Research Theme
The objective of our group's research is to develop theoretical and numerical models that aid more accurate predictions for engineering design and applications. We act as a bridge among mathematical principles, data science and engineering industry. As a result, we emphasize on both the mathematical foundations and the practicality when deriving models for specific engineering problems. The figure below summarizes some of the current and previous work of this research group. Examples of previous and ongoing research conducted by the research group are listed below.
Geometric Learning for computational solid mechanics
In this work, our goal is to incorporate non-Euclidean microstructural data and create interpretable descriptors to create a graph-based elasto-plasticity model. While traditional hyperelasticity models often incorporate homogenized measures of microstructural attributes, such as porosity, averaged orientation of constitutes, these measures cannot reflect the topological structures of the attributes. We fill this knowledge gap by introducing the concept of a weighted graph as a new means to store topological information, such as the connectivity of anisotropic grains in assembles. Then, by leveraging a graph convolutional deep neural network architecture in the spectral domain, we introduce a mechanism to incorporate these non-Euclidean weighted graph data directly as input for training and for predicting the elastic responses of materials with complex microstructures. To ensure smoothness and prevent non-convexity of the trained stored energy functional, we introduce a Sobolev training technique for neural networks such that stress measure is obtained implicitly from taking directional derivatives of the trained energy functional. By optimizing the neural network to approximate both the energy functional output and the stress measure, we introduce a training procedure the improves efficiency and generalize the learned energy functional for different microstructures.
Related publications:
Related publications:
- N. Vlassis, W.C. Sun, Sobolev training of thermodynamic-informed neural network for interpretable elasto-plasticity models with level set hardening, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2021.113695, 2021. [Video][preprint]
- Y. Heider", H.S. Suh, W.C. Sun, An offline multi-scale unsaturated poromechanics model enabled by self-designed/self-improved neural network, International Journal for Numerical and Analytical Methods in Geomechanics, doi:10.1002/nag.3196, 2021.
- N. Vlassis, R. Ma", W.C. Sun, Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity, Computer Methods in Applied Mechanics and Engineering, 2020. [arxiv]
- Nikolaos Vlassis, 09/2017 - current
- Hyoung Suk Suh, 09/2018 - current
- Ran Ma, 01/2019 - current
- Bahador Bahmani, 09/2019 - current
Sobolev training for interpretable machine learning plasticity model
Different plasticity models recovered from the machine learning driven level set yield function. Instead of hand-crafting yield function, flow rules, and hardening laws, these components are generated from data via Sobolev training
To circumvent the lack of interpretability of the classical black-box neural network, we introduce a higher-order supervised machine learning technique that generates components of elasto-plastic models such as elasticity functional, yield function, hardening mechanisms, and plastic flow. The geometrical interpretation in the principal stress space allows us to use convexity and smoothness to ensure thermodynamic consistency. The speed function from the Hamilton-Jacobi equation is deduced from the DNS data to formulate hardening and non-associative plastic flow rules governed by the evolution of the low-dimensional descriptors. By incorporating a non-cooperative game that determines the necessary data to calibrate material models, the machine learning generated model is continuously tested, calibrated, and improved as new data guided by the adversarial agents are generated. A graph convolutional neural network is used to deduce low-dimensional descriptors that encodes the evolutional of particle topology under path-dependent deformation and are used to replace internal variables. The resultant constitutive laws can be used in a finite element solver or incorporated as a loss function for the physical-informed neural network run physical simulations.
Related publications:
- N. Vlassis, W.C. Sun, Sobolev training of thermodynamic-informed neural network for interpretable elasto-plasticity models with level set hardening, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2021.113695, 2021. [Video][preprint]
- Nikolaos Vlassis, 09/2017 - current
- Mian Xiao, 09/2020 - current
- Bahador Bahmani 09/2019 - current
High-strain-rate responses of energetic materials
The thermomechanical response of the energetic material under impacting is closely related to its safety and reliability during processing, storage, and transportation. The goal of this project is to establish a multiscale and multiphysics model to predict the shock loading resistance of the energetic material. In our previous work, we developed a pressure-dependent anisotropic hyperelasticity and crystal plasticity model to incorporate pressure sensitivity while predicting the plastic dissipation. It is found that the external pressure has a strong influence on the plastic dissipation under shock loading, which cannot be captured by traditional crystal plasticity model. The material point method (MPM) is a hybrid Eulerian-Langrangian method, which is immune to mesh distortion and hence suitable for large deformation simulation. Also, MPM provides automatic no-penetration no-slip contact algorithm which enables the pore-collapse simulation. In our preliminary results with Johnson-Cook model, it is found that the heat-induced strain softening and shear band can be reproduced with MPM. We are currently working on introducing the anisotropic phase field fracture model into the MPM to simulate the fracture near the collapsing pores and related heat generation.
Related publications:
Related publications:
- R. Ma, W.C. Sun, C. R. Picu, Atomistic-model informed pressure-sensitive crystal plasticity for crystalline HMX, under review.
- Ran Ma, 09/2019 - current
- Nick Vlassis, 09/2020-current
- Mian Xiao, 09/2021-current
Meta-modeling for computational mechanics: Applications of group, graph and game theories
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In this research, our goal is to leverage the three major machine learning techniques (supervised, unsupervised and reinforcement learning) to discovery new physics of path-dependent materials that cannot be otherwise determined from hand-crafted models. For a given set of data, we seek to find way to gain knowledge not necessarily from excess curve-fitting from training materials, but from finding the right relationships among physical quantities.
In a nutshell, the key departure of our work from the other ML applications for constitutive laws and computational mechanics is that we are not attempting to write a surrogate model or constitutive laws from data. Instead, we are attempting to modeling the actions and behaviors of a mechanician who is tasked with writing a constitutive laws for a given set of data. As such, we introduce a game whose objective is to write a predictive constitutive law and then re-cast a modeler as a player in this game with mathematically defined reward, action, state and environment. Many machine learning models used in mechanical computer simulations employ supervised and unsupervised learning techniques to make predictions with little or no interpretability. This disconnection with human knowledge makes it difficult to assess and manage risk when using such black-box models for engineering applications. In this talk, we present a new framework in which the AI is not simply tasked to make predictions on a mechanical process, but to mimic the actions of a human engineer to create, validate and test hand-crafted models that make predictions. As such, we introduce the concept of meta-modeling in which two AI agents, an experimentalist that generates data and a modeler that interprets data, are tasked with building a directed graph that represents the knowledge of the physical process with the least amount of data required. In this meta-modeling framework, all data accessible by the agents is modeled as labelled vertices (e.g. porosity, permeability) and all possible ways to connect those vertices are modeled as directed edges (e.g. mathematical expression, neural nets, support vector machine). Therefore, all the possible actions of the agents are mathematically represented by a labeled directed multi-graph. The learning process is therefore re-cast as the procedure to find a directed graph that links the input and output data with the optimal set of edges that maximize the reward (the objective function that measures the prediction qualities). With well-defined agents, reward, action space and environment, the AI modeler will then improve its ability to write the models through self-practicing in a deep reinforcement learning framework. Like humans, it will attempt to take different actions to write a model, then estimate the reward of each action via a deep neural network in a Monte Carlo tree search. By leveraging the ability of the AI modeler to repetitively practice and improve its modeling skills, we demonstrate that the proposed algorithm is able to both discover new hidden hierarchical structures of mechanics knowledge and rediscover well-known mechanics knowledge without any human intervention. In the case where availability of data is limited, the meta-modeling algorithm also explores the weakness of links in the constitutive laws and explores the optimal set of experiments to yield the best forward predictions under a limited budget. For instance, in our published work, we have used the deep learning to help us identifying the importance of multiple micro-structural attributes on the macroscopic responses and identify the relative importance of (1) fabric tensor, (2) coordination number of particles and (3) other measurement. Based on the results of the deep learning studies, we then propose models that, for the first time, incorporates the fabric tensors as input for the non-co-axial traction-separation law and yields a model that is suitable to capture the complex damage-plasticity mechanisms of interfaces undergoing a combination of tensile, compressive and shear kinematics (see Figures in the RHS). Our discovery does not only show that the fabric tensor is critical for anisotropic responses of granular materials, but we also find a way to automatically incorporate those influences without hand-crafting a new model every times we want to test a new hypothesis. Another related development is the usage of unsupervised learning to generate reduced-basis models (see Figures below). The idea behind this is to use previous simulations of similar natures (e.g. periodic responses, repeated procedures in manufacture, mixing) to determine a Galerkin projection that enables simulations carried with very limited degree of freedoms associated with the orthogonal basis rather than the nodal responses of a standard finite element or discrete element models. We also introduce a number of new ideas in the training procedure. For instance, we introduce the usage of long-short-term memory neuron to predict history-dependent responses and employ spectral decomposition to represent evolutions of tensorial input and output information such that the frame-dependent issues exhibited in RNN constitutive laws are corrected. We use a dual-permeability problem as a test bed to demonstrate how this new modeling approach works. More information can be found in the published articles. Team Members:
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The meta-modeling model: a modeling effort to model the agent that writes constitutive laws.
Directed graph which represents a computational model. Red arrow represents relations that could be predicted by (1) multiscale simulations, (2) phenomenological laws, and (3) neural network models. A model selection procedure is used such that the optimal configuration is determined.
Finite deformation kinematics of embedded strong discontinuities in a granular material
Traction-separation laws generated from ML.
Comparisons of stress invariants and energy predicted by different neural network models.
Self-improvement of the computer agent over each constitutive model writing session. Over time, the computer agent learns the directed graph that represents the relationships among physical quantities and employ this knowledge to write constitutive laws.
Monte-Carlo Tree Search used in the meta-modeling algorithm to improve the estimation of Q values of each "move" while the AI writes the constitutive modeling law.
Score distribution of the self-derived elasto-plasticity models from five families 1: Generalized plasticity with critical state, 2: Generalized plasticity w/o critical state, 3. Classical non-associative plasticity with critical state, 4. Classical non-associative plasticity w/o critical state, 5. Others.
Orthogonal basis for reduced-dimensional fast predictions
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Modified material point method for complex geometries undergoing finite deformation
Shifted domain technique applied on material point method.
One key drawback of classical discrete element methods for particulate mechanics is that they cannot generate any kinetic and kinematics information at the sub-grain scales. Nevertheless, many dissipative mechanisms of granular materials are actually originated from path-dependent behaviors at the sub-grain scales where wear, damage, fracture and fragmentation occurs. Nevertheless, recovery of these sub-scale information while capturing the geometry and form of each individual grains is inherently a difficult task.
The goal of this research is to establish an efficient image-to-simulation workflow to overcome this technical barrier. We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries undergoing large deformation in the geometrically nonlinear regime. In particular, we adopt the integration scheme of the material point method to resolve the convergent issues for Lagrangian meshes due to mesh distortion, while using a shifted domain technique originated from Scovazzi and coworker to represent the boundary condition implicitly via a level set or signed distance function. Consequently, this method completely bypasses the need to generate high-quality conformal mesh to represent complex geometries and therefore allows modelers to select the space of the interpolation function without the constraints due to the geometrical need. This important simplification enables us to simulate deformation of complex geometries inferred from voxel images. Verification examples on deformable body subjected to finite rotation have shown that the new shifted domain material point method is able to generate frame-indifference results. Meanwhile, simulations using microCT images of a Hostun sand have demonstrated that this method is able to reproduce the quasi-brittle damage mechanisms of single grain without the excessively concentrated nodes commonly displayed in conformal meshes that represent 3D objects with local fine details.
Originally written/last updated 1/31/2019.
Team Members:
Published Work:
The goal of this research is to establish an efficient image-to-simulation workflow to overcome this technical barrier. We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries undergoing large deformation in the geometrically nonlinear regime. In particular, we adopt the integration scheme of the material point method to resolve the convergent issues for Lagrangian meshes due to mesh distortion, while using a shifted domain technique originated from Scovazzi and coworker to represent the boundary condition implicitly via a level set or signed distance function. Consequently, this method completely bypasses the need to generate high-quality conformal mesh to represent complex geometries and therefore allows modelers to select the space of the interpolation function without the constraints due to the geometrical need. This important simplification enables us to simulate deformation of complex geometries inferred from voxel images. Verification examples on deformable body subjected to finite rotation have shown that the new shifted domain material point method is able to generate frame-indifference results. Meanwhile, simulations using microCT images of a Hostun sand have demonstrated that this method is able to reproduce the quasi-brittle damage mechanisms of single grain without the excessively concentrated nodes commonly displayed in conformal meshes that represent 3D objects with local fine details.
Originally written/last updated 1/31/2019.
Team Members:
- Mian Xiao, 09/2020-current
- Chuanqi Liu, 09/2018-09/2020
- Ran Ma, 01/2021-current
Published Work:
- C. Liu, W.C. Sun, Shift domain material point method for solids in the finite deformation range, special thematic issue for Meshfree and Particle Methods for Modeling Extreme Loadings, Computational Particle Mechanics, doi: 10.1007/s40571-019-00239-y, 2019. [PDF]
- C. Liu, W.C. Sun, ILS-MPM: an unbiased implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles, Computer Methods in Applied Mechanics and Engineering, accepted, doi:10.1016/j.cma.2020.113168, 2020. [PDF]
"Stress-chain" of granular assembles simulated via LS-MPM
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Contact stress simulated via LS-MPM
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(a) Micro-CT image of a single particle, (b) signed distance function of particle and (c) surrogate domain and the shifted boundary.
Particle damage occurs during indentation simulated by a nonlocal damage model. Note that classical DEM cannot recover any stress field or energy flux information near the singular tip and hence cannot accurately predict the propagation of crack and crack branching consistent with fracture mechanics theory.
Micromechanics of wetted and dry granular materials
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The reason we can build sand sculpture is due to the presence of liquid bridges among particles that are otherwise cohesionless. From a micromechanical perspective, liquid bridge and the solid grains are two interacting networks that transmits force and moment. As a result, when subjected to external loadings, granular assemblies with a a very small volume fraction of water can behave profoundly different than the dry counterpart. The objective of this research is to predict how this solid-fluid interaction in grain scale affect the macroscopic outcomes. This research is important for a number of engineering applications, including landslides, vehicle mobility and seismic signature of earth materials.
Currently, the research team is working on extending the framework to analyze granular materials beyond the pendular regime using two-phase flow model to simulate the air-water-solid interaction in the void space. To make the multiscale model more accessible, the research team has also studied and proposed new methodology to identify material parameters from micro-CT images. Through collaboration with Prof. Salager and his colleagues, we construct inverse problem that takes account both the macroscopic constitutive responses and micro-structural attributes captured by micro-CT and digital image correlation in the objective function. We are currently expanding this work to consider higher-order (e.g. micro-polar) kinematics obtained from micro-CT. Our preliminary results show that this method may provide a new way to introduce physical length scale directly from the grain particles, without the need to explicitly defining a nonlocal radius or other equivalent nonlocal length scale parameter. Originally written/last updated 1/31/2018. Team Members:
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Evolution of degree of saturation of granular material in simulated suction controlled test (LEFT), and the coordination number time history of the same specimen (RIGHT) .
MircroCT images obtained from drained triaxial compression test (cf. Wang et al. IJMCE, 2016)
Snapshot of inverse problems used to identify material parameter for micropolar plasticity model (Wang et al, IJMCE, 2016)
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Single and poly-crystal plasticity of rock salt for nuclear waste disposal
The thermo-hydro-mechanical behavior of rock salt is strongly depending on the microstructural attributes and micro-mechanics of the halite crystal that forms the rock salt. The desired engineering properties, such as the high thermal conductivity and the low permeability, and self-healing of rock salt are both attributed to the crystalline nature. In a geological system composed of salt or other crystalline rocks, individual grains or crystals are the fundamental building blocks that forms polycrystal assembles. The deformation of these assemblies are then related to both the deformation of each individual crystal and the grain boundary motion. As a result, thermo-mechanical responses at the microscopic scale, such as intergranular and intragranular fractures, as well as plastic slips, dislocation and the creeping due to precipitation may have significant implications for large scale engineering applications. While there are a multitude of macroscopic phenomenological model attempted to capture the complicated responses of rock salt, a multiscale approach that rightfully treated rock salt as polycrystalline materials may allow more robust predictions on the macroscopic anisotropic responses of rock salt in the finite deformation range. The goal of this work is to derive, formulate, predict, verify and validate polycrystalline model for rock salt and propose multiscale method to bridge the spatial and temporal scales.
Simulated responses of single crystal of halite of different orientations.
Currently, we have already completed the theoretical and algorithmic framework for small-strain crystal plasticity specifically designed for halite crystal in high pressure high temperature environment. In particular, we adopt the approach in which an elastic region in the stress space is defined and the sequence of the slip activation of the single crystal halite is considered. The analysis includes the thermo-mechanical creeping and micro-cracking for singly crystals under different loading conditions (orientation, loading rate, temperature, etc.). As a first step, we are interested at the anisotropic damage-plasticity of the slip system in Halite. Using the effective stress hypothesis, we employ a multi-phase-field model to capture the evolution of anisotropic damage of the single crystal, while using the crystal plasticity model to capture the plastic slip developed under different temperature and loading rate. The figures describe the axial stress-strain behavior under different orientations. The orientations of the single crystal of halite are described by Euler angles defining crystal axes (xc, yc, zc) relative to the reference coordinate system (x, y, z). Our next goal is to extend it to polycrystal problems and incorporate more mechanisms such as healing and migrations along grain boundaries.
Originally written/last updated 12/31/2018.
Originally written/last updated 12/31/2018.
Orientation 1
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Orientation 2
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Orientation 3
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The equivalent plastic strain developed during biaxial compression test for single crystal of different orientations are shown above.
Simulation of crack growth in polycrystals under tensile loading
The anisotropic phase field that represents damage of the single crystal are shown above. In a more recent work, our postdoc research scientist Dr. Ran Ma has introduced two FFT solvers to simulate brittle fracture with strongly anisotropic fracture energy. By leveraging the global continuity of the Fourier series, we introduce a generalized frequency vector to compute the higher-order derivative required for the higher-order phase field. This method is compared with the multi-phase-field formulation where multiple phase field evolution equations and the mechanics problems are solved in a staggered update scheme. Results obtained from both phase field models are compared. The FFT provides a simple way to solve the problems without specific mesh generation and treatments to resolve the higher-order terms.
- SeonHong Na, 1/2017 - 12/2018
- Ran Ma, 1/2019-current
- S. Na, W.C. Sun, Computational thermomechanics of crystalline rock salt for nuclear waste disposal. Part I: a combined multi-phase-field/crystal plasticity approach for single crystal simulations, Computer Methods in Applied Mechanics and Engineering, 2018.
- R. Ma, W.C. Sun, FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials and poly-crystals, Computer Methods in Applied Mechanics and Engineering, accepted, 2019.
- R. Ma, W.C. Sun, Computational thermomechanics for crystalline rock. Part II: chemo-damage-plasticity and healing in strongly anisotropic polycrystals, under review.
In a more recent work, our postdoc research scientist Dr. Ran Man extends the FFT solver to incorporate the effect of healing, the precipitation creeping due to the transport, the permeability evolution and the crystal plasticity of polycrystalline salt (see right Figure). To capture the healing process that often begins at the crack tips, an indicator function is used to locate the crack tip and the interfacial diffusion is captured explicitly along the grain boundaries to faithfully capture the solution-precipitation creeping of polycrystals. The resultant rate-dependence and the effect the evolution of damage and plastic deformation are shown below. A manuscript will be submitted in the near future (est. Oct 2019) to document this work.
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Environmental driven fractures and compaction banding of porous brittle solids
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The goal of this study is to analyze the solid-fluid interaction of cohesive-frictional and brittle materials across length scale. Our goal is to analyze the relationships between hydraulic properties (such as permeability, hydraulic and mechanical apertures) and microstructural attributes, (such as connectivity of force chain and bonding strengths) before and after the onset of fractures. At the grain-scale level, We apply graph theory to unveil how the topology and geometry of force chain and flow network leads to the complex macroscopic outcome, such as fracturing and strain localization.
A recent extension of work includes the derivation of a new variational formulation that incorporate the eigen-fracture model for fluid-driven fracture problem and the introduction of eigen-deformation mode to simulate the propagation of compaction band and shear-enhanced compaction band as a Mode I anti-crack. We also propose a new way to compute the hydraulic aperture from the nonlocal phase field fracture and eigen-fracture model and validate the numerical simulations with Nooru-Mohamed tests (see Figure on the RHS). Originally written/last updated 12/31/2018. Team Members:
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Pore pressure gradient induced by propagating fractures.
Micropolar phase field model that exhibits size effect in both elastic and damage regimes
Phase field modeling of the chemo-driven healing process of cracks in polycrystals
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Computational modeling of frozen porous media at finite strain
Deformed frozen soil (Nevada sand) specimen taken after the triaxial compression load at undrained condition
Freeze-thaw cycle of porous media can lead to significant damage in concrete or pavement. Interestingly, due to the surface energy difference, water thin-film often develops in between solid grains and ice crystal. At a sufficiently large scale in which RVE exists, the frozen porous media can be regarded as a three-phase mixture in which ice, water and solid grains all occupied a fraction of volume. However, depending the temperature and pressure, the ice and water constituents may have phase change and that leads to mass exchange. In particular, the thawing of the ice crystal in frozen soil may lead to a very weak and wet soil layers that are likely to undergo large deformation. Nevertheless, the finite strain behavior of the frozen soil with unfrozen water flowing inside the pores is not well understood. The goal of this study is to formulate a new mathematical framework to capture the mechanics of the frozen porous media that undergoing phase transition at the geometrical nonlinear regime. A climate-controlled triaxial apparatus will be utilized to study the thermo-hydro-mechanical coupling effect of the frozen soil. A preliminary study has been conducted by PhD student SeonHong Na to study the strain localization occurred in frozen soil at finite strain. This work was presented at Engineering Mechanics Institute at Nashville in which SeonHong has won the 2nd place in the best paper competition.
Originally written/last updated 12/31/2018.
Team Members:
Originally written/last updated 12/31/2018.
Team Members:
- SeonHong Na, 09/2015 - 12/2018 (now assistant professor at McMaster University)
- Alessandro Milleri, 09/2018 - current
- Hyoung Suk Suh, 09/2018 - current
- S. Na, W.C. Sun, Computational thermo-hydro-mechanics for multiphase freezing and thawing porous media in the finite deformation range, Computer Methods in Applied Mechanics and Engineering, 2017. [URL]
Finite Element simulations of Injecting unfrozen liquid in frozen ground at finite strain regime.
Nonlocal and higher-order continuum-discrete Coupling for porous media
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We propose a nonlocal multiscale framework that couples grain-scale discrete element simulations with a macroscopic continuum-based finite element model. The upshot of this nonlocal coupling model is that it retains the simplicity and efficiency of the continuum-based finite element model, while possessing the original length scale of the granular system. In Liu et al. 2015, the collective mechanical responses of particles at material points are homogenized via a staggered nonlocal operator applied on local regions such that the multi-scale simulations exhibit no pathological mesh dependence. However, the local regions must be sufficiently large in order to collect enough integration points to compute the nonlocal strain in the finite element model.
As a result, the research group has made other attempts to incorporate length scales, such as introducing second-order homogenization techniques. For instance, one may consider the incorporation of the higher-order kinematics, such as micro-rotation, micro-stretch and micro-torsion, and formulate a Hill-Mandel Lemma with more one one energy-conjugated pairs. Team Members:
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Comparison between DEM-FEM and pure DEM simulations.
Void space configuration changes due to grain rearrangement simulated by DEM in DEM-FEM coupling scheme.
High-order homogenization of granular materials
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Configurational Poromechanics with Lie-algebra internal variable recovery
Error due to projections of element in Lie group by interpolating polynomial functions (TOP), and interpolating via Lie Algebra
The motivation of this research is to use the configuration force on poromechanics problems to help solving some of the common problems encountered in modeling material failures. For instance, configurational force can be used as a criterion to detect fracture in brittle materials or used as a criterion to detect needs for re-meshing. While this ability has been exploited since the 1990s, the application to poromechanics problems is relatively rare.
To demonstrate this idea, we are currently working on a critical state plasticity model that exhibits size-dependent anisotropy. Because of this size-dependent effect, re-meshing is a helpful tool to make simulations results more efficient. Typically, re-meshing of problems dealing with path-dependent models is difficult due to (1) the need to mapping history variables and (2) the establishment of new equilibrium after the re-meshing. To resolve (1), we use Lie algebra. As demonstrated previously in Wang and Sun, CMAME, 2018 andd earlier in Mota et al. 2014, the quality of projecting tensorial quantity that represent the history of the material is the key for any adaptions. The fields in the formulation are the deformation mapping, the target or mapped internal variables and a Lagrange multiplier that enforces the equality between the source and target internal variables. This formulation leads to an L2 projection that minimizes the distance between the source and target internal variables as measured in the L2 norm of the internal variable space.
To ensure that the target internal variables remain in their original space, their interpolation is performed by recourse to Lie groups, which allows for direct polynomial interpolation of the corresponding Lie algebras by means of the logarithmic map. Once the Lie algebras are interpolated, the mapped variables are recovered by the exponential map, thus guaranteeing that they remain in the appropriate space.
Team Members:
Related Publication:
To demonstrate this idea, we are currently working on a critical state plasticity model that exhibits size-dependent anisotropy. Because of this size-dependent effect, re-meshing is a helpful tool to make simulations results more efficient. Typically, re-meshing of problems dealing with path-dependent models is difficult due to (1) the need to mapping history variables and (2) the establishment of new equilibrium after the re-meshing. To resolve (1), we use Lie algebra. As demonstrated previously in Wang and Sun, CMAME, 2018 andd earlier in Mota et al. 2014, the quality of projecting tensorial quantity that represent the history of the material is the key for any adaptions. The fields in the formulation are the deformation mapping, the target or mapped internal variables and a Lagrange multiplier that enforces the equality between the source and target internal variables. This formulation leads to an L2 projection that minimizes the distance between the source and target internal variables as measured in the L2 norm of the internal variable space.
To ensure that the target internal variables remain in their original space, their interpolation is performed by recourse to Lie groups, which allows for direct polynomial interpolation of the corresponding Lie algebras by means of the logarithmic map. Once the Lie algebras are interpolated, the mapped variables are recovered by the exponential map, thus guaranteeing that they remain in the appropriate space.
Team Members:
- SeonHong Na, 09/2017-12/2018 (now assistant professor at McMaster University)
- Kun Wang, 09/2015-current
- Eric Bryant, 09/2017-current
Related Publication:
- S. Na, E.C. Bryant, W.C. Sun, A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2019.112572, 2019.
- A. Mota, W.C. Sun, J.T.Ostein, J.W. Foulk III, K.N. Long, Lie-Group interpolation and variational recovery for internal variables, Computational Mechanics, 52:1281-1299, doi:10.1007/s00466-013-0876-1, 2013. [PDF] [Bibtex]
Re-meshing of poromechanics problem with configurational force.
Concurrent and sequential coupling of multiphysics problems at finite strain
Pore pressure distribution of poro-elastic beam obtained by stabilized (BOTTOM) and standard (TOP) finite element.
We design and implement of iterative sequential and monolithic schemes to simulate a variety of multiphysics problems. Our objective is to derive general framework to simulate a variety of multi-physics processes that involve solid mechanics coupled with hydraulic, heat and chemical transport. Since conventionally equal-order finite element space often lead to numerical instability, we formulated adaptively stabilized schemes that eliminate spurious oscillations while preserving correct boundary layer thickness. In addition, a critical state plasticity model is being implemented to replicate the constitutive responses of sands under various fluid saturation condition.
We have recently written a review on the thermo-hydro-mechanical problem for the September issue of the imechanica journal club. The full text can be found at http://imechanica.org/node/17096.
Team Members:
We have recently written a review on the thermo-hydro-mechanical problem for the September issue of the imechanica journal club. The full text can be found at http://imechanica.org/node/17096.
Team Members:
- SeonHong Na, 09/2014 - 12/2018 (now assistant professor at McMaster University)
- Kun Wang, 07/2014 - current
- Eric C. Bryant, 09/2016 - current
- Federica Ronchi (visiting student from Università degli Studi di Perugia)
- O.I. Ulven*, W.C. Sun, A two-way coupling dual-graph lattice model for fluid-driven fracture, International Journal for Numerical and Analytical Methods in Geomechanics, 2018.
- S. Na, W.C. Sun, Thermo-hydro-mechanical coupling effects on dynamic wave propagation in a fully saturated softening porous medium, International Journal for Numerical and Analytical Methods in Geomechanics, doi:10.1002/nag.2505, 2016. [PDF]
- W.C. Sun, A Stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain, International Journal for Numerical Methods in Engineering, 2015.
- W.C. Sun, Q. Chen, J.T. Ostien, Modeling hydro-mechanical responses of strip and circular footings on saturated collapsible geomaterials, Acta Geotechnica, 2014.
- W.C. Sun J.T. Ostien, A. Salinger, A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain, International Journal for Numerical and Analytical Methods in Geomechanics, 2013.
- W.C. Sun, An unified method to predict diffuse and localized instabilities in sands, Geomechanics and Geoengineering, 8(22):65-75, 2013.
Multi-model concurrent analysis with domain overlapping method
Multiphysics Domain coupling model across three length scales (single crack - specimen - field ).
The macroscopic mechanical failures, such as fracture and strain localization, are to a large extent determined by physical processes which occur at a scale several orders of magnitude smaller than the macroscopic observation. In order to model this inherent multiscale character efficiently, models designed specifically for macro- and micro-scales are often blended together in a handshake domain. Bridging the multi-model, multi-scale domain is, however, not a trivial problem. Spurious wave reflection, ghost force, artificial energy dissipation/increase, mesh dependence and incompatible deformation modes are all challenges persisted for this multi-model approach. To allude these drawbacks, we introduced an inf-sup stable domain overlapping method and extended it for large deformation, path-dependent plasticity and poroplasticity problems. To circumvent mesh dependence due to the loss of ellipticity, we introduced nonlocal plasticity model and concurrently coupled it with classical continuum model for far-field responses. Such a numerical treatment allows one to concentrate computation resource in a highly localized region of interest and thus significantly increases efficiency.
Graduate student(s):
Graduate student(s):
- Kun Wang, 09/2015-current
- SeonHong Na, 09/2015-current
- Eric Bryant, 09/2016-current
- Sun, Mota, A multiscale overlapped coupling formulation for large deformation strain localization, Computational Mechanics, 2015.
- W.C. Sun, Z. Cai, J. Choo, Mixed Arlequin method for multiscale poromechanics problems, International Journal for Numerical Methods in Engineering, 2016.
Multi-scale hierarchical analysis with geometrical enhancements from microstructures: material parameter identification across length scales
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Analysis from our studies shows that hierarchical multi-scale flow simulation that neglects pore connectivity may lead to significant error and reduce efficiency. As a result, we introduced a new method based on graph theory to extract geometrical attributes from X-ray CT images. Information of geometrical attributes is used to improve the coupling among the pore-scale lattice Boltzmann and field scale finite element simulations. By applying this improved scheme, my collaborators and I quantified the relations between grain crushing and hydraulic property changes. Such information is important for analyzing material bifurcation that leads to fracture and deformation band formation. This work helps improving our understanding on mechanical/hydraulic interactions of solid skeleton and pore-fluid, which is highly relevant to carbon dioxide storage, nuclear waste management and reservoir management.
Team Members:
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Microstructures of sandstone reproduced from a 3D printer.
Flow simulations on CT images
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Estimating co-seismic deformation with combined deterministic-stochastic Monto Carlos simulations
Simulated vs. recorded acceleration time history
My previous research project at Stanford University focuses on estimating co-seismic deformation during the 1989 Loma Prieta earthquake. In this study, Professor Borja and I investigated the influence of noise on the estimated co-seismic deformation using a combined deterministic-stochastic approach. We compare the classical equivalent linear method with a deterministic nonlinear finite element scheme with stochastic input. By quantifying the impact of noise and baseline offset presented in the input ground motion, we conclude that the sediment deformation may have affected the accuracy of the previously back-figured fault rupture mechanism.
Related Publications:
Related Publications:
Our research at Columbia is proudly sponsored by:
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