Thermodynamic consistent formulation for the multiphysics of a brittle ductile lithosphere - semi-brittle semi-ductile deformation and damage rheology

2020 ◽  
Author(s):  
Mauro Cacace ◽  
Antoine Jacquey
Keyword(s):  
Mechanical Response ◽  
Fluid Phase ◽  
Material Behavior ◽  
Ductile Deformation ◽  
Porous Rocks ◽  
Nonlinear Feedback ◽  
Rate Dependent ◽  
Experimental Rock ◽  
Dissipative Material ◽  
Damage Rheology

<p>We provide details on a novel formulation derived to describe the multiphysics controlling the deformation of porous rock under lithospheric conditions. The theory is developed consistent with the principles of thermodynamics and enables to capture the behaviour of porous rocks at the transition from frictional brittle behaviour to ductile viscous behaviour. It also accounts for the nonlinear feedback mechanisms derived from energetic consideration for the bi-phasic fluid-rock matrix system.</p><p>The formulation depicts a consistent, implicit visco-elasto-(visco)plastic rheology accounting for both a volumetric and a deviatoric response to applied loads, thereby avoiding the use of, the commonly assumed, plasticity limiter concept. The overstress plastic formulation introduces rate dependent mechanical behavior, an aspect that is consistent with experimental rock mechanics evidence and is also demonstrated to improve numerical stability when addressing problems related to plastic strain accumulation even in the absence of energetic feedbacks.</p><p>The introduction of a damage rheology permits to account for microstructural processes responsible for brittle-like material weakening and rate-dependent dissipative material behavior. The presence of a fluid phase is considered via a dynamic porosity, the evolution of which is demonstrated to primarily control the volumetric mechanical response of the stressed rock during incremental loading.</p><p>The above formulation has been integrated in a massively parallel, open source numerical framework with interfaces to state of the art HPC clusters. The results of a scalability and profile performance analysis on multi-core supercomputer are presented alongside with dedicated applications describing lithospheric rock deformation under different confining conditions as well as the bulk macroscopic material response recorded by laboratory experiments under triaxial conditions.</p>

scholarly journals A new methodology to simulate subglacial deformation of water saturated granular material

2015 ◽  
Vol 9 (4) ◽  
pp. 3617-3660 ◽  
Author(s):  
A. Damsgaard ◽  
D. L. Egholm ◽  
J. A. Piotrowski ◽  
S. Tulaczyk ◽  
N. K. Larsen ◽  
...  
Keyword(s):  
Mechanical Response ◽  
Fluid Pressure ◽  
Fluid Phase ◽  
Large Degree ◽  
Numerical Approach ◽  
Unconsolidated Sediments ◽  
Close Monitoring ◽  
Stick Slip ◽  
Rate Dependent ◽  
Water Saturated

Abstract. The dynamics of glaciers are to a large degree governed by processes operating at the ice–bed interface, and one of the primary mechanisms of glacier flow over soft unconsolidated sediments is subglacial deformation. However, it has proven difficult to constrain the mechanical response of subglacial sediment to the shear stress of an overriding glacier. In this study, we present a new methodology designed to simulate subglacial deformation using a coupled numerical model for computational experiments on grain-fluid mixtures. The granular phase is simulated on a per-grain basis by the discrete element method. The pore water is modeled as a compressible Newtonian fluid without inertia. The numerical approach allows close monitoring of the internal behavior under a range of conditions. The rheology of a water-saturated granular bed may include both plastic and rate-dependent dilatant hardening or weakening components, depending on the rate of deformation, the material state, clay mineral content, and the hydrological properties of the material. The influence of the fluid phase is negligible when relatively permeable sediment is deformed. However, by reducing the local permeability, fast deformation can cause variations in the pore-fluid pressure. The pressure variations weaken or strengthen the granular phase, and in turn influence the distribution of shear strain with depth. In permeable sediments the strain distribution is governed by the grain-size distribution and effective normal stress and is typically on the order of tens of centimeters. Significant dilatant strengthening in impermeable sediments causes deformation to focus at the hydrologically more stable ice–bed interface, and results in a very shallow cm-to-mm deformational depth. The amount of strengthening felt by the glacier depends on the hydraulic conductivity at the ice–bed interface. Grain-fluid feedbacks can cause complex material properties that vary over time, and which may be of importance for glacier stick-slip behavior.

scholarly journals A nonlinear strain-rate dependent constitutive model for uncured rubber materials under large deformation

2020 ◽  
Vol 37 ◽  
pp. 118-125
Author(s):  
Weihua Zhou ◽  
Changqing Fang ◽  
Huifeng Tan ◽  
Huiyu Sun
Keyword(s):  
Constitutive Model ◽  
Large Deformation ◽  
Mechanical Response ◽  
Uniaxial Tensile ◽  
Hysteresis Phenomenon ◽  
Mechanical Behaviors ◽  
Nonlinear Constitutive Model ◽  
Rate Dependent ◽  
Parallel Networks ◽  
Non Gaussian

Abstract Uncured rubber possesses remarkable hyperelastic and viscoelastic properties while it undergoes large deformation; therefore, it has wide application prospects and attracts great research interests from academia and industry. In this paper, a nonlinear constitutive model with two parallel networks is developed to describe the mechanical response of uncured rubber. The constitutive model is incorporated with the Eying model to describe the hysteresis phenomenon and viscous flow criterion, and the hyperelastic properties under large deformation are captured by a non-Gaussian chain molecular network model. Based on the model, the mechanical behaviors of hyperelasticity, viscoelasticity and hysteresis under different strain rates are investigated. Furthermore, the constitutive model is employed to estimate uniaxial tensile, cyclic loading–unloading and multistep tensile relaxation mechanical behaviors of uncured rubber, and the prediction results show good agreement with the test data. The nonlinear mechanical constitutive model provides an efficient method for predicting the mechanical response of uncured rubber materials.

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

Strain rate dependent dynamic mechanical response of bainitic multiphase steels

2019 ◽  
Vol 745 ◽  
pp. 279-290 ◽  
Author(s):  
Behnam Shakerifard ◽  
Jesus Galan Lopez ◽  
Mari Carmen Taboada Legaza ◽  
Patricia Verleysen ◽  
Leo A.I. Kestens
Keyword(s):  
Strain Rate ◽  
Mechanical Response ◽  
Dynamic Mechanical ◽  
Rate Dependent ◽  
Multiphase Steels

scholarly journals Experimental and Numerical Characterization of the Cyclic Thermomechanical Behavior of a High Temperature Forming Tool Alloy

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Sean B. Leen ◽  
Aditya Deshpande ◽  
Thomas H. Hyde
Keyword(s):  
High Temperature ◽  
Life Prediction ◽  
Material Constant ◽  
Superplastic Forming ◽  
Material Model ◽  
Fatigue Tests ◽  
Material Behavior ◽  
Future Application ◽  
Rate Dependent ◽  
Numerical Characterization

This paper describes high temperature cyclic and creep relaxation testing and modeling of a high nickel-chromium material (XN40F) for application to the life prediction of superplastic forming (SPF) tools. An experimental test program to characterize the high temperature cyclic elastic-plastic-creep behavior of the material over a range of temperatures between 20°C and 900°C is described. The objective of the material testing is the development of a high temperature material model for cyclic analyses and life prediction of SPF dies for SPF of titanium aerospace components. A two-layer viscoplasticity model, which combines both creep and combined isotropic-kinematic plasticity, is chosen to represent the material behavior. The process of material constant identification for this model is presented, and the predicted results are compared with the rate-dependent (isothermal) experimental results. The temperature-dependent material model is furthermore applied to simulative thermomechanical fatigue tests, designed to represent the temperature and stress-strain cycling associated with the most damaging phase of the die cycle. The model is shown to give good correlation with the test data, thus vindicating future application of the material model in thermomechanical analyses of SPF dies for distortion and life prediction.

A Microstructure-Level Material Model for Simulating the Machining of Carbon Nanotube Reinforced Polymer Composites

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Ashutosh Dikshit ◽  
Johnson Samuel ◽  
Richard E. DeVor ◽  
Shiv G. Kapoor
Keyword(s):  
Carbon Nanotube ◽  
Weight Fraction ◽  
Material Model ◽  
Material Behavior ◽  
Compression Tests ◽  
Linear Elastic ◽  
Rate Dependent ◽  
Wide Range ◽  
Parametrization Scheme ◽  
Fraction Length

A continuum-based microstructure-level material model for simulation of polycarbonate carbon nanotube (CNT) composite machining has been developed wherein polycarbonate and CNT phases are modeled separately. A parametrization scheme is developed to characterize the microstructure of composites having different loadings of carbon nanotubes. The Mulliken and Boyce constitutive model [2006, “Mechanics of the Rate Dependent Elastic Plastic Deformation of Glassy Polymers from Low to High Strair Rates,” Int. J. Solids Struct., 43(5), pp. 1331–1356] for polycarbonate has been modified and implemented to capture thermal effects. The CNT phase is modeled as a linear elastic material. Dynamic mechanical analyzer tests are conducted on the polycarbonate phase to capture the changes in material behavior with temperature and strain rate. Compression tests are performed over a wide range of strain rates for model validation. The model predictions for yield stress are seen to be within 10% of the experimental results for all the materials tested. The model is used to study the effect of weight fraction, length, and orientation of CNTs on the mechanical behavior of the composites.

Osmo-inelastic response of the intervertebral disc annulus fibrosus tissue

2020 ◽  
Vol 234 (9) ◽  
pp. 1000-1010
Author(s):  
Amil Derrouiche ◽  
Ameni Zaouali ◽  
Fahmi Zaïri ◽  
Jewan Ismail ◽  
Zhengwei Qu ◽  
...  
Keyword(s):  
Intervertebral Disc ◽  
Annulus Fibrosus ◽  
Mechanical Response ◽  
Rate Sensitivity ◽  
Image Correlation ◽  
Inelastic Response ◽  
Full Field ◽  
Osmotic Effect ◽  
Rate Dependent ◽  
Optical Strain

The aim of this article is to provide some insights on the osmo-inelastic response under stretching of annulus fibrosus of the intervertebral disc. Circumferentially oriented specimens of square cross section, extracted from different regions of bovine cervical discs (ventral-lateral and dorsal-lateral), are tested under different strain-rates and saline concentrations within normal range of strains. An accurate optical strain measuring technique, based upon digital image correlation, is used in order to determine the full-field displacements in the lamellae and fibers planes of the layered soft tissue. Annulus stress–stretch relationships are measured along with full-field transversal strains in the two planes. The mechanical response is found hysteretic, rate-dependent and osmolarity-dependent with a Poisson’s ratio higher than 0.5 in the fibers plane and negative (auxeticity) in the lamellae plane. While the stiffness presents a regional-dependency due to variations in collagen fibers content/orientation, the strain-rate sensitivity of the response is found independent on the region. A significant osmotic effect is found on both the auxetic response in the lamellae plane and the stiffness rate-sensitivity. These local experimental observations will result in more accurate chemo-mechanical modeling of the disc annulus and a clearer multi-scale understanding of the disc intervertebral function.

Influence of material inhomogeneity on the mechanical response of a tempered martensite steel

2017 ◽  
Vol 231 (1-2) ◽  
pp. 14-22 ◽  
Author(s):  
M Li ◽  
FW Sun ◽  
RA Barrett ◽  
E Meade ◽  
DF Li ◽  
...  
Keyword(s):  
Heat Affected Zone ◽  
Mechanical Response ◽  
Voronoi Tessellation ◽  
Void Formation ◽  
Material Point ◽  
Contributory Factor ◽  
Tempered Martensite ◽  
Material Inhomogeneity ◽  
Rate Dependent ◽  
Intercritical Region

Failure in steel weldments operating at high temperatures often occurs in the heat-affected zone adjacent to the weld. Such failures can be a result of material inhomogeneity within the heat-affected zone and in the case of tempered martensite steels have been linked with regions of untransformed α (ferrite) phase or over-tempered martensite within the intercritical region of the heat-affected zone. In this work, two-dimensional Voronoi tessellation is used to construct polygonal Voronoi cells to represent the microstructure of the heat-affected zone of a weld in a tempered martensite steel. The Voronoi construction is treated as a representative volume element of the material and is discretised by 8-node linear brick elements, with periodic boundary conditions. The lattice orientation at each material point is specified by three Euler angles, which are assumed to be randomly distributed, to represent the initial lack of texture in the intercritical region of the heat-affected zone. The constitutive response is represented by a nonlinear, rate-dependent, finite-strain crystal plasticity model. The results indicate that small amounts of ferrite can induce significant enhancements in stress and inelastic deformation at the interface of the ferrite and martensite grains. This localisation of stress and strain may be critical for microcrack and/or void formation and may be a contributory factor to Type IV cracking.

Effect of Structure on Response of a Three-Dimensional-Printed Photopolymer-Particulate Composite Under Intermediate Strain Rate Loading

2020 ◽  
Vol 87 (11) ◽  
Author(s):  
Amirreza Keyhani ◽  
Min Zhou
Keyword(s):  
Strain Rate ◽  
Mechanical Response ◽  
Local Heating ◽  
Three Dimensional ◽  
Particulate Composite ◽  
Deformation Energy ◽  
Material Behavior ◽  
Localized Deformation ◽  
Failure Initiation ◽  
Lagrangian Finite Element

Abstract The thermo-mechanical response of an additively manufactured photopolymer-particulate composite under conditions of macroscopic uniaxial compression without lateral confinement at overall strain rates of 400–2000 s−1 is studied. The material has a direct-ink-written unidirectional structure. Computations are performed to quantify the effects of microstructure attributes including anisotropy, defects, and filament size on localized deformation, energy dissipations, and temperature rises. To this effect, an experimentally informed Lagrangian finite element framework is used, accounting for finite-strain elastic–plastic deformation, strain-rate effect, failure initiation and propagation, post-failure internal contact and friction, heat generation due to friction and inelastic bulk deformation, and heat conduction. The analysis focuses on the material behavior under overall compression. Despite relatively low contribution to overall heating, friction is localized at fracture sites and plays an essential role in the development of local temperature spikes unknown as hotspots. The microstructural attributes are found to significantly affect the development of the hotspots, with local heating most pronounced when loading is transverse to the filaments or when the material has higher porosities, stronger inter-filament junctions, or smaller filament sizes. Samples with smaller filament sizes undergo more damage, exhibit higher frictional dissipation, and develop larger hotspots that occur primarily at failure sites.

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