Journal of The Mechanics and Physics of Solids最新文献

{"title":"SPiFOL: A Spectral-based physics-informed finite operator learning for prediction of mechanical behavior of microstructures","authors":"Ali Harandi ,&nbsp;Hooman Danesh ,&nbsp;Kevin Linka ,&nbsp;Stefanie Reese ,&nbsp;Shahed Rezaei","doi":"10.1016/j.jmps.2025.106219","DOIUrl":"10.1016/j.jmps.2025.106219","url":null,"abstract":"<div><div>A novel physics-informed operator learning technique based on spectral methods is introduced to model the complex behavior of heterogeneous materials. The Lippmann–Schwinger operator in Fourier space is employed to construct physical constraints with minimal computational overhead, effectively eliminating the need for automatic differentiation. The introduced methodology accelerates the training process by enabling gradient construction on a fixed, finite discretization in Fourier space. Later, the spectral physics-informed finite operator learning (SPiFOL) framework is built based on this discretization and trained to map the arbitrary shape of microstructures to their mechanical responses (strain fields) without relying on labeled data. The training is done by minimizing equilibrium in Fourier space concerning the macroscopic loading condition, which also guarantees the periodicity. SPiFOL, as a physics-informed operator learning method, enables rapid predictions through forward inference after training. To ensure accuracy, we incorporate physical constraints and diversify the training data. However, performance may still degrade for out-of-distribution microstructures. SPiFOL is further enhanced by integrating a Fourier Neural Operator (FNO). Compared to the standard data-driven FNO, SPiFOL shows higher accuracy in predicting stress fields and provides nearly resolution-independent results. Additionally, its zero-shot super-resolution capabilities are explored in heterogeneous domains. Finally, SPiFOL is extended to handle 3D problems and further adapted to finite elasticity, demonstrating the robustness of the framework in handling nonlinear mechanical behavior. The framework shows great potential for efficient and scalable prediction of mechanical responses in complex material systems while also reducing the training time required for training physics-informed neural operators.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106219"},"PeriodicalIF":5.0,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144341109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generative Deep Learning for Designing Printable Multifunctional Microstructural Materials: Application to Piezocomposites","authors":"Mohammad Saber Hashemi, Fatemeh Delzendehrooy, Khiem Nguyen, Levi Kirby, Xuan Song, Azadeh Sheidaei","doi":"10.1016/j.jmps.2025.106253","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106253","url":null,"abstract":"This study presents a novel generative deep learning framework tailored to design printable, multifunctional microstructural materials. Our approach integrates a custom-developed voxelized microstructure generator, HetMiGen, with a new machine learning model, TransVNet, which together facilitates the rapid and accurate design of materials with desirable multifunctional properties, especially those showing competing properties with microstructural changes, such as being soft and piezoelectrically sensitive concurrently. Keys to our methodology are the efficient computational homogenization using fast Fourier transform (FFT) techniques and a bi-directional establishment of structure-property relationships that significantly condenses the design cycle. The effectiveness of our framework is validated through the experimental manufacture and testing of piezocomposite microstructures, confirming computational predictions. Results demonstrate the framework's capability to expedite the development of materials with tailored functionalities, offering significant implications for advancing material design technologies.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"45 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144341089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"From Deterministic Physics-based to Probabilistic Data-driven Modeling: Diffusion-based Prediction of Strain Fields in Deep Drawing Processes","authors":"Paul P. Meyer, Dirk Mohr","doi":"10.1016/j.jmps.2025.106251","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106251","url":null,"abstract":"A new perspective is adopted to solve boundary value problems in structural mechanics. In a compact form, they are described as the mapping from an input vector that defines a mechanical system to an output image that describes mechanical fields. This mapping is then directly learned from data using a deterministic transpose convolutional neural network (CNN) model. Here, we apply this approach to predict the strain fields in deep drawing. The model-specifying input variables include the material properties, the forming tool geometries and the punch displacement. Training data comprised of 10,000 pairs of input vectors and output images is generated through finite element simulations. It is shown that the trained CNN is able to make reliable predictions including complex deformation patterns associated with wrinkling. To facilitate the training on real experimental data, we also develop a diffusion denoising probabilistic (DDP) model. Different from the CNN, the DDP model leans an output image generating distribution from data sets with missing input information. While the DDP is able to perform the same tasks (with comparable accuracy) as the deterministic CNN, it provides also meaningful probabilistic predictions when an input variable such as the friction coefficient is unknown. The successful adoption of the probabilistic neural network approach is seen as an important step towards the development of data-driven models that exceed the predictive capabilities of traditional models. This approach is expected to become particularly valuable in applications where system-defining variables are not measurable or the physical understanding is incomplete.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"45 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144341113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Size effects in metallic polycrystals in the context of strain-integral crystal plasticity","authors":"Charles Mareau","doi":"10.1016/j.jmps.2025.106236","DOIUrl":"10.1016/j.jmps.2025.106236","url":null,"abstract":"<div><div>The development of constitutive models usually relies on the framework of strain-gradient plasticity to consider the size and gradient effects that affect the thermomechanical behavior of crystalline materials. In this work, an alternative strategy, which fits into the category of strain-integral plasticity models, is explored. The underlying idea consists of evaluating the spatial average and the spatial covariance of the plastic deformation gradient tensor. These non-local variables are treated as additional internal state variables that provide some information regarding the spatial distribution of the plastic deformation gradient tensor.</div><div>In the present paper, the method used for the evaluation of the average and the covariance of the plastic deformation gradient tensor is first detailed. Particular attention is paid to the treatment of near-boundary regions, for which different options are proposed. Then, a general strategy to include the average and the covariance of the plastic deformation gradient tensor in constitutive relations in a thermodynamically consistent manner is exposed. Finally, a crystal plasticity-based model developed within the framework of strain-integral plasticity is presented for the purpose of illustration. The numerical results obtained for different polycrystalline microstructures indicate that the hardening behavior is impacted by the mean grain size. However, such a size-dependent behavior largely depends on the method used for the treatment of near-boundary regions.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106236"},"PeriodicalIF":5.0,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144341108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiple scattering of elastic waves in polycrystals","authors":"Anubhav Roy, Christopher M. Kube","doi":"10.1016/j.jmps.2025.106237","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106237","url":null,"abstract":"Elastic waves that propagate in polycrystalline materials attenuate due to scattering of energy out of the primary propagation direction in addition to becoming dispersive in their group and phase velocities. Attenuation and dispersion are modeled through multiple scattering theory to describe the mean displacement field or the mean elastodynamic Green’s function. The Green’s function is governed by the Dyson equation and was solved previously (Weaver 1990) by truncating the multiple scattering series at first-order, which is known as the first-order smoothing approximation (FOSA). FOSA allows for multiple scattering but places a restriction on the scattering events such that a scatterer can only be visited once during a particular multiple scattering process. In other words, recurrent scattering between two scatterers is not permitted. In this article, the Dyson equation is solved using the second-order smoothing approximation (SOSA). The SOSA permits scatterers to be visited twice during the multiple scattering process and, thus, provides a more complete picture of the multiple scattering effects on elastic waves. The derivation is valid at all frequencies spanning the Rayleigh, stochastic, and geometric scattering regimes without additional approximations that limit applicability in strongly scattering cases (like the Born approximation). The importance of SOSA is exemplified through analyzing specific weak and strongly scattering polycrystals. Multiple scattering effects contained in SOSA are shown to be important at the beginning of the stochastic scattering regime and are particularly important for transverse (shear) waves. This step forward opens the door for a deeper fundamental understanding of multiple scattering phenomena in polycrystalline materials.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"44 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144341116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanics informatics: A paradigm for efficiently learning constitutive models","authors":"Royal C. Ihuaenyi ,&nbsp;Wei Li ,&nbsp;Martin Z. Bazant ,&nbsp;Juner Zhu","doi":"10.1016/j.jmps.2025.106239","DOIUrl":"10.1016/j.jmps.2025.106239","url":null,"abstract":"<div><div>Efficient and accurate learning of constitutive laws is crucial for accurately predicting the mechanical behavior of materials under complex loading conditions. Accurate model calibration hinges on a delicate interplay between the information embedded in experimental data and the parameters that define our constitutive models. The information encoded in the parameters of the constitutive model must be complemented by the information in the data used for calibration. This interplay raises fundamental questions: How can we quantify the information content of test data? How much information does a single test convey? Also, how much information is required to accurately learn a constitutive model? To address these questions, we introduce <em>mechanics informatics</em>, a paradigm for efficient and accurate constitutive model learning. At its core is the <em>stress state entropy</em>, a metric for quantifying the information content of experimental data. Using this framework, we analyzed specimen geometries with varying information content for learning an anisotropic inelastic law. Specimens with limited information enabled accurate identification of a few parameters sensitive to the information in the data. Furthermore, we optimized specimen design by incorporating stress state entropy into a Bayesian optimization scheme. This led to the design of cruciform specimens with maximized entropy for accurate parameter identification. Conversely, minimizing entropy in Peirs shear specimens yielded a uniform shear stress state, showcasing the framework’s flexibility in tailoring designs for specific experimental goals. Finally, we addressed experimental uncertainties, demonstrated the potential of transfer learning for replacing challenging testing protocols with simpler alternatives, and extension of the framework to different material laws.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106239"},"PeriodicalIF":5.0,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144341114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Impedance theory-based elastic metasurface enabling precise mode conversion and preservation","authors":"Mu Jiang ,&nbsp;Hong-Tao Zhou ,&nbsp;Tong Zhu ,&nbsp;Yan-Feng Wang ,&nbsp;Badreddine Assouar ,&nbsp;Yue-Sheng Wang","doi":"10.1016/j.jmps.2025.106231","DOIUrl":"10.1016/j.jmps.2025.106231","url":null,"abstract":"<div><div>The coupling between longitudinal and transverse waves poses challenges for achieving precise and flexible wave modulation. Metasurface provides a promising platform for wave modulation. Designs derived from the generalized Snell’s law are constrained by unit-based analysis, lacking the versatility and efficiency required for complex two-dimensional wavefields. Inspired by recent developments in acoustics, impedance theory for precise manipulation of in-plane elastic waves is established in this work. As verification of this theoretical framework, we demonstrate mode preservation and mode conversion with wavefront manipulation by the design of metasurfaces. Their impedance interface conditions are derived, and the limitations of the generalized Snell’s law for precise manipulation are analyzed. Through topology optimization, unit cells satisfying the impedance requirements are obtained and further assembled into elastic metasurfaces. The effectiveness of this impedance-based approach for precise in-plane wave modulation is successfully validated through both numerical simulations and experimental measurements.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106231"},"PeriodicalIF":5.0,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite-PINN: A physics-informed neural network with finite geometric encoding for solid mechanics","authors":"Haolin Li ,&nbsp;Yuyang Miao ,&nbsp;Zahra Sharif Khodaei ,&nbsp;M.H. Aliabadi","doi":"10.1016/j.jmps.2025.106222","DOIUrl":"10.1016/j.jmps.2025.106222","url":null,"abstract":"<div><div>PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems. These challenges become evident when comparing the limitations of PINN with the well-established numerical methods commonly used in solid mechanics, such as the finite element method (FEM). Specifically: a) PINN models generate solutions over an infinite domain, which conflicts with the finite boundaries typical of most solid structures; and b) the solution space utilised by PINN is Euclidean, which is inadequate for addressing the complex geometries often present in solid structures.</div><div>This work presents a PINN architecture for general solid mechanics problems, referred to as the Finite-PINN model. The model is designed to effectively tackle two key challenges, while retaining as much of the original PINN framework as possible. To this end, the Finite-PINN incorporates finite geometric encoding into the neural network inputs, thereby transforming the solution space from a conventional Euclidean space into a hybrid Euclidean–topological space. The model is trained using both strong-form and weak-form loss formulations, enabling its application to a wide range of forward and inverse problems in solid mechanics For forward problems, the Finite-PINN model efficiently approximates solutions to solid mechanics problems when the geometric information of a given structure has been preprocessed. For inverse problems, it effectively reconstructs full-field solutions from very sparse observations by embedding both physical laws and geometric information within its architecture.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106222"},"PeriodicalIF":5.0,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144341115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Impact of gas/liquid phase change of CO2 during injection for sequestration","authors":"Mina Karimi ,&nbsp;Elizabeth S. Cochran ,&nbsp;Mehrdad Massoudi ,&nbsp;Noel Walkington ,&nbsp;Matteo Pozzi ,&nbsp;Kaushik Dayal","doi":"10.1016/j.jmps.2025.106232","DOIUrl":"10.1016/j.jmps.2025.106232","url":null,"abstract":"<div><div>CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> sequestration in deep saline formations is an effective and important process to control the rapid rise in CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> emissions. The process of injecting CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> requires reliable predictions of the stress in the formation and the fluid pressure distributions – particularly since monitoring of the CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> migration is difficult – to mitigate leakage, prevent induced seismicity, and analyze wellbore stability. A key aspect of CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> is the gas–liquid phase transition at the temperatures and pressures of relevance to leakage and sequestration, which has been recognized as being critical for accurate predictions but has been challenging to model without <em>ad hoc</em> empiricisms.</div><div>This paper presents a robust multiphase thermodynamics-based poromechanics model to capture the complex phase transition behavior of CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> and predict the stress and pressure distribution under super- and sub- critical conditions during the injection process. A finite element implementation of the model is applied to analyze the behavior of a multiphase porous system with CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> as it displaces the fluid brine phase. We find that if CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> undergoes a phase transition in the geologic reservoir, the spatial variation of the density is significantly affected, and the migration mobility of CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> decreases in the reservoir. A key feature of our approach is that we do not <em>a priori</em> assume the location of the CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> gas/liquid interface – or even if it occurs at all – but rather, this is a prediction of the model, along with the spatial variation of the phase of CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> and the change of the saturation profile due to the phase change.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106232"},"PeriodicalIF":5.0,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local resonance of mechanosensitive channels","authors":"Bing Qi ,&nbsp;Shujuan Lin ,&nbsp;Yaohua Guo ,&nbsp;Linglin Feng ,&nbsp;Lijun Su ,&nbsp;Yang Liu ,&nbsp;Alain Goriely ,&nbsp;Tian Jian Lu ,&nbsp;Shaobao Liu","doi":"10.1016/j.jmps.2025.106249","DOIUrl":"10.1016/j.jmps.2025.106249","url":null,"abstract":"<div><div>Mechanosensitive channels are crucial biological structures that respond to mechanical stimuli by altering cellular processes. Recent studies suggest that these channels can be activated by ultrasound at specific frequencies, yet the underlying physical mechanisms remain unclear. Membrane tension is known to play a pivotal role in the regulation of mechanosensitive channels. Here, we investigate whether ultrasound can modulate membrane tension to facilitate channel activation. To do so, we develop a theoretical model based on the local resonance of mechanosensitive channels embedded in lipid membranes when subjected to ultrasonic excitation. Our results reveal that ultrasound can induce localized membrane resonance, leading to increased membrane tension in the vicinity of the channel. This tension increase, when occurring at specific resonant frequencies, is sufficient to activate mechanosensitive channels. Furthermore, we establish the effective frequency range for channel activation and examine the influence of key parameters such as ultrasound intensity, channel molecular mass, and damping effects on this range. Our findings provide a mechanistic explanation for ultrasound-induced activation of mechanosensitive channels, offering valuable insights for applications in neuromodulation, targeted therapy, and mechanomedicine.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106249"},"PeriodicalIF":5.0,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}