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Nikolaos Bouklas

Publications and source records attributed to Nikolaos Bouklas.

At least 37 records · Page 2Linked to original sources
arXiv2025

A chain stretch-based gradient-enhanced model for damage and fracture in elastomers

In this study, we introduce a novel stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials, they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening. This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. We discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

cond-mat.soft↗
arXiv2024

Condensed Stein Variational Gradient Descent for Uncertainty Quantification of Neural Networks

We propose a Stein variational gradient descent method to concurrently sparsify, train, and provide uncertainty quantification of a complexly parameterized model such as a neural network. It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed condensed Stein variational gradient (cSVGD) method provides uncertainty quantification on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a representation problem in solid mechanics.

cs.LG↗
arXiv2024

Evaluating fracture energy predictions using phase-field and gradient-enhanced damage models for elastomers

Recently, the phase field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft materials, the convergence of the phase-field method becomes challenging, especially in scenarios of unstable crack growth. To overcome these numerical difficulties, several approaches have been introduced, with artificial viscosity being among the most widely utilized. This study investigates the energy release rate due to crack propagation in hyperelastic nearly-incompressible materials and compares the phase-field method and a novel gradient-enhanced damage (GED) approach. First, we simulate unstable loading scenarios using the phase-field method, which leads to convergence problems. To address these issues, we introduce artificial viscosity to stabilize the problem and analyze its impact on the energy release rate utilizing a domain J-integral approach giving quantitative measurements during crack propagation. It is observed that the measured energy released rate during crack propagation does not comply with the imposed critical energy release rate, and shows non-monotonic behavior. In the second part of the paper, we introduce a novel stretch-based GED model as an alternative to the phase-field method for modeling crack evolution in elastomers. It is demonstrated that in this method, the energy release rate can be obtained as an output of the simulation rather than as an input which could be useful in the exploration of rate-dependent responses, as one could directly impose chain-level criteria for damage initiation. We show that while this novel approach provides reasonable results for fracture simulations, it still suffers from some numerical issues that strain-based GED formulations are known to be susceptible to.

cond-mat.mtrl-sci↗
arXiv2024

Improving the performance of Stein variational inference through extreme sparsification of physically-constrained neural network models

Most scientific machine learning (SciML) applications of neural networks involve hundreds to thousands of parameters, and hence, uncertainty quantification for such models is plagued by the curse of dimensionality. Using physical applications, we show that $L_0$ sparsification prior to Stein variational gradient descent ($L_0$+SVGD) is a more robust and efficient means of uncertainty quantification, in terms of computational cost and performance than the direct application of SGVD or projected SGVD methods. Specifically, $L_0$+SVGD demonstrates superior resilience to noise, the ability to perform well in extrapolated regions, and a faster convergence rate to an optimal solution.

cs.LG↗
arXiv2024

Establishing the relationship between generalized crystallographic texture and macroscopic yield surfaces using partial input convex neural networks

In this study, we present a methodology to predict the macroscopic yield surface of metals and metallic alloys with general crystallographic textures. In previous work, we have established the use of partially input convex neural networks (pICNN) as macroscopic yield functions of crystal plasticity simulations. However, this work was performed with an over-abundance of data, and on limited crystallographic textures. Here, we extend this study to approach more realistic material states (i.e., complex crystallographic textures), and consider data-availability as a major driver for our approach. We present our modified framework capable of handling generalized material states and demonstrate its effectiveness on samples with multi-modal textures deformed under plane stress conditions. We further describe an adaptive algorithm for the generation of training data as informed by the shape of yield surfaces to reduce the time for both the generation of training data as well as pICNN training. Finally, we will discuss errors in both training and test datasets, limitations, and future extensibility.

cond-mat.mtrl-sci↗
arXiv2024

Multiscale simulation of spatially correlated microstructure via a latent space representation

When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure-property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. We demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.

cond-mat.mtrl-sci↗
arXiv2024

A review on data-driven constitutive laws for solids

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits and drawbacks of the various techniques for interpreting and forecasting mechanics behavior across different scales. Distinguishing between machine-learning-based and model-free methods, we further categorize approaches based on their interpretability and on their learning process/type of required data, while discussing the key problems of generalization and trustworthiness. We attempt to provide a road map of how these can be reconciled in a data-availability-aware context. We also touch upon relevant aspects such as data sampling techniques, design of experiments, verification, and validation.

cs.CE↗
arXiv2023

Modeling the mechanosensitive collective migration of cells on the surface and the interior of morphing soft tissues

Cellular contractility, migration, and extracellular matrix (ECM) mechanics are critical for a wide range of biological processes including embryonic development, wound healing, tissue morphogenesis, and regeneration. Even though the distinct response of cells near the tissue periphery has been previously observed in cell-laden microtissues, including faster kinetics and more prominent cell-ECM interactions, there are currently no models that can fully combine coupled surface and bulk mechanics and kinetics to recapitulate the morphogenic response of these constructs. Mailand \textit{et al.} (2019) had shown the importance of active elastocapillarity in cell-laden microtissues, but modeling the distinct mechanosensitive migration of cells on the periphery and the interior of highly deforming tissues has not been possible thus fur, especially in the presence of active elastocapillary effects. This paper presents a framework for understanding the interplay between cellular contractility, migration, and ECM mechanics in dynamically morphing soft tissues accounting for distinct cellular responses in the bulk and the surface of tissues. The major novelty of this approach is that it enables modeling the distinct migratory and contractile response of cells residing on the tissue surface and the bulk, where concurrently the morphing soft tissues undergoes large deformations driven by cell contractility. Additionally, the proposed model is validated through simulation results that capture the changes in shape and cell concentration for wounded and intact microtissues, enabling the interpretation of experimental data.

physics.bio-ph↗
arXiv2023

Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow to obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. In this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^{0}$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a-priory but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, for synthetic and experimental data.

cs.CE↗
arXiv2023

Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen

Data-driven constitutive modeling frameworks based on neural networks and classical representation theorems have recently gained considerable attention due to their ability to easily incorporate constitutive constraints and their excellent generalization performance. In these models, the stress prediction follows from a linear combination of invariant-dependent coefficient functions and known tensor basis generators. However, thus far the formulations have been limited to stress representations based on the classical Rivlin and Ericksen form, while the performance of alternative representations has yet to be investigated. In this work, we survey a variety of tensor basis neural network models for modeling hyperelastic materials in a finite deformation context, including a number of so far unexplored formulations which use theoretically equivalent invariants and generators to Finger-Rivlin-Ericksen. Furthermore, we compare potential-based and coefficient-based approaches, as well as different calibration techniques. Nine variants are tested against both noisy and noiseless datasets for three different materials. Theoretical and practical insights into the performance of each formulation are given.

cond-mat.soft↗
arXiv2023

NN-EVP: A physics informed neural network-based elasto-viscoplastic framework for predictions of grain size-aware flow response under large deformations

We propose a physics informed, neural network-based elasto-viscoplasticity (NN-EVP) constitutive modeling framework for predicting the flow response in metals as a function of underlying grain size. The developed NN-EVP algorithm is based on input convex neural networks as a means to strictly enforce thermodynamic consistency, while allowing high expressivity towards model discovery from limited data. It utilizes state-of-the-art machine learning tools within PyTorch's high-performance library providing a flexible tool for data-driven, automated constitutive modeling. To test the performance of the framework, we generate synthetic stress-strain curves using a power law-based model with phenomenological hardening at small strains and test the trained model for strain amplitudes beyond the training data. Next, experimentally measured flow responses obtained from uniaxial deformations are used to train the framework under large plastic deformations. Ultimately, the Hall-Petch relationship corresponding to grain size strengthening is discovered by training flow response as a function of grain size, also leading to efficient extrapolation. The present work demonstrates a successful integration of neural networks into elasto-viscoplastic constitutive laws, providing a robust automated framework for constitutive model discovery that can efficiently generalize, while also providing insights into predictions of flow response and grain size-property relationships in metals and metallic alloys under large plastic deformations.

cs.CE↗
arXiv2023

A finite element implementation of finite deformation surface and bulk poroelasticity

We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on surface. Nonlinear theories allow us to systematically study porous solids in a wide range of applications, such as drug delivery, biomaterial design, fundamental study of biomechanics and mechanobiology, and the design of sensors and actuators. As we aim to understand the physical phenomena at a smaller length scale towards comprehending the fundamental biological processes and the miniaturization of devices, the surface effect becomes more pertinent. Although existing methodologies provide the necessary tools to study coupled bulk effects for deformation and diffusion; however, very little is known about fully coupled bulk and surface poroelasticity at finite strain. Here we develop a thermodynamically consistent formulation for multiphysics processes of surface and bulk poroelasticity, specialized for soft hydrated solids, along with a corresponding finite element implementation. Our multiphysical approach captures the interplay between competing processes of finite deformation and species diffusion through the bulk and surface, and provides invaluable insight when surface effects are important.

cond-mat.soft↗
arXiv2023

Physics-informed Data-driven Discovery of Constitutive Models with Application to Strain-Rate-sensitive Soft Materials

A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress-strain-strain rate responses in both training and testing regimes, and provide improvements in terms of prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.

cs.CE↗
arXiv2022

Modular machine learning-based elastoplasticity: generalization in the context of limited data

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish stress-evolution laws that avoid user-chosen functional forms by relying on machine learning representations and algorithms. However, these approaches not only require a significant amount of data but also need data that probes the full stress space with a variety of complex loading paths. Furthermore, they rarely enforce all necessary thermodynamic principles as hard constraints. Hence, they are in particular not suitable for low-data or limited-data regimes, where the first arises from the cost of obtaining the data and the latter from the experimental limitations of obtaining labeled data, which is commonly the case in engineering applications. In this work, we discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information and the complexity of the response. The method is tested on synthetic uniaxial data coming from simulations as well as cyclic experimental data for structural materials. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data. Training aspects and details of the implementation of these models into Finite Element simulations are discussed and analyzed.

cs.LG↗
arXiv2022

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level to macroscopic quantities that govern damage and failure must be established. Constitutive models based upon statistical mechanics have used variants of the freely jointed chain (FJC) model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the FJC model (as derived in the uFJC framework of Buche and colleagues), which we have extended to yield a tractable, closed-form model that is amenable to constitutive model development. Inspired by the asymptotically matched uFJC model response, a simple, quasi-polynomial, and anharmonic bond potential energy function is derived. Using this bond potential, approximate yet highly-accurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This framework is based upon a force-modified tilted bond potential that accounts for distortional bond potential energy, allowing for the calculation of dissipated chain scission energy. The model is fit to single-chain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can be straightforwardly implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.

cond-mat.soft↗
arXiv2022

Deep Convolutional Ritz Method: Parametric PDE surrogates without labeled data

Parametric surrogate models for partial differential equations (PDEs) are a necessary component for many applications in the computational sciences, and convolutional neural networks (CNNs) have proved as an excellent tool to generate these surrogates when parametric fields are present. CNNs are commonly trained on labeled data based on one-to-one sets of parameter-input and PDE-output fields. Recently, residual-based convolutional physics-informed neural network (CPINN) solvers for parametric PDEs have been proposed to build surrogates without the need for labeled data. These allow for the generation of surrogates without an expensive offline-phase. In this work, we present an alternative formulation termed Deep Convolutional Ritz Method (DCRM) as a parametric PDE solver. The approach is based on the minimization of energy functionals, which lowers the order of the differential operators compared to residual-based methods. Based on studies involving the Poisson equation with a spatially parameterized source term and boundary conditions, we found that CNNs trained on labeled data outperform CPINNs in convergence speed and generalization ability. Surrogates generated from DCRM, however, converge significantly faster than their CPINN counterparts and prove to generalize faster and better than surrogates obtained from both CNNs trained on labeled data and CPINNs. This hints that DCRM could make PDE solution surrogates trained without labeled data possible.

cs.CE↗
arXiv2022

Learning hyperelastic anisotropy from data via a tensor basis neural network

Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel neural network layers, and L1 regularization. The proposed tensor-basis neural network can discover both the type and orientation of the anisotropy and provide an accurate model of the stress response. The method is demonstrated with data from hyperelastic materials with off-axis transverse isotropy and orthotropy, as well as materials with less well-defined symmetries induced by fibers or spherical inclusions. Both plain feed-forward neural networks and input-convex neural network formulations are developed and tested. Using the latter, a polyconvex potential can be established, which, by satisfying the growth condition can guarantee the existence of boundary value problem solutions.

cond-mat.mtrl-sci↗
arXiv2022

Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT-AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. Furthermore, this BT-AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.

cs.CE↗