Multiscale Modeling Technique Research Articles

Challenges in Mathematics Arising from Theoretical and Computational Chemistry

The combination of theoretical chemistry and mathematics represents a significant advancement in science since it has yielded insights into the enigmas surrounding atoms and molecules. The advancement of technology has greatly benefited drug development, leading to significant advancements in both medicine and materials research. This summary discusses innovative methodologies and computational challenges in the expansive domain of theoretical and computational chemistry. Despite the computational challenges associated with the Schrodinger equation and Density Functional Theory (DFT), quantum mechanics offers a basic understanding of the behaviour of molecules and atoms. While MD simulations may not handle long-range interactions and complex configuration spaces, they nonetheless excel at capturing various time scales of molecular behaviour. Nevertheless, the process of transforming abstract notions into computer models for the purpose of solving MD simulations continues to be difficult; statistical mechanics offers a theoretical framework for understanding MD simulations. Data-driven methodologies and machine learning have significantly transformed the perspective of computational chemistry by enabling the observation and comprehension of very complex chemical interactions. We must also address concerns about interpretability, reliability in limited data streams, and system transferability. These challenges expedite the advancement of novel materials, product designs, and pharmaceuticals by leveraging machine learning and integrating it with specialised domain expertise. We used available data from many reputable databases, spanning the time period from 2010 to 2024. It is imperative to prioritise the advancement of multiscale modelling techniques and hybrid quantum-classical tools in order to achieve sufficient mastery over chemical phenomena. Another potential benefit is the use of novel mathematical models to uncover previously unknown patterns and connections in genetic data. The most effective way to tackle mathematical problems is by employing a straightforward approach and engaging in collaboration with experts from other fields. By adopting this approach, we can effectively address significant societal issues and propel advancements in chemistry. Keywords: mathematics, computational, chemistry, theoretical, challenges, quantum mechanics

A multi-scale modeling approach for predicting and mitigating thermal runaway in electric vehicle batteries

This study presents a unique multi-scale modelling technique for electric vehicle (EV) battery thermal runaway prediction models using electrochemical, thermal, and machine learning approaches. This modelling framework has illuminated the thermal runaway’s physical process and the race between heat production and dissipation at the cell module, and pack levels.Experimental evaluation has demonstrated solid predictive performance for each component. The modified pseudo-two-dimensional (P2D) electrochemical model has achieved high voltage prediction accuracy (mean absolute error: 8.5 mV), and the 3D thermal model has captured battery module temperatures with an average error of ± 1.5 °C.The machine learning model has exhibited 96.8% accuracy, excellent classification precision, and an 18.3-minute early warning time. It was also demonstrated that the integrated multi-scale model outperformed standalone single-scale models with 15% higher prediction accuracy and 32% higher average early warning time.Based on these findings, adaptive cooling techniques, unique charge/discharge procedures, and early isolation methods were created. Simulations showed that these mitigation techniques decreased thermal runaway occurrence by 78% and severity by 93%. Despite its high computing cost, this technique might improve EV battery safety, guide battery pack design, and accelerate EV adoption, which would cut carbon emissions.

Modeling the Swelling Behavior of Clayey Geomaterials Across Scales: Advances and Challenges

ABSTRACTMost soils and rocks contain varying fractions of clay minerals within their solid matrix. These geomaterials can exhibit a significant swelling potential toward chemo‐thermo‐hydromechanical loadings. Several multiscale modeling techniques have been developed to ascertain their swelling behavior across various scales, with molecular dynamics (MD), micromechanics‐based approaches, and double‐porosity models being the most common. MD simulation is a computational technique that applies Newton's second law of motion to depict the movement of particles within a granular system. Micromechanics‐based approaches upscale the poro‐elasticity law from the clay layer level to the sample scale through homogenization. Dual‐porosity models are generally based on elasto‐plasticity, incorporating different hydro‐mechanical laws at two distinct scales. These models have been extensively used, particularly for clayey soils and bentonites, though their application to clayey rocks has not been reported in the literature. Although their significant contribution to the understanding of clay swelling behavior, these techniques have been insufficiently reviewed, compared, and discussed mutually in the literature. This paper aims to provide a cross‐look on these multiscale approaches by presenting the theoretical background of existing formulations, highlighting breakthrough results, discussing major differences and current challenges, and proposing future perspectives.

The dual role of dissolution at a crack tip

The scientific literature is rife with conflicting reports regarding the effect of dissolution on fracture. The complexity arises, in part, due to dissolution often being intertwined with various other mechanisms such as hydrogen embrittlement and the formation of debris behind an advancing crack, which can obfuscate the sole contribution of dissolution. Here, we report on the effect of dissolution when acting in isolation via the utilization of an efficient atomistic-based multiscale modeling technique and a specialized interatomic potential. Our results reveal a dual role of dissolution on crack behavior, introducing an additional layer of complexity to the mechanistic basis of environmental effects. This finding, while challenging for engineering prognosis, provides a route for engineering improved materials. Recognizing and navigating this duality could be pivotal to precluding potentially disastrous consequences in a broad array of engineering applications, from harnessing earth’s energy resources to aerospace technologies.

Unraveling the Dynamics of Solid-Electrolyte Interphase (SEI) Formation on Lithium Metal: Insights from Multiscale Modeling

We need batteries to get the best out of renewable energies and other low-carbon energy sources, and the most promising path forward is to invest in high-energy-density battery technologies. In this regard, lithium metal is the best candidate for the anode electrode as it is the lightest metal on earth and has the lowest electrochemical potential (-3.04 V vs. SHE). However, the challenge to overcome for mass commercializing lithium-metal batteries (LMB) is stabilizing the solid electrolyte interphase that naturally grows at the electrode-electrolyte interface to avoid uncontrolled reactions leading to lithium depletion. Since the successful introduction of lithium-ion batteries (LIB), it has been known that tuning of the SEI composition and morphology is fundamental to prolong the battery life span; a well-engineered SEI layer simultaneously serves as an electron barrier and favors Li+ ion conduction across it, ensuring proper battery performance. However, the engineering of the SEI layer in LMB is more complex than its counterpart LIB batteries, given that lithium metal is overwhelmingly more reactive than graphite and the overall Li+ ion current across it is orders of magnitude higher. The up-to-date knowledge on the SEI morphology indicates that inorganic phases produced upon the decomposition of lithium salts present in the electrolyte tends to grow dominantly buried within the SEI layer, acting as an intermediate between the surviving lithium metal and the outermost organic SEI phase grown after decomposition of solvent molecules. The effect of electrolyte additives and diluents is to tweak the SEI composition. The narrative built after years of experimentation tells that proper battery functioning depends heavily on the ability of the incoming Li+ ions to desolve near the SEI outermost layer without triggering further side reactions, penetrate the inner SEI, and deposit in the anode as reduced lithium. However, the intricacies of the elementary reactions and the stage where the reduction takes place still fall beyond detailed comprehension, even though the development of in situ and operando analytical techniques has brought us a level of understanding on the subject that was unimaginable a few decades ago.In this talk, we discuss the instrumental impact that multiscale modeling techniques have played in clarifying the elementary steps of the SEI formation on pristine lithium metal, providing a comprehensive understanding of the precursors formed in the early stages of Solid-Electrolyte Interphase (SEI) growth. For instance, density functional theory (DFT) calculations have revealed that electrolyte diluents, such as TTE, previously considered inert to lithium metal, actively modify the liquid electrolyte solvation structure by weakly interacting with Li+ ions. Additionally, these diluents decompose against lithium metal, releasing fluoride ions and inundating the SEI layer with LiF. Similarly, DFT-based molecular dynamics (MD) techniques, including ab initio (AIMD) and reactive classical molecular dynamics methods (ReaxFF MD, among others), have facilitated a picoseconds (ps) scale observation of the temporal evolution of these SEI precursors, propelling a mechanistic understanding of the dynamics of the SEI formation; it is now recognized that there is an initial and rapid electrolyte decomposition occurring within the first tens of picoseconds after contact with lithium metal, preceding a longer-scale mass transfer segregation process leading to the formation of a myriad of organic and inorganic microphases within the SEI structure. However, the accessible time and space windows to MD methods fall within few hundred ps, leaving out the study of the morphological aspects of the SEI over extended cycling. In this sense, we discuss through kinetic Monte Carlo (kMC) calculations the evolution of the SEI formation on lithium metal and confirm the critical role that dislocations and grain boundaries play in ensuring proper lithium plating and mobility within the SEI layer over cycling. We confirm that bulk lithium diffusion within the inorganic SEI microphases, such as LiF and Li2O, is significantly lower than lithium mobility across LiF/Li2O interfaces. We also discuss the impact of electrolyte tunning on SEI morphology and provide insights into developing an SEI formation strategy based on the electrolyte molecules electrochemical stability and their relative contents of heteroatom species, such as F and O, to seed in the SEI composition and morphology, which we believe could have a significant impact on the development of stable LMB batteries.

Beyond reduction and emergence: a framework for tailoring multiscale modeling techniques to specific contexts

Beyond reduction and emergence: a framework for tailoring multiscale modeling techniques to specific contexts

Multiscale modeling for enhanced battery health analysis: Pathways to longevity

AbstractThe issues of health assessment and lifespan prediction have always been prominent challenges in the large‐scale application of lithium‐ion batteries (LIBs). This paper reviews the multiscale modeling techniques and their applications in battery health analysis, including atomic scale computational chemistry, particle scale reaction simulations, electrode scale structural models, macroscale electrochemical models, and data‐driven models at the system level. Multiscale modeling offers a profound insight into material behavior and the aging process of batteries, thereby providing a valuable reference for both estimation and management strategies of battery state of health. To extend the battery lifespan, the utilization of artificial intelligence for material discovery and manufacturing process optimization, the implementation of end‐cloud collaborative battery management systems, and the design of a multiscale simulation integration platform are considered. A management framework aimed at extending battery life is further proposed. This framework offers a promising roadmap for addressing health analysis challenges in LIBs, ultimately leading to more reliable, efficient, and durable solutions for next‐generation batteries.

Coverage- and Facet-Dependent Multiscale Modeling of O* and H* Adsorption on Pt Catalytic Nanoparticles.

Within computational heterogeneous catalysis, two critical factors exist-coverage and multifaceted effects-which are challenging to incorporate and contribute to differences between the results obtained from computational and experimental studies. Such disparities exist when significant adsorbate-adsorbate interactions are present, particularly when coupled with computationally limited facet sampling. Here, we designed a study to demonstrate the significance of coverage and facet effects on the predicted coverages for O* and H* on Pt nanoparticles. This is accomplished by employing multiscale modeling techniques using a three-pronged approach consisting of density functional theory (DFT), ab initio phase diagrams, and mean-field microkinetic models. Overall, adsorbate-adsorbate interactions are repulsive and far stronger for O*/Pt than for H*/Pt. For O* on Pt(111), repulsive interactions are both two- and three-body, but on Pt(100) and Pt(110), they are predominantly three-body. Through benchmarks to existing experimental literature, we demonstrate that experimentally observed coverages and desorption temperatures can be accurately estimated by computational models when the adsorbate-adsorbate interactions are included. Finally, by combining microkinetic models at the equilibrium limit with kubic harmonic interpolation, we model the impacts of the treatment of adsorbate-adsorbate interactions on the predicted O* and H* coverages over multifaceted Pt nanoparticles. Omitting adsorbate-adsorbate interactions over Pt nanoparticles leads to an overestimation of equilibrium coverages of the adsorbates (maximum of 0.29 and 0.11 ML for O* and H*, respectively) across a wide range of temperatures and pressures relevant to heterogeneous catalysis. Altogether, our work demonstrates that the inclusion of coverage and facet effects increases the accuracy of computational models for heterogeneous catalysts.

Experimental and numerical investigation on the elastic properties of luffa–cenosphere‐reinforced epoxy hybrid composite

AbstractEstimating the elastic characteristics of natural fiber‐reinforced polymer composites such as luffa fiber reinforced with epoxy is challenging. The structure of luffa cylindrica is complex, like a three‐dimensional natural fibrous mat, netting‐like structure. The multiscale modeling of such structures is the challenge to be addressed. The prime objective of this work is to determine the specific elastic properties of luffa–cenosphere‐reinforced epoxy (LCE) composite, considering the effect of filler volume fractions. Furthermore, multiscale modeling techniques, such as representative volume elements (RVEs) of finite element techniques with chopped, unidirectional, plain, and twill weaving fiber arrangements, were employed. The longitudinal modulus, transverse modulus, shear modulus, and Poisson's ratio were predicted through these modeling approaches. However, experimental and analytical methodologies, including the rule of mixture and Halpin–Tsai, were considered to validate the finite element analysis results. The elastic characteristics of LCE composite were therefore shown to be enhanced by increasing filler volume fraction. However, the cenosphere's 20% volume fraction has the highest elastic properties as determined by analytical, experimental, and computational models. Analytical and finite element simulation results were compared with the experimental results, and based on the findings, the most suitable (unidirectional, chopped, plain, and twill weaving) RVE was identified for finite element modeling of LCE composite for the evaluation of elastic properties. Results from practical approaches and the RVE twill weaving model showed good agreement, with less than 1% error, compared to the other analytical and finite element methods.Highlights NFCs are gaining ground in polymer composites. Overcoming challenges in modeling of luffa fiber inside epoxy matrix. The study uses multiscale modeling with diverse fiber arrangements. Experimental and analytical methods used to confirm FEA results. Increased cenosphere volume fraction boosts LCE composite properties.

Characterization of fatigue crack growth behavior in welded tubular T-joint

This paper focuses on investigating the fatigue crack growth (FCG) characteristics and residual fatigue life of tubular T-joints which are prone to suffer fatigue damage at the brace and chord intersections under multi-axial stress. Static and fatigue loading tests are performed to investigate the FCG behaviors of tubular T-joints, combining beach marking technique. The evolution of FCG characteristics is studied during the crack growth, convergence and wall penetration through an efficient co-simulation system that established using the multi-scale modeling technique. Fracture morphology analysis is conducted to gain insight into the FCG behaviors combining the scanning electron microscope (SEM) observation. Results indicate that multiple cracks initiate at the crown regions and subsequently evolve circumferentially around the weldments in a doubly-curved shape towards wall-thickness. Interaction effects between adjacent cracks extend the fatigue life along the outer surface, attributed to the premature exposure of converged crack front and the induced variation of stress intensify factor (SIF) distribution along the crack front. The dominant failure mode of tubular T-joints is characterized by an opening mode crack, with the contribution of anti-plane shear mode crack gradually increasing as structural symmetry diminishes. The established co-simulation system shows advantage in capturing the FCG behavior, predicting the fatigue life and characterizing the FCG characteristics with a good balancing of simulation efficiency and calculation accuracy.

Modeling-driven materials by design for conjugated polymers: insights into optoelectronic, conformational, and thermomechanical properties.

Conjugated polymers (CPs) have emerged as pivotal functional materials in the realm of flexible electronics and optoelectronic devices due to their unique blend of mechanical flexibility, solution processability, and tunable optoelectronic properties. This review synthesizes the latest molecular simulation-driven insights obtained from various multiscale modeling techniques, including quantum mechanics (QM), all-atomistic (AA) molecular dynamics (MD), coarse-grained (CG) modeling, and machine learning (ML), to elucidate the optoelectronic, structural, and thermomechanical properties of CPs. By integrating findings from our recent computational work with key experimental studies, we highlight the molecular mechanisms influencing the multifunctional performance of CPs. This comprehensive understanding aims to guide future research directions and applications in the modeling assisted design of high-performance CP-based materials and devices.

Review of Multiscale Modeling and Simulation Techniques in Metal Forming, Bending, Welding, and Casting Processes for Enhanced Predictive Design and Analysis

Multiscale modeling and simulation offer crucial insights for designing and analyzing metal forming, bending, welding, and casting processes, all of which are vital across automotive, aerospace, and construction industries. This paper overviews multiscale techniques used in these areas. Macroscopically, continuum-based methods like finite element analysis (FEA) model the overall process and its impact on metal materials. FEA reveals deformation, stress distribution, and temperature changes during manufacturing processes. Mesoscale techniques, including crystal plasticity, phase field methods, and cellular automata, focus on microstructural evolution and mechanical properties. They model the behavior of grains and phases within the metal. These models combine macro and mesoscale data for accuracy. This allows for the prediction of grain growth, recrystallization, and phase transformations – critical for optimizing processes, refining component design, and ensuring quality. For example, multiscale modeling successfully captured microstructural evolution during casting (demonstrating ±2% average grain growth deviation) and predicted defect formation in welded joints with high accuracy (demonstrating a 0.95 correlation coefficient with non-destructive testing).

A machine learning method of accelerating multiscale analysis for spatially varying microstructures

Multiscale computing for heterogeneous materials provides a powerful and fidelity approach to handling situations where a suitable macroscopic constitutive model is unavailable. However, there have been very few instances in the industrial sector where concurrent multiscale modeling techniques have been adopted, primarily because they require significant computational resources. In particular, when dealing with large numbers of representative volume elements (RVEs) with different microstructure morphologies throughout the macrostructure. In this paper, the novelty lies in providing an artificial neural network (ANN) model-based multiscale approach for accelerating multiscale analysis of the elliptical inclusion-reinforced composites with spatially varying microstructures, which give up the assumption of global periodicity. To tackle this challenge, firstly, a series of RVEs with different microstructure morphologies characterized by inclusion orientations and aspect ratios, under different load conditions, are simulated to generate training data. Second, the back propagation neural network (BPNN) is trained offline using data acquired from the RVE simulation for learning the underlying and possibly RVE morphologies. The trained BPNN replaces the complex microscopic mechanical solution problems over each macroscopic integration point at each iteration, to update the macroscopic stress-strain responses and it significantly reduces the computational cost of multiscale simulations. Then, the trained neural network is implemented on ABAQUS via user-defined materials (UMAT) and its effectiveness is verified by comparison with the classical multiscale finite element method (FE2) method. Finally, the outstanding computational capability of the proposed approach is further demonstrated through two numerical examples.

Mapping the configurational landscape and aggregation phase behavior of the tau protein fragment PHF6.

The PHF6 (Val-Gln-Ile-Val-Tyr-Lys) motif, found in all isoforms of the microtubule-associated protein tau, forms an integral part of ordered cores of amyloid fibrils formed in tauopathies and is thought to play a fundamental role in tau aggregation. Because PHF6 as an isolated hexapeptide assembles into ordered fibrils on its own, it is investigated as a minimal model for insight into the initial stages of aggregation of larger tau fragments. Even for this small peptide, however, the large length and time scales associated with fibrillization pose challenges for simulation studies of its dynamic assembly, equilibrium configurational landscape, and phase behavior. Here, we develop an accurate, bottom-up coarse-grained model of PHF6 for large-scale simulations of its aggregation, which we use to uncover molecular interactions and thermodynamic driving forces governing its assembly. The model, not trained on any explicit information about fibrillar structure, predicts coexistence of formed fibrils with monomers in solution, and we calculate a putative equilibrium phase diagram in concentration-temperature space. We also characterize the configurational and free energetic landscape of PHF6 oligomers. Importantly, we demonstrate with a model of heparin that this widely studied cofactor enhances the aggregation propensity of PHF6 by ordering monomers during nucleation and remaining associated with growing fibrils, consistent with experimentally characterized heparin-tau interactions. Overall, this effort provides detailed molecular insight into PHF6 aggregation thermodynamics and pathways and, furthermore, demonstrates the potential of modern multiscale modeling techniques to produce predictive models of amyloidogenic peptides simultaneously capturing sequence-specific effects and emergent aggregate structures.

High temperature viscoplastic deformation behavior of sintered nanocopper paste used in power electronics packaging: Insights from constitutive and multi-scale modelling

As a promising technology for high-power and high-temperature power electronics packaging, nanocopper (nanoCu) paste sintering has recently received increasing attention as a die-attachment. The high-temperature deformation of sintered nanoCu paste and its underlying mechanisms challenge the reliability of high-power electronics packaging. In this study, the tensile deformation behaviors of sintered nanoCu paste were firstly characterized by high-temperature tensile tests performed at various temperatures and strain rates ranging from 180 °C to 360 °C, 1 × 10−4 s−1 to 1 × 10−3 s−1 respectively. It was found that the elastic modulus and tensile strength decreased at the higher tensile temperature while the ductility increased accordingly. The highest elastic modulus and tensile strength results were 12.15 GPa and 46.97 MPa, respectively. Second, failure analysis was conducted based on the fracture surface after tensile testing. Recrystallization was revealed as the main factor for ductility improvement. Subsequently, an Anand model was fitted by stress-strain curves to describe the tensile constitutive behavior of the sintered nanoCu paste. Multi-scale modelling techniques also investigated the impact of tensile temperature and strain rate on the tensile response. Molecular dynamics simulation was implemented using a hemispherical Cu nanoparticle model to reveal the properties from an atomistic perspective. In addition, a two-dimensional equivalent model was further established by using a stochastically distributed void morphology. The multi-scale modelling techniques successfully describe the evolution of tensile response to the different tensile temperatures and strain rates. Besides, the equivalent model with random void morphology was demonstrated as the finite element simulation results were highly consistent with the high-temperature tensile experiments.

Representative volume element: Existence and extent in cracked heterogeneous medium

Acknowledging the ever-increasing demand for composites in the engineering industry, this paper focuses on the failure of composites at the microscale and augmenting the use of multiscale modelling techniques to make them better for various applications. This work aims to increase the representativeness of the volume element by attenuating the mesh and size sensitivities in representative volume element (RVE) modelling. A technique to alleviate mesh sensitivity in RVE modelling is proposed, which equalises the fracture energy observed from computational analysis with the real phenomenon, thereby keeping the response independent of the bandwidth of strain localisation. Based on the hypothesis that ensuring periodicity of strain, in addition to displacement periodicity across the domain boundary and supplementing the capability of periodic boundary conditions (PBCs) to attenuate the size dependency in RVE modelling, a set of modified PBCs (MPBCs) are formulated. One thousand two hundred RVE samples falling into combinations of five fibre volume fractions and four RVE sizes are analysed under transverse loading, and the ability of MPBCs to attenuate the effect of RVE size on the precision of material response, particularly in the softening regime, is verified. This work also focuses on various factors affecting damage initiation in 2D composite RVEs. The arrangement of a pair of fibres with their members placed close to each other, such that the angle between the direction of loading and an imaginary line drawn between their centres is less, is observed to make the region between them more favourable to damage.

Investigation of the Pd(1−x)Zn x alloy phase diagram using ab initio modelling approaches

The identification of the stable phases in alloy materials is challenging because composition affects the structural stability of different intermediate phases. Computational simulation, via multiscale modelling approaches, can significantly accelerate the exploration of phase space and help to identify stable phases. Here, we apply such new approaches to understand the complex phase diagram of binary alloys of PdZn, with the relative stability of structural polymorphs considered through application of density functional theory coupled with cluster expansion (CE). The experimental phase diagram has several competing crystal structures, and we focus on three different closed-packed phases that are commonly observed for PdZn, namely the face-centred cubic (FCC), body-centred tetragonal (BCT) and hexagonal close packed (HCP), to identify their respective stability ranges. Our multiscale approach confirms a narrow range of stability for the BCT mixed alloy, within the Zn concentration range from 43.75% to 50%, which aligns with experimental observations. We subsequently use CE to show that the phases are competitive across all concentrations, but with the FCC alloy phase favoured for Zn concentrations below 43.75%, and that the HCP structure favoured for Zn-rich concentrations. Our methodology and results provide a platform for future investigations of PdZn and other close-packed alloy systems with multiscale modelling techniques.

New approach for modeling randomly distributed CNT reinforced polymer nanocomposite with van der Waals interactions

This paper presents a new approach for the prediction of the stiffness of randomly distributed CNT/polymer nanocomposites using molecular and micromechanics methods with the van der Waals (VdW) interactions. A multi-scale modeling technique was designed for CNT nanoparticles randomly embedded in the polymer using an AMBER force field. This multi-scale model constitutes a representative volume element. The representative volume element consists of polymer, CNT nanoparticle, CNT-polymer interfacial region and Van der Waals bonds. A programming code was developed that randomly distributes nanoparticles according to the desired volume fraction. Python scripting language was used for the modeling technique performed in a finite element environment. By modeling the interfacial regions around randomly distributed CNTs, van der Waals bonds are modeled stochastically. In this study, the subject of interest is the number of CNTs positioned in the RVE according to the volume fraction. These numbers were determined at the level allowed by finite element equations and computational solvers and their effects were investigated by calculated stiffness behavior.

A two-scale framework for coupled mechanics-diffusion-reaction processes

There is a wide range of industrially-relevant problems where mechanical stresses directly affect kinetics of chemical reactions. For example, this includes formation of oxide layers on parts of micro-electro-mechanical systems (MEMS) and lithiation of Si in Li-ion batteries. Detailed understanding of these processes requires thermodynamically-consistent theories describing the coupled thermo-chemo-mechanical behaviour of those systems. Furthermore, as the majority of materials used in those systems have complex microstructures, multiscale modelling techniques are required for efficient simulation of their behaviour. Hence, the purpose of the present paper is two-fold: (1) to derive a thermodynamically-consistent thermo-chemo-mechanical theory; and (2) to propose a two-scale modelling approach based on the concept of computational homogenisation for the considered theory. The theory and the two-scale computational approach are implemented and tested using a number of computational examples, including the case of the reaction locking due to mechanical stresses.

Physically-Based Simulation for Fluid and Solid Dynamics

The potential for physical-based fluid and solid-dynamics simulation to transform many branches of engineering and science makes this an important field of study. In this study, we survey the state-of-the-art of physically-based simulation for fluid and solid dynamics, discussing the many methods, tools, and approaches currently in use. We also offer a methodology for simulating the behavior of fluids and solids that combines a particle-based approach with a continuum-based approach. The simulation framework, particle- and continuum-based simulation, and their coupling are all parts of our proposed technique. Future directions for research are also discussed, such as machine learning, multiscale modeling, real-time simulations, coupled simulations, validation and verification techniques, and computational resources for physically-based simulations. The discipline of physically-based modeling for fluid and solid dynamics is expanding rapidly, and there are many areas where new discoveries could be made. Many branches of engineering and research stand to benefit greatly by tackling these problems and looking in new ways.