Evolution Of Shear Modulus Research Articles

Hydro‐Mechanical Characterization of a Fractured Aquifer Using Groundwater Level Tidal Analysis: Effect of Pore Pressure and Seismic Dynamic Shear Stresses on Permeability Variations

AbstractGroundwater level tidal analysis is a powerful technique to monitor aquifer's permeability and hence its change over time. Earthquakes are known to affect aquifer's properties, in their vicinity through static stress changes but also further away through dynamic stresses. Most often changes are in the form of permeability increases, but sometimes decreases; the changes can be either permanent or transient. These observations are relatively well documented but the physical processes behind these changes are not well understood. By combining solid‐earth and barometric tidal groundwater level responses in a borehole in a coherent poroelastic theoretical framework, and a bi‐layer hydrogeological model, we recover a 15 years‐long time series evolution of aquifer transmissivity and shear modulus. This study showcases the full potential of the tidal analysis method, coupling pore pressure diffusion and rock deformation, at the frontier of hydrogeology and rock physics. This unprecedented measurement of permeability and shear modulus evolution by tidal analysis reveals, during interseismic period, high sensitivity of this shallow aquifer to effective stress, and thus to pore pressure. Thanks to additional finite element simulation of seismic wave propagation, we explore the different mechanisms affecting permeability and shear modulus in the studied fractured andesite aquifer. This study confirms the predominant role of seismic dynamic stresses, and more precisely of dynamic shear stresses, in the change of permeability following an earthquake.

A coupled elastic constitutive model for high porosity sandstone

An elastic constitutive model is developed to predict the mechanical unloading response for high porosity sandstone. The resulting model is sufficiently complex to represent known mechanical response, yet reasonably straightforward to calibrate. A mechanical dataset from a suite of true triaxial tests on Castlegate sandstone is used to develop, calibrate, and validate the model, which incorporates the experimentally observed evolutions of the elastic bulk and shear moduli with stress and plastic strain. Furthermore, to properly represent the hydrostatic unloading response, a coupled term is required, in which the plastic volume strain (accumulated during both hydrostatic and deviatoric loading) modifies the nonlinear stress dependence of the bulk modulus. Omission of this coupling term causes significant over prediction of the plastic volume strain and bulk modulus after complete unloading. However, the coupled term is not required to model deviatoric response and shear modulus evolution. While a suite of 28 tests was used to develop the model, only one carefully controlled test is required to calibrate the model for a chosen high porosity sandstone.

Rheology and application of buoyant foam concrete for digital fabrication

In the fresh state, conventional lightweight foam concrete (LWFC) has low yield stress which challenges shape retention and buildability in digital construction. Several literatures attempt to address the rheological performance of 3D printable lightweight foam concrete (3DP-LWFC) in essence. This research presents a comprehensive rheological characterisation with controlled shear rate tests and flow curve tests over different foam volume fractions and densities of 700, 1000 and 1400 kg/m3. LWFC is appropriately adapted for extrusion-based 3D printing in the experimental program by incorporating a small amount of nanopowder (replacing 2% of cement mass) for increased yield shear stress, and calcium sulfoaluminate cement replacing 10% of cement mass for improved thixotropy in the fresh state. Accordingly, this raises the yield stress to 347–812 Pa for 700–1400 kg/m3 LWFC compared to static yield stress below 100 Pa of conventional LWFC, improves thixotropic performance in terms of the rate of reflocculation (Rthix 0.21–3.15 Pa/s) and rate of structuration (Athix 0.06–1.02 Pa/s), viscosity (2.5–3.4 Pa⋅s), and elastic shear modulus evolution. Foam volume is found to significantly influence the rheological properties. To analyse the constructability, shape retention and buildability are investigated, resulting in up to 15 deposited filament layers to be reached in a buildability test. Lastly, a practical example is presented whereby a façade element is printed with 3DP-LWFC at a wet density less than 1000 kg/m3, yielding a lightweight element with buoyant characteristics that further expands the application potential of 3D concrete printing.

Self-similar length-displacement scaling achieved by scale-dependent growth processes: Evidence from the Atacama Fault System

The complex process of tip-propagation and growth of natural faults remains poorly understood. We analyse field structural data of strike-slip faults from the Atacama Fault System using fracture mechanics theory to depict the mechanical controls of fault growth in crystalline rocks. We calculate the displacement-length relationship of faults developed in the same rock type and tectonic regime, covering a range of five orders of magnitude, showing a linear scaling defined by dmax=0.0337L1.02. A multiple linear regression approach based on the cohesive end zone (CEZ) crack model was formulated to estimate the range of possible effective elastic moduli, cohesive endzone lengths, stress drops, and fracture energies from displacement distributions mapped on natural faults. Our results challenge the existent paradigm wherein the self-similarity of fault growth is only achieved under the condition of invariable stresses and elastic properties. We propose a model of self-similar fault growth with scale-dependent evolution of shear modulus, cohesive end zone length and stress drop. These results also have implications for determination of stress drop for small earthquakes that are consistent with recent advances in observational seismology.

Real-time in situ observation of shear modulus evolution during Ostwald ripening of colloidal crystallization

Real-time in situ observation of evolution of shear modulus during the crystallization and ripening of colloidal particles suspensions was conducted by using reflection spectrum and torsional resonance spectroscopy simultaneously. According to the structural information obtained by reflection spectrum, after the completion of nucleation, the crystallization can be basically divided into four stages: crystallization-dominated stage, crystallization and ripening coexistence stage, ripening-dominated stage and crystallization completion stage. Colloidal particles volume fraction significantly affects the duration of each stage. Our experiments showed that the ripening process is the main cause for the improvement of the mechanical strength (the increase of shear modulus). This observation is supposed to be associated with the diminishing of crystal interface as the result of the increase in crystallites size and the decrease in crystallites number during the ripening process. In addition, a theoretical analysis is given briefly on the softening effect induced by nonaffinity of disordered particles in interface region.

Isothermal Microphase Separation Kinetics in Blends of Asymmetric Styrene–Isoprene Block Copolymers

The microphase separation behavior of Kraton D1161, a highly asymmetric styrene–isoprene triblock and diblock copolymer mixture often used as the base polymer in pressure-sensitive adhesives, was studied using time-resolved small-angle X-ray scattering (SAXS) and oscillatory rheological analysis during temperature ramp and temperature quench experiments. The total scattering intensity obtained from SAXS was represented as a sum of the scattering from disordered and ordered polystyrene domains. A modified Percus–Yevick hard-sphere model was used to describe the scattering from disordered spheres, while Gaussian functions were used to model scattering from ordered domains. The temperature- and time-dependent SAXS experiments suggest a sequence of four stages in the development of the copolymer morphology during the isothermal phase separation kinetics experiments. Avrami analysis of the shear modulus evolution following a temperature quench indicates that domain growth is preceded by nucleation process. The ordering of polystyrene domains as observed during rheological and SAXS analysis is dominated by polymer chain mobility, which resulted in slower kinetics at lower temperatures.

Mechanical Behavior of Sandwich Composites Under Three-Point Bending Fatigue

The mechanical behavior of sandwich composite materials in fatigue loading is investigated. Fatigue tests in three-point bending were conducted on two types of sandwich materials, [04] and [0/902/0]. The rupture mode observed on tested specimens showed a debond between the core and skins, as well as cracks in the core at 45∙ to the neutral axis of sandwich. Degradation of the rigidity modulus in fatigue was determined from the deflection equation for the two sandwiches. The experiments revealed that the modulus of the [04] sandwich degraded faster than that of [0/902/0]. The evolution of shear modulus in fatigue of both sandwiches is also described analytically using exponential and polynomial models.

Using centrifuge tests data to identify the dynamic soil properties: Application to Fontainebleau sand

Knowledge of the dynamic properties of the soil is of great importance as the dynamic shear modulus and damping ratio are necessary input data in finite element modeling programs. This paper presents a post-processing strategy to identify the shear modulus and damping ratio vs. shear strain curves using the experimental results of a dynamic centrifuge program. Application is presented for the Fontainebleau sand. The proposed methodology is fast, robust and able to capture the nonlinear hysteretic behavior of the material. Based on the results, specific parameters for the Fontainebleau sand are identified for the empirical equation of shear modulus and damping ratio proposed by Ishibashi and Zhang [1]. It is found that confining pressure has an important influence on both shear modulus evolution and damping ratio.

Are the dynamics of a glass embedded in its elastic properties?

The low temperature dynamics of glass are critically important for many high-tech applications. According to the elastic theory of the glass transition, the dynamics of glass are controlled by the evolution of shear modulus. In particular, the elastic shoving model expresses dynamics in terms of an activation energy required to shove aside the surrounding atoms. Here, we present a thorough test of the shoving model for predicting the low temperature dynamics of an oxide glass system. We show that the nonequilibrium viscosity of glass is governed by additional factors beyond changes in shear modulus.

Multiscale Modeling Approach toward the Prediction of Viscoelastic Properties of Polymers.

We report a multiscale modeling approach to study static and dynamical properties of polymer melts at large time and length scales. We use a bottom-up approach consisting of deriving coarse-grained models from an atomistic description of the polymer melt. We use the iterative Boltzmann inversion (IBI) procedure and a pressure-correction function to map the thermodynamic conditions of the atomistic configurations. The coarse-grained models are incorporated in the dissipative particle dynamics (DPD) method. The thermodynamic, structural, and dynamical properties of the cis-1,4-polybutadiene melt are very well reproduced by the coarse-grained DPD models with a significative computational gain. We complete this study by addressing the challenging question of the investigation of the shear modulus evolution. As expected from experiments, the stress correlation functions show behaviors that are dependent on the molecular weights defining unentangled and weakly entangled polymer melts.

A small-strain model to simulate the curing of thermosets

This contribution presents a newly developed phenomenological model to describe the curing process of thermosets undergoing small strain deformations. The governing equations are derived from a number of physical and chemical presuppositions and details of the numerical implementation within the finite element method are given. The curing of thermosets is a very complex process involving a series of chemical reactions which result in the conversion of liquid low molecular weight monomer mixtures into highly cross-linked solid macromolecular structures. This phase transition from a viscous fluid to a viscoelastic solid can be modelled by a constitutive relation which is based on a temporal evolution of shear modulus and relaxation time. Some numerical examples demonstrate the capability of the model to correctly represent the evolution of elastic and inelastic material properties as well as the volume shrinkage taking place during the curing process.

Viscoelastic Micellar Solutions in Nonionic Fluorinated Surfactant Systems

The formation and rheological behavior of a viscoelastic wormlike micellar solution in an aqueous solution of a nonionic fluorinated surfactant, perfluoroalkyl sulfonamide ethoxylate, of structure C8F17SO2N(C3H7)(CH2CH2O)10H was studied. Temperature-induced viscosity growth is observed even at low-surfactant concentration (approximately 1 wt %), and viscosity reaches the maximum at a temperature T(eta)-max. Upon successive increases in the temperature, the viscosity decreases, and ultimately a phase separation occurs. Small-angle X-ray scattering (SAXS) measurements confirm the presence of cylindrical aggregates at low temperature, which undergo continuous one-dimensional growth with increasing temperature, and ultimately, an indication of a slight lamellarlike structural pattern is observed, which probably comes from the formation of micellar joints or branching. Such changes in the microstructure result in a decrease in the viscosity and stress-relaxation time, while the network structure is retained; the trends in the evolution of shear modulus (Go) and relaxation time (tauR) with temperature are in agreement with this. With increased surfactant concentration, the temperature corresponding to the viscosity maximum (T eta-max) in the temperature-viscosity curve shifts to lower values, and the viscosity at temperatures below or around T eta-max increases sharply. A viscoelastic solution with Maxwellian-type dynamic rheological behavior at low-shear frequency is formed, which is typical of entangled wormlike micelles. Rheological parameters, eta(o) and Go, show scaling relationships with the surfactant concentrations with exponents slightly greater than the values predicted by the living-polymer model, but the exponent of tauR is in agreement with the theory. Dynamic light-scattering measurements indicate the presence of fast relaxation modes, associated with micelles, and medium and slow modes, associated with transient networks. The disappearance of the slow mode and the predominance of the medium mode as the temperature increases support the conclusions derived from SAXS and rheometry.

Quantifying thermomechanical fatigue of light-metal-matrix composites by mechanical spectroscopy

This article reviews recent progress in understanding the stress-relaxation mechanisms in metal-matrix composites (MMCs) subjected to thermomechanical fatigue. Mechanical loss, dynamic shear modulus, and permanent torsional-strain measurements have been performed with forced oscillations during thermal cycling. A transient mechanical-loss maximum, which is absent in the monolithic material, appears during cooling. It has been attributed to the development of plastic zones around the reinforcements by dislocation generation and motion, which result from the differential thermal contraction of the matrix and reinforcement. This damping maximum is strongly dependent on both measurement and material parameters. The reversible shear-modulus evolution during thermal cycling suggests that no interfacial debonding occurs. In unalloyed matrices, extended thermal-stress-induced pleasicity occurs, leading to a plateau in the shear modulus, which is recovered at low temperatures by plastic-zone overlapping and matrix strain hardening. Simultaneously measured strain-temperature loops exhibit both reversible and permanent plasticity during thermal cycling (strain ratcheting).

Ageing effects in the shear modulus of soils

Results of in situ tests of shear wave propagation are presented and analysed to evaluate the effects of geologic processes, stress history and ageing on the shear modulus of soils. These results show clear tendencies of soil structures to get stiffer as consequence of ageing or surcharging to high stress levels. The evolution of shear modulus, as verified by these results, is significant as it changes the response of soil deposits to seismic loadings.

Mechanical spectroscopy of thermal stress relaxation at metal–ceramic interfaces in Aluminium-based composites

The micromechanisms of thermal stress relaxation in aluminum-based metal-matrix composites (MMCs) have been investigated by mechanical loss and dynamic shear modulus measurements during thermal cycling between 100 and 500 K. A transient mechanical loss maximum, which is absent in the monolithic material, appears during cooling. This damping maximum is strongly dependent on the measurement parameters: oscillation frequency, oscillation amplitude and cooling rate. In addition, it increases with the volumetric reinforcement content and decreases if the matrix strength is improved. The shear modulus evolution during thermal cycling shows that no detectable interfacial debonding occurs. Compared with alloyed MMCs, Al4N-based MMCs show the highest damping maximum simultaneously with a plateau in the elastic shear modulus. The mechanical loss maximum is attributed to dislocation generation and motion near the interfaces, resulting from the differential thermal contraction of matrix and reinforcement. A new model is proposed which describes this specific mechanical behavior of MMCs in terms of the development of microplastic zones in the matrix near the metal–ceramic interfaces.

Evolution of shear modulus and fabric during shear deformation : Chen, Y C; Hung, H Y Soils FoundV31, N4, Dec 1991, P148–160

Evolution of shear modulus and fabric during shear deformation : Chen, Y C; Hung, H Y Soils FoundV31, N4, Dec 1991, P148–160

Evolution of Shear Modulus and Fabric During Shear Deformation

Numerical studies of shear modulus and fabric for sphere assemblies were performed by a discrete element code, TRUBAL. Results of numerical experiments were compared with physical experiments. In general, numerical experiments simulate the stress-strain behavior and shear modulus of physical results quite well both qualitatively and quantitatively. Shear modulus has a close relationship with the coordination number. After a cycle of loading and unloading, there is an induced anisotropic fabric and are locked-in inter-particle shear forces which reflect the previous stress history. This is also reflected in a decrease in both the shear modulus and the coordination number. During reshear locked-in inter-particle shear forces would influence the behavior of shear modulus. When resheared in the previous direction inter-particle shear forces decrease first which results in an increase of shear modulus in the initial portion of loading. While resheared opposite to the previous direction initially high inter-particle shear forces would decrease the shear modulus.

A fatigue crack growth model for fibre-reinforced metal-matrix composites: Chan, K.S. Fatigue Fract. Eng. Mater. Struct. 1990 13, (2), 171–183

The micromechanisms of thermal stress relaxation in aluminum-based metal-matrix composites (MMCs) have been investigated by mechanical loss and dynamic shear modulus measurements during thermal cycling between 100 and 500 K. A transient mechanical loss maximum, which is absent in the monolithic material, appears during cooling. This damping maximum is strongly dependent on the measurement parameters: oscillation frequency, oscillation amplitude and cooling rate. In addition, it increases with the volumetric reinforcement content and decreases if the matrix strength is improved. The shear modulus evolution during thermal cycling shows that no detectable interfacial debonding occurs. Compared with alloyed MMCs, Al4N-based MMCs show the highest damping maximum simultaneously with a plateau in the elastic shear modulus. The mechanical loss maximum is attributed to dislocation generation and motion near the interfaces, resulting from the differential thermal contraction of matrix and reinforcement. A new model is proposed which describes this specific mechanical behavior of MMCs in terms of the development of microplastic zones in the matrix near the metal–ceramic interfaces.