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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

25 ENERGY STORAGE↗
DOE OSTI2024

Leveraging a Neural Network-Enhanced Reproducing Kernel Particle Method for Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation has been developed to analyze this system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. Here, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RKPM is additionally used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

degradation↗
DOE OSTI2023

Neural Network-Enhanced Reproducing Kernel Particle Method for Image-Based Multiphysics Damage Modeling of Energy Storage Materials

Energy storage materials undergo significant stresses during charge/discharge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), image-based modeling techniques are used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electrochemical-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in capturing crack propagation due to mesh dependency. Additionally, commonly used damage models, such as the continuous damage model and the cohesive zone model, often have steep tradeoffs between discontinuous field accuracy and computational expense. In this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022.

damage modeling↗
DOE OSTI2022

A neural network‐enhanced reproducing kernel particle method for modeling strain localization

Abstract Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh‐based methods to perform while modeling the evolving localizations. In this work, neural network‐enhanced reproducing kernel particle method (NN‐RKPM) is proposed, where the location, orientation, and shape of the solution transition near a localization is automatically captured by the NN approximation via a block‐level neural network (NN) optimization. The weights and biases in the blocked parameterization network control the location and orientation of the localization. The designed basic four‐kernel NN block is capable of capturing a triple junction or a quadruple junction topological pattern, while more complicated localization topological patters are captured by the superposition of multiple four‐kernel NN blocks. The standard RK approximation is then utilized to approximate the smooth part of the solution, which permits a much coarser discretization than the high‐resolution discretization needed to capture sharp solution transitions with the conventional methods. A regularization of the NN approximation is additionally introduced for discretization‐independent material responses. The effectiveness of the proposed NN‐RKPM is verified by a series of numerical verifications.

Baek, Jonghyuk↗
DOE OSTI2024

Multiphysics Degradation Modeling of Energy Storage Materials via RKPM with a Neural Network-Enhancement

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation is developed, and a patch-test is formulated to certify optimal convergence of the proposed RKPM method for the coupled physics system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is then used to represent the complex material microstructures for modeling the coupled physics of these systems. Further, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

electro-chemo-mechanical coupling↗
DOE OSTI2023

Neural Network Enhanced RKPM for Electrochemical-Mechanical Coupled Damage Modeling of Energy Storage Materials

Energy storage materials undergo significant charge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. For Li-ion batteries, for example, lithium moving between electrodes during charging and discharging process causes expansion and contraction of grains, and the strongly anisotropic and nonlinearly [Li]-dependent grain material properties can cause grains to expand into and contract away from each other, leading to chemo-mechanical cracking. In the first part of this work, a RKPM based computational framework for solving the coupled solid-phase lithium conservation with Fickian diffusion and the lithium concentration dependent anisotropic mechanical problem subjected to a highly nonlinear Butler-Volmer boundary condition is introduced. The choice of RKPM completeness conditions for lithium concentration and mechanical deformation fields, and the variational consistency condition for the domain integration of the coupled problem is first determined. In the second part of this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material, by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that is necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure.

damage modeling↗
DOE OSTI2026

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗
NASA NTRS2012

Determining Wheel-Soil Interaction Loads Using a Meshfree Finite Element Approach Assisting Future Missions with Rover Wheel Design

A wheel experiencing sinkage and slippage events poses a high risk to rover missions as evidenced by recent mobility challenges on the Mars Exploration Rover (MER) project. Because several factors contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc., there are significant benefits to modeling these events to a sufficient degree of complexity. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree finite element approaches enable simulations that capture sufficient detail of wheel-soil interaction while remaining computationally feasible. This study demonstrates some of the large deformation modeling capability of meshfree methods and the realistic solutions obtained by accounting for the soil material properties. A benchmark wheel-soil interaction problem is developed and analyzed using a specific class of meshfree methods called Reproducing Kernel Particle Method (RKPM). The benchmark problem is also analyzed using a commercially available finite element approach with Lagrangian meshing for comparison. RKPM results are comparable to classical pressure-sinkage terramechanics relationships proposed by Bekker-Wong. Pending experimental calibration by future work, the meshfree modeling technique will be a viable simulation tool for trade studies assisting rover wheel design.

Contreras, Michael T.↗
DOE OSTI2024

Image-Based Digital Twin for Assessing the Coupled Electro-Chemo-Mechanical Behavior of Li-Ion Batteries

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. In this work, a digital twin is created to investigate the performance of a Li-ion battery cathode and simulate degradation accumulation. Pixel-based model construction is used to represent the complex material geometries from microstructural images supplied by the National Renewable Energy Laboratory (NREL). Because of the expected large deformation and crack opening, the reproducing kernel particle method (RKPM), a meshfree method with discretization at the image pixels, is used to approximate the field variables: electrostatic potential, concentration, and displacement. An interface modified reproducing kernel (IM-RK) is constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The discrete nature of the images' pixel points is employed throughout the model and approximation construction. The mechanical model is verified using an image-based microstructure under tensile loading. A transient electro-chemo-mechanical coupled simulation is performed to evaluate the potential micro-cracking induced degradation of the battery cathode material subjected to charge/discharge cycling.

battery degradation↗
DOE OSTI2024

Image-Based Failure Assessment of Li-Ion Batteries

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. In this work, a digital twin is created to investigate the performance of a heterogeneous Li-ion battery cathode and simulate degradation accumulation. Pixel-based model construction is used to represent the complex material geometries from microstructural images supplied by the National Renewable Energy Laboratory (NREL). Because of the expected large deformation and crack opening, the reproducing kernel particle method (RKPM), a meshfree method with discretization at the image pixels, is used to approximate the field variables: electrostatic potential, concentration, and displacement. An interface modified reproducing kernel (IM-RK) is constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. IM-RK is additionally used to inform how crack evolution in turn affects the coupled electro-chemo-mechanical behavior of the Li-ion battery cathode.

image-based modeling↗
DOE OSTI2022

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

Abstract The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed $$u$$ u – $$p$$ p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

Baek, Jonghyuk↗
DOE OSTI2023

Meshfree Multiphysics Damage Modeling of Li-ion Battery Materials

Through repeated charging and discharging cycles, the electrodes of a Li-ion battery experience significant swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries and material interfaces. Chemo-mechanical damage models are generally simulated by one of two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a coupled chemo-mechanical crack propagation model that enhances accuracy while maintaining high computational efficiency. This model features a fully coupled, iterative electrochemistry solution, which informs the meshfree damage model of impending crack formation. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.

damage modeling↗
DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗
DOE OSTI2022

Meshfree Methods for Modeling Chemo-Mechanical Cathode Cracking in Li-Ion Batteries

Through repeated charging and discharging, the electrodes of a Li-ion battery experience cyclic loading causing swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries. Chemo-mechanical models are simulated mainly by two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a chemo-mechanical crack propagation model that achieves both intermediate accuracy and computational time between a CDM and CZM. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.

cathode cracking↗
DOE OSTI2023

An $\bar{F}$ Meshfree Treatment for Nearly Incompressible Materials

The computational modeling of nearly incompressible materials is a difficult task for many numerical methods, and even after several decades of investigation, it is still an active research area. This report seeks to address the treatment of incompressible materials in meshfree methods using a synergistic combination of two treatments. The first treatment is an $\bar{F}$ method, where the decomposed dilatational and deviatoric parts are calculated over different smoothing domains. The second treatment “activates” additional nodes throughout the domain to increase the flexibility of the model. We implement this synergistic combination in the context of the reproducing kernel particle method (RKPM) and present results for the Cook’s membrane benchmark problem. The results are compared with those using the composite tet10 finite element with a volume-averaged J formulation. We show that the combined treatment is an effective way to deal with nearly incompressible materials in a meshfree framework and compares well with other highly-effective treatments.

97 MATHEMATICS AND COMPUTING↗