scholarly journals Numerical Modeling of Temperature Effect on Tensile Strength of Granitic Rock

2021 ◽  
Vol 11 (10) ◽  
pp. 4407
Author(s):  
Timo Saksala
Keyword(s):  
Tensile Strength ◽  
Temperature Effect ◽  
Curie Point ◽  
Granitic Rock ◽  
Critical Time ◽  
Slow Heating ◽  
Single Element ◽  
Target Temperature ◽  
Time Step ◽  
Mass Scaling

The aim of this paper is to numerically predict the temperature effect on the tensile strength of granitic rock. To this end, a numerical approach based on the embedded discontinuity finite elements is developed. The underlying thermo-mechanical problem is solved with a staggered method marching explicitly in time while using extreme mass scaling, allowed by the quasi-static nature of the slow heating of a rock sample to a uniform target temperature, to increase the critical time step. Linear triangle elements are used to implement the embedded discontinuity kinematics with two intersecting cracks in a single element. It is assumed that the quartz mineral, with its strong and anomalous temperature dependence upon approaching the α-β transition at the Curie point (~573 °C), in granitic rock is the major factor resulting in thermal cracking and the consequent degradation of tensile strength. Accordingly, only the thermal expansion coefficient of quartz depends on temperature in the present approach. Moreover, numerically, the rock is taken as isotropic except for the tensile strength, which is unique for each mineral in a rock. In the numerical simulations mimicking the experimental setup on granitic numerical rock samples consisting of quartz, feldspar and biotite minerals, the sample is first heated slowly to a target temperature below the Curie point. Then, a uniaxial tension test is numerically performed on the cooled down sample. The simulations demonstrate the validity of the proposed approach as the experimental deterioration of the tensile strength of the rock is predicted with agreeable accuracy.

3D Numerical Prediction of Thermal Weakening of Granite under Tension

Geosciences ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 10
Author(s):  
Timo Saksala
Keyword(s):  
Tensile Strength ◽  
Rock Fracture ◽  
Critical Time ◽  
Heterogeneous Material ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Numerical Approach ◽  
Numerical Prediction ◽  
Time Step ◽  
Mass Scaling

This paper deals with numerical prediction of temperature (weakening) effects on the tensile strength of granitic rock. A 3D numerical approach based on the embedded discontinuity finite elements is developed for this purpose. The governing thermo-mechanical initial/boundary value problem is solved with an explicit (in time) staggered method while using extreme mass scaling to increase the critical time step. Rock fracture is represented by the embedded discontinuity concept implemented here with the linear (4-node) tetrahedral elements. The rock is modelled as a linear elastic (up to fracture by the Rankine criterion) heterogeneous material consisting of Quartz, Feldspar and Biotite minerals. Due to its strong and anomalous temperature dependence upon approaching the α-β transition at the Curie point (~573 °C), only Quartz in the numerical rock depends on temperature in the present approach. In the numerical testing, the sample is first volumetrically heated to a target temperature. Then, the uniaxial tension test is performed on the cooled down sample. The simulations demonstrate the validity of the proposed approach as the experimental deterioration, by thermally induced cracking, of the rock tensile strength is predicted with a good accuracy.

Increasing the critical time step: micro-inertia, inertia penalties and mass scaling

2011 ◽  
Vol 47 (6) ◽  
pp. 657-667 ◽  
Author(s):  
Harm Askes ◽  
Duc C. D. Nguyen ◽  
Andy Tyas
Keyword(s):  
Critical Time ◽  
Time Step ◽  
Mass Scaling ◽  
Critical Time Step

scholarly journals A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

2021 ◽  
Author(s):  
Chennakesava Kadapa
Keyword(s):  
Wave Propagation ◽  
Wave Speed ◽  
Critical Time ◽  
Incompressible Material ◽  
Implicit Scheme ◽  
Bulk Wave ◽  
Lumped Mass ◽  
Time Step ◽  
Material Models ◽  
Shear Wave Speed

AbstractThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

Temperature effect on the tensile behaviors of carbon/polyimide composite laminate

2016 ◽  
Vol 231 (24) ◽  
pp. 4592-4602 ◽  
Author(s):  
Liang Li ◽  
Purong Jia ◽  
Wenge Pan
Keyword(s):  
Temperature Effect ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Thermomechanical Coupling ◽  
Single Element ◽  
Element Analysis ◽  
Open Hole ◽  
Dimensional Finite Element ◽  
Different Temperatures ◽  
Three Dimensional Finite Element

Experimental and numerical investigations were carried out to study the temperature effect on the stiffness, strength, and failure behaviors of carbon/polyimide composite laminates. Both unnotched laminates and open-hole laminates were tested under tension load at three temperatures (room temperature, 200 ℃, and 250 ℃). A three-dimensional finite element analysis was carried out to study the thermomechanical coupling behavior in the notched laminate. The model considers each layer and interface as a single element in the thickness direction so that in-plane stress and interlaminar stress could be analyzed in the model. The stresses around the open-hole changing characteristics with the temperature and tensile loading have been discussed in detail. Failure analysis was carried out to predict the residual strength of the notched laminates at different temperatures. Compared to the experimental data, the numerical results have an excellent agreement.

scholarly journals Assessment of Susceptibility to Liquefaction of Saturated Road Embankment Subjected to Dynamic Loads

2014 ◽  
Vol 36 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Anna Borowiec ◽  
Krzysztof Maciejewski
Keyword(s):  
Factor Of Safety ◽  
Stress Component ◽  
Critical Time ◽  
Water Reservoir ◽  
Constitutive Relationship ◽  
Plastic Behavior ◽  
Shear Stresses ◽  
Time Step ◽  
The Road ◽  
Liquefaction Susceptibility

Abstract Liquefaction has always been intensely studied in parts of the world where earthquakes occur. However, the seismic activity is not the only possible cause of this phenomenon. It may in fact be triggered by some human activities, such as constructing and mining or by rail and road transport. In the paper a road embankment built across a shallow water reservoir is analyzed in terms of susceptibility to liquefaction. Two types of dynamic loadings are considered: first corresponding to an operation of a vibratory roller and second to an earthquake. In order to evaluate a susceptibility of soil to liquefaction, a factor of safety against triggering of liquefaction is used (FSTriggering). It is defined as a ratio of vertical effective stresses to the shear stresses both varying with time. For the structure considered both stresses are obtained using finite element method program, here Plaxis 2D. The plastic behavior of the cohesionless soils is modeled by means of Hardening Soil (HS) constitutive relationship, implemented in Plaxis software. As the stress tensor varies with time during dynamic excitation, the FSTriggering has to be calculated for some particular moment of time when liquefaction is most likely to occur. For the purposes of this paper it is named a critical time and established for reference point at which the pore pressures were traced in time. As a result a factor of safety distribution throughout embankment is generated. For the modeled structure, cyclic point loads (i.e., vibrating roller) present higher risk than earthquake of magnitude 5.4. Explanation why considered structure is less susceptible to earthquake than typical dam could lay in stabilizing and damping influence of water, acting here on both sides of the slope. Analogical procedure is applied to assess liquefaction susceptibility of the road embankment considered but under earthquake excitation. Only the higher water table is considered as it is the most unfavorable. Additionally the modified factor of safety is introduced, where the dynamic shear stress component is obtained at a time step when its magnitude is the highest - not necessarily at the same time step when the pore pressure reaches its peak (i.e., critical time). This procedure provides a greater margin of safety as the computed factors of safety are smaller. Method introduced in the paper presents a clear and easy way to locate liquefied zones and estimate liquefaction susceptibility of the subsoil - not only in the road embankment.

Numerical Investigation of Combustion Instabilities in a Single Element Lean Direct Inject (LDI) Combustor Using Flamelet Based Approaches

2019 ◽  
Author(s):  
Saurabh Patwardhan ◽  
Pravin Nakod ◽  
Stefano Orsino ◽  
Carlo Arguinzoni
Keyword(s):  
Experimental Data ◽  
Equivalence Ratio ◽  
Single Element ◽  
Pressure Amplitude ◽  
Combustion Instabilities ◽  
Time Step ◽  
Impedance Boundary ◽  
Combustion Models ◽  
Flamelet Generated Manifold ◽  
Simulation Results

Abstract In this paper, high-fidelity large eddy simulations (LES) along with flamelet based combustion models are assessed to predict combustion dynamics in low-emissions gas turbine combustor. A model configuration of a single element lean-direct-injection (LDI) combustor from Purdue University [1] is used for the validation of simulation results. Two combustion models based on the flamelet concept, i.e., steady diffusion flamelet (SDF) model and flamelet generated manifold (FGM) model are employed to predict combustion instabilities. Simulations are carried out for two equivalence ratios of φ = 0.6, and 0.4 and the results in the form of mode shapes, peak to peak pressure amplitude and power spectrum density (PSD) are compared with the experimental data of Huang et al. [1]. The effect of variation in the time step size for transient simulations is also studied. The time step sizes corresponding to Acoustic Courant numbers of 4, 8 and 16 are tested. Further, two numerical solver options, i.e., pressure based segregated solver and pressure based coupled solver are used in understanding their effect on the solution convergence regarding the number of time steps required to reach the limit cycle of the pressure oscillations. An additional test for reducing the overall simulation time is explored using a truncated (half) calculation domain and applying an appropriate acoustic impedance boundary condition at the truncated location. The simulation results from this test for the equivalence ratio of φ = 0.6 are compared with the simulation results from the corresponding full domain test. Overall, the simulation results compare well with the experimental data and trends are captured accurately. A clear dominant acoustic mode of 4L is observed for the equivalence ratio of 0.6 that compares well with the experimental data. For the equivalence ratio of 0.4, simulation results show that there is no dominant frequency and the energy is distributed among the first five modes. It is consistent with the observations in the experiments. Both combustion models (SDF and FGM) used in this study capture the combustion instabilities accurately. It builds confidence in flamelet based combustion models for the use in combustion instability modeling which is traditionally done using finite rate chemistry models based on reduced kinetics.

Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory

1978 ◽  
Vol 45 (2) ◽  
pp. 371-374 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Transient Analysis ◽  
Critical Time ◽  
Unconditional Stability ◽  
Time Step ◽  
Explicit Finite Element ◽  
New Family ◽  
Critical Time Step ◽  
Analysis Stability

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.

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