Continuum Mechanics Research Articles

CoupNeRF: Property‐aware Neural Radiance Fields for Multi‐Material Coupled Scenario Reconstruction

AbstractNeural Radiance Fields (NeRFs) have achieved significant recognition for their proficiency in scene reconstruction and rendering by utilizing neural networks to depict intricate volumetric environments. Despite considerable research dedicated to reconstructing physical scenes, rare works succeed in challenging scenarios involving dynamic, multi‐material objects. To alleviate, we introduce CoupNeRF, an efficient neural network architecture that is aware of multiple material properties. This architecture combines physically grounded continuum mechanics with NeRF, facilitating the identification of motion systems across a wide range of physical coupling scenarios. We first reconstruct specific‐material of objects within 3D physical fields to learn material parameters. Then, we develop a method to model the neighbouring particles, enhancing the learning process specifically in regions where material transitions occur. The effectiveness of CoupNeRF is demonstrated through extensive experiments, showcasing its proficiency in accurately coupling and identifying the behavior of complex physical scenes that span multiple physics domains.

Strain energy density maximization principle for material design and the reflection in trans-scale continuum theory

Traditional efforts in the design of damage-tolerant structural materials were largely exercises in optimizing the combination of strength and ductility. However, the simultaneous consideration of these two conflicting mechanical indices, improving one inevitably sacrifices the other, makes the design extremely complex and difficult, due to the dilemma of choosing between them. Here, physically guided by the energy variational expression in trans-scale continuum mechanics theory, we propose a general mechanics principle for material design that involving only one index: towards strong and tough material the strain energy density limit (w) should be maximized, i.e., strain energy density maximization principle, referred to as wmax principle. It aims to guide the attainment of exceptional comprehensive mechanical properties, while circumventing the dual-index dilemma by employing a singular index w. Extensive experimental data analyses prove that (i) the maximum wmax always exists, at a critical dimension of characteristic microstructure dc,micro, and (ii) w can effectively index strength-ductility synergy and the wmax is conjugated with both high strength and high ductility, verifying the validity of wmax principle. The universality, practicality and downward compatibility are also examined. The dc,micro approaches twice the span of strain gradient region around internal boundary, suggesting that the microstructure state with wmax is the critical state with strongest strain gradient. Importantly, the w improvement as a function of the characteristic size of either microstructure or deformation field can be well captured by strain gradient theory, confirming the consistence between the wmax principle, experimental results and trans-scale continuum theories. This principle opens up a new design concept for advanced structural materials from the perspective of microstructure-w-mechanical properties relationship.

Redesign of a Balance Rehabilitation Device Based on a Parallel Continuum Mechanism

In the present work, a parallel continuum manipulator for trunk rehabilitation tasks for patients who have suffered a stroke was analyzed and redesigned. The manipulator had to perform active assistance exercises for the motor recovery of the patient. Based on this background, a series of requirements were defined, which determined the design framework during the modeling of the manipulator. Finally, an improved prototype was built and tested to verify that the model can properly characterize the behavior of the manipulator. Such tests were carried out using a self-made dummy that replicates the simplifying hypotheses and conditions assumed in the mathematical model.

Continuum Mechanics Applied to the Biomechanics of Motion.

Continuum Mechanics is the discipline that studies the motion and deformation of material bodies, and is at the basis of both Solid Mechanics and Fluid Mechanics. This works aims at highlighting how a basic education in modern Continuum Mechanics can be of fundamental importance not only in the Biomechanics of Tissue, but also in the Biomechanics of Movement. The latter is largely based on Rigid Body Mechanics, which can be considered as a simple particular case of the general theory of Continuum Mechanics. As an example, a straightforward methodology for the extraction of the angular velocity from motion analysis data is illustrated. The method is based on a quantity that is more primitive than the angular velocity: the spin tensor.

Size-dependency and lattice-discreetness effect on fracture toughness in 2D crystals under antiplanar loading

AbstractFracture toughness is the material property characterizing resistance to failure. Predicting its value from the solid structure at the atomistic scale remains elusive, even in the simplest situations of brittle fracture. We report here numerical simulations of crack propagation in two-dimensional fuse networks of different periodic geometries, which are electrical analogs of bidimensional brittle crystals under antiplanar loading. Fracture energy is determined from Griffith’s analysis of energy balance during crack propagation, and fracture toughness is determined from fits of the displacement fields with Williams’ asymptotic solutions. Significant size dependencies are evidenced in small lattices, with fracture energy and fracture toughness both converging algebraically with system size toward well-defined material-constant values in the limit of infinite system size. The convergence speed depends on the loading conditions and is faster when the symmetry of the considered lattice increases. The material constants at infinity obey Irwin’s relation and properly define the material resistance to failure. Their values are approached up to $$\sim 15\%$$ ∼ 15 % using the recent analytical method proposed in Nguyen and Bonamy (Phys Rev Lett 123:205503, 2019). Nevertheless, the deviation remains finite and does not vanish when the system size goes to infinity. We finally show that this deviation is a consequence of the lattice discreetness and decreases when the super-singular terms of Williams’ solutions (absent in a continuum medium but present here due to lattice discreetness) are taken into account.

Multiscale homogenized constrained mixture model of the bio-chemo-mechanics of soft tissue growth and remodeling.

Constrained mixture models have successfully simulated many cases of growth and remodeling in soft biological tissues. So far, extensions of these models have been proposed to include either intracellular signaling or chemo-mechanical coupling on the organ-scale. However, no version of constrained mixture models currently exists that includes both aspects. Here, we propose such a version that resolves cellular signal processing by a set of logic-gated ordinary differential equations and captures chemo-mechanical interactions between cells by coupling a reaction-diffusion equation with the equations of nonlinear continuum mechanics. To demonstrate the potential of the model, we present 2 case studies within vascular solid mechanics: (i) the influence of angiotensin II on aortic growth and remodeling and (ii) the effect of communication between endothelial and intramural arterial cells via nitric oxide and endothelin-1.

Tensorial harmonic bases of arbitrary order with applications in elasticity, elastoviscoplasticity and texture-based modeling

In continuum mechanics, one regularly encounters higher-order tensors that require tensorial bases for theoretical or numerical calculations. By using results from [Formula: see text] representation theory, we present a method to derive tensorial harmonic bases which unifies existing approaches in one framework. Applying this convention to symmetric second-order tensors results in a second-order harmonic basis which, for example, simplifies the depiction and numerical handling of stiffness tensors for most common material symmetries and reduces the computational effort involved in implementations of incompressible elastoviscoplastic material laws. The same convention can be applied to texture analysis to yield tensorial texture coefficients for both polycrystals and fiber-reinforced composites. Rotations of higher-order tensors are particularly efficient in harmonic bases as both material and index symmetries can be exploited. While special attention is given here to the examples of small-strain material laws and texture analysis, the framework is entirely general and can be used to simplify calculations in other physical contexts involving tensors of arbitrary order and symmetry. A Python implementation of the harmonic basis convention defined in this work is available as a Supplementary Material.

Peridynamic computations for thin elastic rods

AbstractPeridynamics is a nonlocal continuum mechanics formulation well suited for simulating dynamic fracture phenomena. Various peridynamic material formulations have been developed in recent years. These models have some differences, particularly regarding the correct handling of elastic deformation. This study investigates the elastic wave propagation characteristics of bond‐based, ordinary state‐based, continuum‐kinematics‐inspired peridynamics and a local continuum consistent correspondence formulation. Specifically, it examines the behavior of longitudinal pressure waves within thin rods. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. In contrast, the local continuum consistent formulation exhibits outstanding accuracy in modeling wave propagation. Moreover, the fascinating “spaghetti fracture” phenomenon, where a bent thin rod always breaks into three or more pieces, motivates additional investigations. It is shown that reproducing a different number of fragments using peridynamic simulations is possible. Although initial experiments can be replicated, the sensitivity to numerous parameters necessitates further investigations for a more comprehensive understanding and validation.

Strain-gradient and damage failure behavior in particle reinforced heterogeneous matrix composites

A strain gradient plasticity model with strengthening effect and damage effect (SGSED) is developed under the continuum medium framework for particle-reinforced heterogeneous matrix composites (PRHMCs). Boron carbide (B4C) particle-reinforced ultrafine-grained (UFG)/fine-grained (FG) heterogeneous matrix composites (B4Cp/(UFG/FG)) are fabricated, in which the UFG region consisted of carbon nanotubes (CNTs)/6061 aluminum (Al) flakes with grains in the ultrafine range and the FG region is processed via 6061Al. The SGSED model is written into the user subroutines using commercial finite element (FE) calculation software, and the three-dimensional (3D) FE representative volume element (RVE) for B4Cp/(UFG/FG) composites is established, from which the distribution of the interface-affected-zone (IAZ) formed of the strain gradient caused by the uncoordinated deformation of the UFG-FG heterogeneous matrix and reinforced phase-matrix is calculated. The evolution of the strain gradient in the deformation process of composites and the influence of the strain gradient on the progressive damage and crack evolution of composites are analyzed, and the strain gradient strengthening-toughening mechanism of composites is revealed. It is found that the IAZ has a considerable strengthening-toughening effect on the composites, which can reduce stress concentration at the interface between the reinforced phase and the matrix, and slow down the crack propagation of the matrix.

Research Progress of Three-dimensional Geological Modeling and Multi-field Coupling of Fractured Oil and Gas Reservoirs

Fractured oil and gas reservoirs play an important role in oil and gas exploration and development due to their complex fracture network structure. As the main fluid channel in the reservoir, fractures have a significant impact on the migration, accumulation and exploitation efficiency of oil and gas. This paper summarizes the key geological characteristics of fractured reservoirs, including fracture types, distribution rules and main controlling factors of fracture development, and discusses the influence of fractures on reservoir physical properties. Furthermore, the deterministic and stochastic modeling methods of three-dimensional geological modeling of fractured reservoirs and the latest progress of discrete fracture network modeling technology are introduced in detail. In addition, this paper also discusses in detail the application of multi-field coupling model in the numerical simulation of fluid flow in fractured reservoirs, including continuous medium model and discrete medium model, and their advantages and disadvantages in simulating fluid flow in fractured reservoirs. Finally, this paper summarizes the research progress of multi-physics coupling model of fractured reservoirs, and points out the direction and challenges of future research. Through these studies, it can provide theoretical support and technical guidance for oil and gas exploration and development, in order to achieve more effective development and management of fractured reservoirs.

TESTING OF ROCK SAMPLES FROM OIL AND GAS FIELDS TO DETERMINE THEIR PHYSICAL AND MECHANICAL CHARACTERISTICS

Determination of the physical and mechanical properties of anisotropic limestone rocks is an important and urgent task, since carbonate deposits are very often found in oil and gas fields of the Mangistau region. The data show that limestone creates from 70% to 90% of all problems related to the stability of wells, which is due to the peculiarities of their physical and mechanical properties. Experimental studies of the physical and mechanical properties of limestone have features both in terms of monolith selection and in terms of preparation of samples for research, and in the methods of conducting and processing experiments. These features are due to extremely low permeability, anisotropy of elastic and strength properties due to their layered structure. The experience of testing core samples of layered limestone is considered, tests are carried out on equipment under the program of consolidated-undrained loading in accordance with the standards. As a result of experiments on core samples cut at an angle, along and across the layering, the anisotropic elastic properties of rocks, as well as their dependencies on geophysical parameters, were studied. The anisotropy of elastic properties has a significant effect both on the stress-strain state when solving specific problems of continuum mechanics and on the design values of the initial stress field as a whole. Taking into account the anisotropy parameters obtained in this paper will make it possible to solve Geomechanics problems in relation to layered limestones of the Sarmatian stage.

On the expansion of a flow into vacuum for spherically symmetric relativistic hydrodynamic equations

Fluid expansion into a vacuum is an interesting and important problem in continuum physics as well as in mathematics. This paper studies the relativistic Euler equations with an initial value that is a combination of a radial flow in a spherical domain and vacuum in the remaining domain. We prove that this expansion into vacuum problem admits a global-in-time classical solution, provided that the initial mass-energy density in the spherical domain is sufficiently small.

Shear Band Formation with Split Hopkinson Bar Experiments

The essence of dynamic failure is closely linked to dramatic shear deformations which often lead to the formation of adiabatic shear bands (ASB). Under high loading velocities and the subsequent rapid temperature increase, the localization of shear strain is crucial in view of safety issues of systems in mechanical and aircraft engineering, especially with respect to fast rotating components and diverse crash scenarios. In this research, we perform high speed impact tests at the split Hopkinson pressure bar (SHPB) setup and use particular hat-shaped specimen geometries that resemble the stresses and failure conditions at the component level.In the first step, we specify a notched specimen geometry using finite element (FE) simulations to ensure pure shear. Further, quasi-static compressive tests and a series of impact tests at high strain rates of 103−104s−1 are conducted on specimens manufactured from a fine-grain structural steel with the properties of S355. Optical microscopy and electron backscatter diffraction (EBSD) of the sheared zones unveil significant localization to maximal shear strains of about 0.9 accompanied by grain refinement by factors 5 to 14. The displacements across the surface of the specimens are captured with subset-based local digital image correlation (DIC) during the impact time, and serve as an objective to validate a viscoplastic constitutive relationship. More precisely, the deformation distribution is accurately reproduced by the widely recognized Johnson-Cook (JC) model, which features an enhanced description of damage evolution. Thus, combining experimental and characterization techniques, continuum mechanics and reasonable optimization strategies for the identification of model parameters provides an efficient approach for comprehensive insights into the strain localization behaviour and its impact on the mechanical performance of S355 under extreme strain rates and deformations.

Pore collapse, shear bands, and hotspots using atomistics-consistent continuum models for RDX (1,3,5-trinitro-1,3,5-triazinane): Comparison with molecular dynamics calculations

Shock-induced energy localization is a crucial mechanism for determining shock sensitivity of energetic materials (EMs). Hotspots, i.e., localized areas of elevated temperature, arise when shocks interact with defects (cracks, pores, and interfaces) in the EM microstructure. The ignition and growth of hotspots in a shocked energetic material contribute to rapid chemical reactions that can couple with the passing shock wave, potentially leading to a self-sustained detonation wave. Predictive models for shock-to-detonation transition must correctly capture hotspot dynamics, which demands high-fidelity material models for meso-scale calculations. In this work, we deploy atomistics-guided material models for the energetic crystal RDX (1,3,5-trinitro-1,3,5-triazinane) and perform tandem continuum and all-atom molecular dynamics (MD) simulations. The computational setup for the continuum and MD simulations are nearly identical. The material models used for the calculations are derived from MD data, particularly the equations of state, rate-dependent Johnson–Cook strength model, and pressure-dependent shear modulus and melting temperature. We show that a modified Johnson–Cook model that accounts for shear-induced localization at the pore surface is necessary to represent well—relative to MD as the ground truth—the inelastic response of the crystal under a range of shock conditions. A head-to-head comparison of continuum and atomistic calculations across several metrics of pore collapse and energy deposition demonstrates that the continuum calculations are in good overall agreement with MD. Therefore, this work provides improved RDX material models to perform physically accurate meso-scale simulations, to enhance understanding of hot spot formation, and to use meso-scale hot spot data to inform macro-scale shock simulations.

From the Cosserats mechanics backgrounds to modern field theory

In the paper, yet weekly known, Cosserats’ original four concepts as follow: the four-time unification of rigid body dynamics, statics of flexible rods, statics of elastic surfaces and 3D deformable body dynamics; the intrinsic formulation based on the local, von Helmholtz symmetry group of monodromy; the invariance under the Euclidean group. The concept of a set of low-dimensional branes immersed into Euclidean space are revalorized and explained in terms of the modern gauge field theory and the extended strings theory. Additionally, some useful mathematical tools that connect the continuum mechanics and the classical field theory (for instance, the convective coordinates, von Mises’ “Motorrechnung”, the Grassmann extensions, Euclidean invariance, etc.) are involved in the historical explanation that how the ideas were developing themself.

Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network

Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser lattices, thereby allowing one to circumvent problems with critical slowing down and topological freezing toward the continuum limit. A crucial ingredient for practical applications is to find an accurate and compact parametrization of a fixed point action, since many of its properties are only implicitly defined. Here we use machine learning methods to revisit the question of how to parametrize fixed point actions. In particular, we obtain a fixed point action for four-dimensional SU(3) gauge theory using convolutional neural networks with exact gauge invariance. The large operator space allows us to find superior parametrizations compared to previous studies, a necessary first step for future Monte Carlo simulations and scaling studies. Published by the American Physical Society 2024

The Problem With National Institute of Standards and Technology Thermodynamics Tables in Continuum Mechanics.

Thermodynamics is a fundamental topic of continuum mechanics and biomechanics, with a wide range of applications to physiological and biological processes. This study addresses two fundamental limitations of current thermodynamic treatments. First, thermodynamics tables distributed online by the U.S. National Institute of Standards and Technology (NIST) report properties of fluids as a function of absolute temperature T and absolute pressure P. These properties include mass density ρ, specific internal energy u, enthalpy h=u+P/ρ, and entropy s. However, formulations of jump conditions across phase boundaries derived from Newton's second law of motion and the first law of thermodynamics employ the gauge pressure p=P-Pr, where Pr is an arbitrarily selected referential absolute pressure. Interchanging p with P is not innocuous as it alters tabulated NIST values for u while keeping h and s unchanged. Using p for functions of state and governing equations solves the problem with using NIST entries for the specific internal energy u in standard thermodynamics tables and analyses of phase transformation in continuum mechanics. Second, constitutive models for the free energy of fluids, such as water and air, are not typically provided in standard thermodynamics treatments. This study proposes a set of constitutive models and validates them against suitably modified NIST data.

Full-scale modeling and experimental study of a gas neutron tube with a Penning ion source

This paper studies full-scale gas neutron tube modeling, including the following processes: gas discharge combustion in a Penning ion source, particle motion in an ion optical system, and modeling the in-target processes, such as sputtering, diffusion, thermal desorption of hydrogen isotopes, and nuclear reactions. Plasma modeling in quadrupole electric and axial magnetic fields was based on the electrostatic particle-in-cell method with molecular kinetic processes. The TechX Vsim software package was used. The neutron tube element sputtering by ions was simulated using SRIM/TRIM software based on Monte–Carlo methods. The OpenFOAM, as an open integrated platform for numerical simulation in continuum mechanics, was used to calculate the hydrogen thermal desorption activated by ion irradiation. The time-dependent neutron yield modeling was performed using the Geant4 software based on Monte–Carlo methods with CHIPS-TPT VNIIA-developed library. In addition, an experimental study of a gas neutron tube with a Penning ion source was conducted here as well. Details are given on the experiment and measurement technique used in this study. The operating characteristics for the gas neutron tube, including amplitude-time characteristics of current flashes (discharge and extraction currents), were determined. The neutron flux dependencies on the discharge current at various accelerating voltages were also obtained. Finally, a comparison between the experimental and calculated results is presented.

A nonequilibrium statistical mechanics derivation of the hydrodynamic equations of simple fluids using a noncanonical form of the Poisson bracket

The continuum level hydrodynamic equations of a simple fluid were derived by Irving and Kirkwood directly from discrete particle dynamics using statistical mechanics almost 75 years ago. Their elegant derivation demonstrated the fundamental molecular basis of macroscopic fluid flow and culminated in molecular expressions for the stress tensor and heat current density that have since been employed in countless molecular simulations to date. In this article, an alternative derivation is presented, which leads to more general expressions for the fundamental transport relationships and which arrives at them in a more straightforward chain of consistency that ensues directly from the Principle of Least Action. The main point of departure from the Irving–Kirkwood derivation is the application of a transformation mapping of the total momentum of each individual particle onto the sum of its peculiar momentum and its momentum relative to the local velocity field. This mapping provides a phase-space distribution function applicable in the space of particle positions and peculiar momentum, from which a noncanonical Poisson bracket can be derived in terms of the same set of microscopic variables. For a given dynamic variable, expressed in terms of particle positions and peculiar momenta, the expectation value of the noncanonical Poisson bracket of the dynamic variable is shown to correspond to the evolution equation of the expectation value of the dynamic variable. This allows for a direct derivation of all macroscopic density evolution equations (mass, momentum, and energy density fields) using a systematic procedure free of assumptions concerning the macroscopic state of the system. Furthermore, an explicit expression of the time evolution of the entropy density at the hydrodynamic level is derived following the same procedure. Finally, in the limit of short-range interparticle interactions, a molecular-based expression for the local stress tensor as properly defined from continuum mechanics is developed at the hydrodynamic level that elucidates the continuum mechanics connection of the general stress expression of Irving and Kirkwood.

Contribution to the numerical modelling analysis of displacements caused by tunnel construction in discontinuous rock masses

This paper presents a comprehensive study of the stability conditions of a rock mass surrounding a tunnel, using numerical modelling analysis of displacements induced by the tunnel construction. The case study focuses on the Boukhadra iron ore mine in Algeria. This research employs empirical equations from literature based on geomechanical classifications to provide the most appropriate geotechnical input data for simulation. In addition to those equations, a novel correlation equation relating the rock mass ratio (RMR) and the rock quality index (Q) was developed. This equation gives a high regression coefficient, revealing a strong correlation (R2) of 0.878. It gives a better estimation of the rock mass characteristics: Young’s moduli (E), Poisson’s ratio (υ), cohesion (C), and friction angle (φ), compared to the existing literature-based correlation equations. The estimated parameters were used to pass from a discontinuous to a continuous equivalent medium, making the numerical modelling easier with the finite element method. Compared with intact rock and direct equations, the numerical simulation results based on the new equation fit well with the in-situ observations and provide a more reliable comprehension of rock mass behaviour. The new equation proposed in this paper provides a substantial evaluation of the rock mass parameters needed in the design process of underground structures once used with respect to their acceptable ranges.