Abstract For material modeling and discovery, synthetic microstructures play a critical role as digital twins. They provide stochastic samples upon which direct numerical simulations can be conducted to populate databases. A large ensemble of simulation data on may supplemental inform refine macroscopic models, might not feasible from physical experiments alone. However, synthesizing realistic with microstructural attributes is highly challenging. Thus, it often oversimplified via rough...

Abstract We present a machine learning framework capable of consistently inferring mathematical expressions hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose polyconvex neural additive model (PNAM) that enables us to express the in learnable feature space while enforcing polyconvexity. An upshot obtained via PNAM is (1) it spanned by set univariate basis functions can be re‐parametrized with more...

Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, unavoidable. Polynomial Chaos Expansion (PCE) widely recognized a to-go method constructing stochastic solutions both intrusive and non-intrusive ways. Its application becomes challenging, however, complex or high-dimensional processes, achieving accuracy requires higher-order polynomials, which can increase...

The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two networks to map between infinite-dimensional function spaces. This allows for the evaluation of solution field at any location within domain but requires input functions be discretized identical locations, limiting practical applications. We introduce general framework learning from input-output data with arbitrary sensor locations and counts. begins by introducing resolution-independent DeepONet...

We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used drive evaluate the effective tensor. However, they typically fail correctly fracture in compression. propose force based on Mohr-Coulomb failure criterion an relation that remedy this problem. An evolution equation specifies rate at which tends quasi-static limit. relaxation time introduces intrinsic length scale dynamic addresses mesh...

We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicts the formation factor and effective permeability from micro-CT images. Fast Fourier Transform (FFT) solvers are established to compute both permeability, while topology geometry of pore space represented by persistence-based Morse graph. Together, they constitute database for training, validating, testing networks. While Euclidean convolutional approaches employ networks generate low-dimensional latent...

This paper presents a PINN training framework that employs (1) pre-training steps accelerates and improve the robustness of physics-informed neural network with auxiliary data stored in point clouds, (2) net-to-net knowledge transfer algorithm improves weight initialization (3) multi-objective optimization may performance physical-informed competing constraints. We consider multi-task learning (PINN) as problems where physics constraints such governing equation, boundary conditions,...

To accurately simulate fracture, it is necessary to account for small-scale randomness in the properties of a material. Apparent statistical volume element (SVE) can be characterized below scale representative (RVE). cannot defined uniquely an SVE, manner that unique effective RVE. Both constitutive behavior and material strength SVE must statistically characterized. The geometrical partitioning method critically important affecting probability distributions mesoscale property parameters....

The response of quasi-brittle materials is greatly influenced by their microstructural architecture and variations. To model such statistical variability, Statistical Volume Elements (SVEs) are used to derive a scalar fracture strength for domains populated with microcracks. By employing the moving window approach probability density function covariance field obtained. Karhunen-Loève method generate realizations that consistent SVE-derived statistics. effect homogenization scheme, through...

To accurately predict fracture patterns in quasi-brittle materials, it is necessary to characterize heterogeneity the properties of a material microstructure. This influences crack propagation at weaker points. Also, inherent randomness localized creates variability population nominally identical samples. In order account for strength small scale (or “microscale”), mesoscale model developed an intermediate scale, smaller than size overall structure. A central challenge characterizing...

A bulk damage formulation is presented for failure analysis of brittle materials under dynamic loading. time-delay ordinary differential equation (ODE) used to model evolution. The evolution driven by the difference between a target static value and instantaneous value. length scale introduced from model's intrinsic relaxation time elastic wave speeds. This addresses mesh sensitivity problem some existing formulations fracture, with less computational effort than other remedies. authors use...

We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicting the formation factor and effective permeability from micro-CT images. FFT solvers are established to compute both permeability, while topology geometry of pore space represented by persistence-based Morse graph. Together, they constitute database for training, validating, testing networks. While Euclidean convolutional approaches employ networks generate low-dimensional latent represent features...

Maintaining material inhomogeneity and sample-to-sample variations is crucial in fracture analysis, particularly for quasibrittle materials. We use statistical volume elements (SVEs) to homogenize elastic properties of ZrB2-SiC, a two-phase composite often used thermal coating. At the mesoscale, 2D finite element mesh generated from microstructure using Conforming Interface Structured Adaptive Mesh Refinement (CISAMR), which non-iterative algorithm that tracks interfaces yields high-quality...

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical interpretable by human experts. In particular, we introduce surrogate model where yield surfaces expressed in terms of set single-variable feature mappings obtained from supervised learning. A post-processing step is then used to re-interpret the mapping functions into form through symbolic regression....

We present a machine learning framework capable of consistently inferring mathematical expressions hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose polyconvex neural additive model (PNAM) that enables us to express the in learnable feature space while enforcing polyconvexity. An upshot obtained via PNAM is (1) it spanned by set univariate basis can be re-parametrized with more complex form, (2)...

The main goal of the current study is developing an advanced and robust numerical tool for accurate capturing heat front propagation. In some applications such as impermeable medium, Heat transfer in surrounding domain fracture acts just a conduction process but through fractures appears convection process. From mathematical point view, parabolic partial differential equation (PDE) should be solved whereas hyperbolic PDE fractures. fact, they have completely different treatments this one...