Interlaced Characterization and Calibration of Elastoplastic Constitutive Models
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An incremental theory and numerical procedure to analyze a three-dimensional thermoelastoplastic structure subjected to high temperature, surface heat flux, and volume heat supply as well as mechanical loadings are presented. Heat conduction equations and equilibrium equations are derived by assuming a specific form of incremental free energy, entropy, stresses and heat flux together with the first and second laws of thermodynamics, von Mises yield criteria and Prandtl-Reuss flow rule. The finite element discretization using the linear isotropic three-dimensional element for the space domain and a difference operator corresponding to a linear variation of temperature within a small time increment for the time domain lead to systematic solutions of temperature distribution and displacement and stress fields. Various boundary conditions such as insulated surfaces and convection through uninsulated surface can be easily treated. To demonstrate effectiveness of the present formulation a number of example problems are presented.
The following topics are discussed in this paper: (1) the basic interactive nature of classical elasto-plasticity and a redefinition of elastic and plastic processes that facilitates numerical calculations, (2) generalized mid-point or end-point algorithms to determine the stress increment in an elastic-plastic solid from a given strain increment, (3) an endochronic (internal time) rate theory of time-independent plasticity which encompasses various multiple-yield-surface theories and nonlinear kinematic hardening theories as its specializations, and (4) comments on finite element and boundary element methods for solving boundary value problems in elasto-plasticity.
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PLAN2D is FORTRAN computer program for plastic analysis of planar frame structures. Given structure and loading pattern as input, calculates ultimate load that structure sustains before collapse. Element moments and plastic hinge rotations calculated for ultimate load. Locations of hinges required for collapse mechanisms to form also determined. Nonlinear collapse phenomena simulated by iterative linear analyses.
The influence of crack closure and elastoplastic flow on the bending behavior of thin cracked plates is investigated using an incremental elastoplastic plate bending finite element computer program. The finite element program was developed using assumptions consistent with Kirchhoff fourth-order plate theory while the material property treatment permits general isotropic work hardening with local elastic unloading. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.
A user's guide for the computer program OPTCOMP is presented in this report. This program provides a capability to optimize the fabrication or service-induced residual stresses in uni-directional metal matrix composites subjected to combined thermo-mechanical axisymmetric loading using compensating or compliant layers at the fiber/matrix interface. The user specifies the architecture and the initial material parameters of the interfacial region, which can be either elastic or elastoplastic, and defines the design variables, together with the objective function, the associated constraints and the loading history through a user-friendly data input interface. The optimization procedure is based on an efficient solution methodology for the elastoplastic response of an arbitrarily layered multiple concentric cylinder model that is coupled to the commercial optimization package DOT. The solution methodology for the arbitrarily layered cylinder is based on the local-global stiffness matrix formulation and Mendelson's iterative technique of successive elastic solutions developed for elastoplastic boundary-value problems. The optimization algorithm employed in DOT is based on the method of feasible directions.
The results of an extensive experimental characterization and a preliminary analytical modeling effort for the elastoplastic mechanical behavior of 8-harness satin weave carbon/copper (C/Cu) composites are presented. Previous experimental and modeling investigations of woven composites are discussed, as is the evolution of, and motivation for, the continuing research on C/Cu composites. Experimental results of monotonic and cyclic tension, compression, and Iosipescu shear tests, and combined tension-compression tests, are presented. With regard to the test results, emphasis is placed on the effect of strain gauge size and placement, the effect of alloying the copper matrix to improve fiber-matrix bonding, yield surface characterization, and failure mechanisms. The analytical methodology used in this investigation consists of an extension of the three-dimensional generalized method of cells (GMC-3D) micromechanics model, developed by Aboudi (1994), to include inhomogeneity and plasticity effects on the subcell level. The extension of the model allows prediction of the elastoplastic mechanical response of woven composites, as represented by a true repeating unit cell for the woven composite. The model is used to examine the effects of refining the representative geometry of the composite, altering the composite overall fiber volume fraction, changing the size and placement of the strain gauge with respect to the composite's reinforcement weave, and including porosity within the infiltrated fiber yarns on the in-plane elastoplastic tensile, compressive, and shear response of 8-harness satin C/Cu. The model predictions are also compared with the appropriate monotonic experimental results.
In geological CO 2 storage operations, wellbore deformations and leakage pathways formations can occur around injection and abandoned wells subjected to high rates and long-term CO 2 injection. To guide engineering design and prevent CO 2 leakage risks, a full understanding of the underlying physics and robust numerical models is necessary to evaluate the response of underground formations in the near wellbore region and in the reservoir. In this study, a multi-scale and multi-physics open-source simulator (GEOS) is used to simulate multiphase flow and poromechanical deformations over time in three dimensions. The governing equations for mechanical deformations of the rock body and multiphase compositional fluid flow within the rock matrix are solved with a fully coupled finite element and finite volume approach. The Drucker–Prager model with friction hardening is applied to simulate elastoplastic deformation and a multiphase fluid model with power-law correlations for relative permeability is used to model the migration of CO 2 plume, which are coupled with numerical implicit scheme. Simulation results are verified against multiple analytical solutions for multiphase flow and wellbore problems, thus demonstrating the accuracy of this advanced simulator. In two engineering applications, here we highlight the impact of elastoplastic deformation and coupled modeling for assessing induced displacements and stress perturbations, which are more pronounced in the near wellbore regions. This work focuses on short-term processes in the vicinity of injection wells where stress evolutions, rock deformations and multiphase compositional flow and transport are simulated jointly to ensure wellbore stability and prevent damage. This fully coupled geomechanical model can simulate multiphase flow and any associated poromechanical effects within the CO 2 storage site and in the surrounding formations. Such a large-scale, long-term, multi-physics simulation model is useful in many ways: it can guide operational decisions for CO 2 injection, assess the containment potential and risks of a site, and analyze the wellbore stability and integrity during and after CO 2 injection.
Here we propose an elastoplastic phase-field (PF) model to investigate the mechanics of tetragonal-to-monoclinic phase transformation (TMPT) and elastoplastic deformation of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ). A Landau polynomial with non-vanishing chemical energy at the equilibrium temperature is introduced to account for the actual formation energies of the phases. The effects of different grain orientations, latent heat, and temperature on TMPT and deformation mechanisms are considered. The suppressive transformation effects of the grain boundaries (GBs) is modeled using an inhomogeneous kinetic coefficient in the bulk and GBs. The simulation results for single crystals demonstrate the capability of the model to reproduce the orientation-dependent compressive deformation of YSTZ similar to atomistic simulations and micropillar experiments. The single crystal with [100] crystallographic orientation along the loading direction (SC[100]) displays both TMPT and plasticity, SC[101] experiences only phase transformation, while SC[001] undergoes only plastic yielding. The TMPT induced by compressive loading exhibits shape memory effect (SME) below the equilibrium transformation temperature and pseudoelasticity above it, while the critical transformation stress increases with increasing loading temperature. The irrecoverable plastic strain is found to trap a part of the monoclinic phase, which prevents a complete reverse transformation. The polycrystalline cases also display SME and PE at low and high temperatures, respectively. Due to the orientation differences between grains and the stress concentrations at geometric nonlinearities, plastic deformation occurs in polycrystalline YSTZ for an applied load less than the yield stress. The results suggest a possible limitation of plasticity and an improvement of the shape recovery of YSTZ if one can control the orientation of the grains and/or increase the density of stacking faults at the GBs during material processing.
Here, this paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response.
Task D of DECOVALEX-2023 is focused on the simulation of the coupled thermal hydraulic-mechanical (THM) behaviour in the full-scale engineered barrier system (EBS). The Horonobe EBS experiment is the demonstration of the full-scale EBS in the underground research laboratory (URL) (performed by JAEA in the Horonobe URL in Japan). Task D consisted of the three steps, a preliminary step (Step 0), simulation of the laboratory tests (Step 1) and simulation of the in-situ full-scale EBS experiment (Step 2). Since the Horonobe EBS experiment demonstrates the vertical emplacement option of the EBS, the experiment gallery is also backfilled with the backfill material. Therefore, interaction between the EBS and the backfill material can also be demonstrated, such as deformation (change of density) of the buffer material. The underground water in the Horonobe URL is saline. This fact adds chemical processes to THM behaviour. For example, mechanical properties (such as swelling pressure of the buffer material and backfill material) and hydraulic properties (such as permeability of the buffer material and backfill material) change depending on the water chemistry. Task D was therefore a challenging Task focused on not only the relatively simple THM behaviour but also complex THM behaviour including chemical processes. Six research teams (BGR, CAS, JAEA, KAERI, SNL and Taipower) participated the Task D. BGR, CAS, JAEA, KAERI and Taipower research teams selected a THM approach, while the SNL research team selected a TH approach. Step 1 involved the simulation of laboratory test results and was important to check the numerical codes developed by the research teams. Step 1 was divided into four sub steps. The simulation results through the Step 1 identified the parameters for simulation of the Step 2. Basic parameters of the materials (buffer material, backfill material, rock mass, concrete, sand) were provided by JAEA. Special parameters which research team needed were identified by back analysis of Step 1. Most notably the mechanical behaviour of swelling and displacement depended on the applied model (elastic model or elastoplastic model). Parameters such as Young’s modulus were found to need smaller values than characterised in the fundamental laboratory test results (Step 1-1, 1-2) for the elastic model. Although laboratory experiments are usually simple, test results contained some error. For example, if the saturation level is 100 % or higher, it should be considered an error. This situation was presented in the Step 1-3. A possible reason is that the buffer material is a mixture of bentonite and silica sand. When a specimen is cut to measure volume or weight, sand grains will affect the measurement data. In Step 2, boundary conditions such as temperature on the surface of the simulated overpack, heater power of the electrical heaters installed in the simulated overpack, injection pressure and inflow rate of the test water, were applied. The outer boundary conditions can be selected using measured data (injection pressure and inflow rate of the test water that is controlled by the injection systems installed in the sand layer around the buffer material and in the boundary between backfill material and concrete support). Since such measured data has some noise, research teams developed their own simplified boundary conditions. Inner boundary conditions can be selected using measured data as heater power and temperature on the surface of the simulated overpack. These data also contain some noise, so research teams developed their own simplified developed boundary conditions. Task D validated various approaches thorough the simulation of the in-situ full scale EBS system including backfill of the gallery: variations in the coupling processes (THM or THC), analysis codes, and boundary conditions. Temperature distribution in the buffer material was simulated well by all research teams. This means thermal behaviour is not sensitive to the simulation approaches. Although the water content distribution on the outside of the buffer material was well simulated by all research teams, the simulation results differ from the measured values inside the buffer material (at the centre and inside, near the simulated overpack). The buffer material is made from tap water, but in the in-situ experiment, saline groundwater infiltrates the buffer material. Therefore, the selection of the hydraulic parameters of the buffer material greatly affects the simulation results of the re saturation behaviour of the buffer material. In the Horonobe EBS experiment, measured values suitable for validating the simulation results were not obtained near the simulated overpack. When simulating the pressure and deformation of the buffer material, the measurement data is easily affected by the installation conditions of the measurement sensors, so verifying the measurement data itself remains an issue. Mechanical simulation results differ depending on whether they are considered as elastic or elastoplastic phenomena. The accuracy of measured in-situ data can be assessed by detailed analysis comparing sampling specimen analysis and measured data. The Horonobe EBS experiment is scheduled to be dismantled in the future (FY2026 and 2027). This detailed dismantling investigation will finally confirm the measured data.
The geomechanical behavior of methane hydrate bearing sediments (MHBS) is influenced by many factors, including temperature, fluid pressure, hydrate saturation, stress level, and strain rate. The paper presents a visco-elastoplastic constitutive model for MHBS based on an elastoplastic model that incorporates the effect of hydrate saturation, stress history, and hydrate morphology on hydrate sediment response. The upgraded model is able to account for additional critical features of MHBS behavior, such as, high-dilatancy, temperature, and rate effects. The main components and the mathematical formulation of the new constitutive model are described in detail. The upgraded model is validated using published triaxial tests involving MHBS. The model agrees overly well with the experimental observations and is able to capture the main features associated with the behavior of MHBS.
Estimates of the magnitudes of elastic stresses and elastoplastic stresses and strains were made for tungsten fiber-reinforced 80Ni + 20Cr matrix composites. Heating or cooling between 80 and 2000 F was assumed. The calculated elastic stresses exceeded representative or estimated strengths of constituents. For composites with less than 0.65 volume fraction of fiber, plastic flow was considered possible, and elastoplastic solutions indicated that stresses would be reduced but with the concomitant occurrence of sufficiently large strain ranges, particularly in the matrix, to pose a possible thermal fatigue problem. Limited experimental studies on tungsten fiber-copper matrix composites heated and cooled a number of times between 80 and 1600 F in a conventional furnace and then heated from 80 to 1652 F in a hot-stage microscope resulted in matrix microfracture for a 70 volume fraction fiber composite and substantial matrix strain for a 40 volue fraction fiber composite.