.39\pm 0.04$ that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some typical value $σ_\text{c}\simeq 0.2 σ_\text{y}$, the microgel experiences a more complex, anomalous creep behaviour, characterized by an initial decrease of the strain, that we attribute to the existence of residual…
Dilute Laponite suspensions in water at low salt concentration form repulsive colloidal glasses which display physical aging. This phenomenon is still not completely understood and in particular, little is known about the connection between the flow history, as a determinant of the initial state of the system, and the subsequent aging dynamics. Using a stress controlled rheometer, we perform stress jump experiments to observe the elastic component of the flow stress that remains on cessation of flow or flow quenching. We investigate the connection between the dynamics of these residual stresse…
This paper models stress softening during cyclic loading and unloading of an elastomer. The paper begins by remodelling the primary loading curve to include a softening function and goes on to derive non-linear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain and creep of residual strain. These ideas are combined with a transversely isotropic version of the Arruda-Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress-softening for a transversely isot…
The distribution of local residual stresses (threshold to instability) that controls the statistical properties of plastic flow in athermal amorphous solids is examined with an atomistic simulation technique. For quiescent configurations, the distribution has a pseudogap (power-law) form with an exponent that agrees well with global yielding statistics. As soon as deformation sets in, the pseudogap region gives way to a system size dependent plateau at small residual stresses that can be understood from the statistics of local residual stress {\em differences} between plastic events. Results f…
The history dependence of the glasses formed from flow-melted steady states by a sudden cessation of the shear rate $\dotγ$ is studied in colloidal suspensions, by molecular dynamics simulations, and mode-coupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function of $\dotγt$, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this h…
Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growth-induced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters. This modelling provides promising avenues for designing and directing some ap…
Exponential Stress Relaxation Driven by Elementary Plastic Events in Non-Ageing Liquid Foams
Lund University（隆德大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Paul Scherrer Institut（保罗谢尔研究所）；Université Côte d’Azur（蔚蓝海岸大学）；Technical University of Denmark（丹麦技术大学）；ENS de Lyon（里昂高等师范学校）；Institut Universitaire de France (IUF)（法国高等研究院）
We show that the long time tail of the shear stress autocorrelation, whose growth at large supercooling is responsible for the apparent divergence of the shear viscosity, is a direct result of a residual shear stress in the structures associated with the local potential minima. We argue that the essential mechanical transition experienced by a liquid on cooling occurs at a temperature well above the glass transition temperature and corresponds to the crossover from the high temperature liquid to the viscous liquid, the latter characterised by stress relaxation dominated by the residual stress.…
The multiplicative decomposition model is widely employed for predicting residual stresses and morphologies of biological tissues due to growth. However, it relies on the assumption that the tissue is initially in a stress-free state, which conflicts with the observations that any growth state of tissue is under a significant level of residual stresses that helps to maintain its ideal mechanical conditions. Here, we propose a modified multiplicative decomposition model where the initial state (or reference configuration) of biological tissue is endowed with residual stress instead of being str…
A thermodynamic framework has been developed for a class of amorphous polymers used in fused deposition modeling (FDM), in order to predict the residual stresses and the accompanying distortion of the geometry of the printed part (warping). When a polymeric melt is cooled, the inhomogeneous distribution of temperature causes spatially varying volumetric shrinkage resulting in the generation of residual stresses. Shrinkage is incorporated into the framework by introducing an isotropic volumetric expansion/contraction in the kinematics of the body. We show that the parameter for shrinkage also a…
On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the deformation with the initial stress and in general, for a compressible material, it requires 10 invariants, reducing to 9 for an incompressible material. Expressions for the Cauchy and nominal stress tensors in a finitely deformed configuration are given along with the elasticity tensor and its specialization to the initially stressed undeformed configuration. The equations gov…
In this paper we derive a model to describe the important inelastic features associated with the cyclic softening, often referred to as stress-softening, of soft biological tissue. The model developed here includes the notion of multiple stress-strain cycles with increasing values of the maximum strain. The model draws upon the similarities between the cyclic softening associated with carbon-filled rubber vulcanizates and soft biological tissue. We give non-linear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain. These idea…
A model is proposed that considers aging and rejuvenation in a soft glassy material as respectively a decrease and an increase in free energy. The aging term is weighted by inverse of characteristic relaxation time suggesting greater mobility of the constituents induce faster aging in a material. A dependence of relaxation time on free energy is proposed, which under quiescent conditions, leads to power law dependence of relaxation time on waiting time as observed experimentally. The model considers two cases namely, a constant modulus when aging is entropy controlled and a time dependent modu…
We derive an orthotropic model to describe the cyclic stress-softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic mo…
Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel, which induces randomness in the residual stress and Lame coefficients. Second, a semi-microscopic model network is explored using replica statistical mechanics. The Goldstone fluctuations of the semi-microscopic model are shown to reproduce the phenomenological model, and via this correspondence the statistical properties of the residual stress and Lame coeffici…
The internal (or residual) stress is among the key notions to describe the state of the systems far from equilibrium. Such stress is invisible on the macroscopic scale where the system is regarded as a blackbox. Yet nonequilibrium macroscopic operations allow to create and observe the internal stress. We present in this lecture some examples of the internal stress and its operations. We describe the memory effect in some detail, the process in which the history of past operations is recalled through the relaxation of internal stress.
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initially flat, straight ribbon, with prescribed magnitudes and orientations of the principal curvatures when subjected to arbitrary surface stress and/or internal residual strain distribution. The helix angle, radius, axis and chirality of the deformed helical ribbons are predicted with…
