arXiv subjects

Betim Bahtiri

Publications and source records attributed to Betim Bahtiri.

6 recordsLinked to original sources

arXiv2026

PI-GINOT: Data-free geometry-informed neural operator learning for finite-strain hyperelasticity on parametric DogBone specimens

Parametric nonlinear solid-mechanics simulations are widely used in virtual testing, optimisation, and uncertainty analysis, but repeated finite-element simulations become costly when geometry changes. This paper presents PI-GINOT, a physics-informed neural operator that predicts finite-strain hyperelastic responses across a four-parameter family of DogBone specimens without using finite-element training data. Each specimen is described by a boundary point cloud, which is encoded into geometry features. A cross-attention decoder then predicts displacement at arbitrary points. Displacement boundary conditions are enforced exactly, while stresses are computed using automatic differentiation and a compressible Neo-Hookean plane-stress model. Training is guided by equilibrium, traction-free and symmetry conditions, deformation stability, and internal force consistency. Abaqus simulations are used only after training for validation. Across eight test geometries, PI-GINOT achieves displacement errors of 2.1%-7.1%, peak von Mises stress errors of 0.9%-13.3%, and section-force errors below 10.3%. Larger errors occur in individual stress components, especially for narrow specimens, mainly because of steep stress gradients near the gauge-to-fillet transition. These results show that PI-GINOT can provide useful geometry-dependent predictions for nonlinear solid mechanics without labelled simulation data, while also revealing where better local stress resolution is still needed.

physics.comp-ph↗

arXiv2026

A multiphysics deep energy method for fourth-order phase-field fracture with piezoresistive self-sensing

Piezoresistive materials can act as self-sensing media because deformation and cracking modify their electrical resistance. This paper presents a fracture-informed multiphysics framework for phase-field fracture using the Deep Energy Method. Mechanical deformation and fracture are solved first, after which the converged strain and damage fields determine a passive electrical-conduction readout. The electrical field does not contribute to the fracture-driving energy, and a control calculation confirmed that removing the electrical contribution produced no observable change in the crack morphology or global mechanical response. The mechanics-fracture formulation combines small-strain elasticity, a spectral tension-compression split, history-field irreversibility, and a fourth-order AT2-type regularization. The subsequent steady-conduction problem employs a conductivity law that accounts for linearized piezoresistivity and crack-induced degradation. The implementation uses admissible neural trial functions, quadrature-based energy evaluation, warm-started load stepping, and a bounded phase-field variable. Component-level verification includes analytical conduction tests, a reference-aligned single-edge-notched tension benchmark, and a perforated tensile-plate example. The results show that substantial local damage does not necessarily cause an immediate global resistance increase; a pronounced signal emerges only when major current-carrying ligaments are disrupted. The framework thus provides a transparent forward model for interpreting resistance-based self-sensing in fractured piezoresistive materials.

physics.comp-ph↗

arXiv2026

A hybrid electromechanical phase-field and deep learning framework for predicting fracture in dielectric nanocomposites

The accurate and efficient prediction of crack propagation in dielectric materials is a critical challenge in structural health monitoring and the design of smart systems. This work presents a hybrid modeling framework that combines an electromechanical phase-field fracture model with deep learning-based surrogate modeling to predict fracture evolution in dielectric nanocomposite plates. The underlying finite element simulations capture the coupling between mechanical deformation and electrical field perturbations caused by cracks, using a variational phase-field formulation. High-fidelity simulation outputs - namely, phase-field damage variables and electric potential fields -- are used to train convolutional neural networks (CNNs) with ResNet-U-Net architectures for pixel-wise segmentation of crack paths. The study systematically compares the performance of CNNs trained on phase-field versus electric potential data across multiple ResNet backbones. The results reveal that electric potential fields, although they encode damage indirectly, offer superior segmentation accuracy, faster convergence, and enhanced generalization, owing to their smoother gradient distribution and global spatial coverage. The proposed framework significantly reduces computational costs while preserving high accuracy, offers potential when appropriately adapted for sensor-based input data.

physics.comp-ph↗

arXiv2024

A thermodynamically consistent physics-informed deep learning material model for short fiber/polymer nanocomposites

This work proposes a physics-informed deep learning (PIDL)-based constitutive model for investigating the viscoelastic-viscoplastic behavior of short fiber-reinforced nanoparticle-filled epoxies under various ambient conditions. The deep-learning model is trained to enforce thermodynamic principles, leading to a thermodynamically consistent constitutive model. To accomplish this, a long short-term memory network is combined with a feed-forward neural network to predict internal variables required for characterizing the internal dissipation of the nanocomposite materials. In addition, another feed-forward neural network is used to indicate the free-energy function, which enables defining the thermodynamic state of the entire system. The PIDL model is initially developed for the three-dimensional case by generating synthetic data from a classical constitutive model. The model is then trained by extracting the data directly from cyclic loading-unloading experimental tests. Numerical examples show that the PIDL model can accurately predict the mechanical behavior of epoxy-based nanocomposites for different volume fractions of fibers and nanoparticles under various hygrothermal conditions.

cs.LG↗

arXiv2024

Cyclic viscoelastic-viscoplastic behavior of epoxy nanocomposites under hygrothermal conditions: A phase-field fracture model

In this study, a finite deformation phase-field formulation is developed to investigate the effect of hygrothermal conditions on the viscoelastic-viscoplastic fracture behavior of epoxy nanocomposites under cyclic loading. The formulation incorporates a definition of the Helmholtz free energy, which considers the effect of nanoparticles, moisture content, and temperature. The free energy is additively decomposed into a deviatoric equilibrium, a deviatoric non-equilibrium, and a volumetric contribution, with distinct definitions for tension and compression. The proposed derivation offers a realistic modeling of damage and viscoplasticity mechanisms in the nanocomposites by coupling the phase-field damage model with a modified crack driving force and a viscoelastic-viscoplastic model. Numerical simulations are conducted to study the cyclic force-displacement response of both dry and saturated boehmite nanoparticle (BNP)/epoxy samples, considering BNP contents and temperature. Comparing numerical results with experimental data shows good agreement at various BNP contents. In addition, the predictive capability of the phase-field model is evaluated through simulations of single-edge notched nanocomposite plates subjected to monolithic tensile and shear loading.

cs.CE↗

arXiv2023

A machine learning-based viscoelastic-viscoplastic model for epoxy nanocomposites with moisture content

In this work, we propose a deep learning (DL)-based constitutive model for investigating the cyclic viscoelastic-viscoplastic-damage behavior of nanoparticle/epoxy nanocomposites with moisture content. For this, a long short-term memory network is trained using a combined framework of a sampling technique and a perturbation method. The training framework, along with the training data generated by an experimentally validated viscoelastic-viscoplastic model, enables the DL model to accurately capture the rate-dependent stress-strain relationship and consistent tangent moduli. In addition, the DL-based constitutive model is implemented into finite element analysis. Finite element simulations are performed to study the effect of load rate and moisture content on the force-displacement response of nanoparticle/ epoxy samples. Numerical examples show that the computational efficiency of the DL model depends on the loading condition and is significantly higher than the conventional constitutive model. Furthermore, comparing numerical results and experimental data demonstrates good agreement with different nanoparticle and moisture contents.

cs.LG↗