Finite Strain Research Articles

Finite strain formulation of the discrete equilibrium gap principle: application to direct parameter estimation from large full-fields measurements

Finite strain formulation of the discrete equilibrium gap principle: application to direct parameter estimation from large full-fields measurements

A Finite Element Method orthotropic multi-yield elastic-inelastic model of a wood-adhesive-steel composite

Composite elements made of wood reinforced by adhesively inter-layered steel lamina can be employed as structural elements in building engineering, thanks to their favorable ratios of strength and stiffness to mass and their ductility. The mechanical response of such composite, under loading, can be predicted by employing a Finite Element Method with a proper model of each material. In this work, the Finite Element Method model is formulated within the theories of Continuum Mechanics and irreversible thermodynamics of deformation, finite strains hypothesis, and kinematics of large displacements. For the wood material constituent an orthotropic elastic–plastic-damage constitutive law is adopted, to address the effects of irreversible strains, formulated by a multi-surface yield, both for plasticity and damage, where each yield surface operates disjointedly each other, at the level of stress–strain component. The validity of the proposed model and its computational technique is revealed by analyzing the stress–strain path until the failure of a composite element. Thus, the numerical results are compared with the experimental data obtained in a tension test of that composite element. The proposed model adequately represents the mechanical behavior of the composite.

Differentiable neural-integrated meshfree method for forward and inverse modeling of finite strain hyperelasticity

Differentiable neural-integrated meshfree method for forward and inverse modeling of finite strain hyperelasticity

Acoustic Waves in Axial Crystals and Quasicrystals with Preliminary Finite Strains

The dynamic problem of acoustic wave propagation in elastic bodies with preliminary finite deformations is formulated. Several types of anisotropic elastic materials are considered: hexagonal crystals of class [Formula: see text], transversally isotropic materials and axial quasicrystals with an arbitrary order of the rotary axis. A variant of nonlinear hypoelasticity relations is constructed for these materials. In the constitutive relations, the tensor connecting the rate of change of the stress tensor and the strain rate tensor is a function of deformations. The propagation of acoustic waves in a hypoelastic material with preliminary finite deformations and stresses is described as a process of weak perturbations superimposed on finite strains. The characteristic features of elastic wave propagation in hexagonal crystals and axial quasicrystals are revealed. Within the framework of the constructed models, the most significant differences are found in the phase velocities of a transverse wave with a polarization vector located in the crystallographic plane (110). Unlike hexagonal crystals, in axial quasicrystals, there are such directions of acoustic wave propagation for which the phase velocities of transverse waves are insensitive to the degree of preliminary deformations. Based on the solution of the problem of elastic wave propagation, a program of dynamic experiments with macrosamples, which allows to distinguish axial quasicrystals from hexagonal crystals by the peculiarities of acoustic wave propagation, is proposed.

A comprehensive DFT study of the effect of the pressure on the structural, stability, electronic, optical, and mechanical properties of cubic RbSrI3

Abstract This study examines the structural, electrical, optical, and mechanical effects of hydrostatic pressure on cubic I-II-halide perovskite RbSrI3. The exchange–correlation term of the Khon-Sham equation is expressed using PBE-GGA. For all calculations, QuantumESPRESSO is used. PBE-GGA and pseudopotentials have been employed for ion-valence interaction. Under hydrostatic pressure, the lattice parameter a dropped from 6.34 Å. The structure is thermodynamically stable since the formation energy E f is negative and lowers as the negativity falls until pressure 31 GPa, when it becomes positive. This material depicts the transition from an indirect band gap at ambient pressure to a direct band gap that accelerates electron valence-to-conduction band transition. The band gap rises to 7 GPa, then falls to 1.49 eV at 50 GPa. The PDOS explains that the states that contribute to creating VBM and CBM changes in overlapping status and value which leads to such behavior of electronic nature. Optical properties show a stronger response at 50 GPa pressure, with ε 1 ( ω ) and ε 2 ( ω ) exhibiting similar behavior and a maximum value of nearly 10. However, ε 1 ( ω ) peaks in the visible light zone, while ε 2 ( ω ) peaks in the ultraviolet zone. This means the material absorbs and retains visible and ultraviolet radiation at its optimal level. Mechanical and elastic parameters were determined using finite strain theory. Born stability confirms mechanical stability since C 11 , C 44 , C 11 − C 12 , and C 11 + 2 C 12 have positive values and remain positive as pressure increases. Elastic moduli such bulk modulus ( B ), shear modulus ( G ), and Young’s modulus ( E ) indicate moderate hardness and resistance to pressure. Additionally, Poisson’s ratio ( υ ), Pugh’s ratio, and Cauchy pressure ( σ ) indicate ductility at ambient pressure, since they align with boundary values of υ (0.2959 > 0.26), σ (0.92) (positive), and B / G (2.23 > 1.75) (at ambient pressure). Increased pressure enhances ductility.

A general thermodynamical model for finitely-strained continuum with inelasticity and diffusion, its GENERIC derivation in Eulerian formulation, and some application

A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the Eulerian framework and is shown to be consistent with the thermodynamic framework given by General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). For the latter we use that the transport terms are given in terms of Lie derivatives. Application is illustrated by two examples, namely volumetric phase transitions with dehydration in rocks and martensitic phase transitions in shape-memory alloys. A strategy toward a rigorous mathematical analysis is only very briefly outlined.

Microlayer Framework: Extension to Viscoelastic Material Behaviour for Finite Strains

ABSTRACTThe microlayer framework is a novel, powerful method for the numerical simulation of heterogeneous materials, such as aggregate‐matrix composites across different scales. In this work, the microlayer framework is prepared for viscoelastic material behaviour for the first time. The kinematics of the representative volume element on the microlevel is selected in a manner that the material behaviour of typical composites, such as asphalt or concrete, can be modelled. The constitutive relationships on the microscale are developed independently from the macroscale. The prerequisites for correct computational homogenisation are thus met. The thermodynamically motivated scale transition is demonstrated using the Principle of Multiscale Virtual Power. Numerical examples are presented to show that the chosen formulation can reproduce the typical characteristics of viscoelastic material behaviour.

Elasto-plastic solution for undrained cylindrical cavity expansion in refuse soil

To address geotechnical engineering issues such as pile driving, lateral pressure tests, and static cone penetration tests on increasing number of infrastructure projects being constructed on landfills, an elasto-plastic theoretical solution for the undrained cylindrical cavity expansion in refuse soil is proposed in this paper based on an elasto-plastic constitutive model for refuse soil considering the reinforcement effect of fibers, along with a large deformation theory. The correctness of the results is validated through comparison with existing solutions based on the modified Cam-clay model. The results indicate that the response of columnar pore expansion in refuse soil is significantly different from that in ordinary soil. Near the pore, refuse soil does not enter a critical state, only the slurry-like components do. Subsequently, the reinforcement effect of the fiber material begins to manifest. Refuse soils with different fiber contents undergo both elastic and plastic stages before reaching the critical state line of the slurry-like components in the soil. They then move a certain distance along this line to reach a maximum. Given the rarity of engineering construction on similar sites in the past, the unique response of refuse soil during cylindrical cavity expansion should be given special attention.

An Analytical Frame for Predicting Residual Contact Pressure for Mechanically Lined Pipe using von Mises Criterion and Finite Strain Theory

Mechanically Lined Pipe (MLP) is a bi-metallic pipe consists of an external carbon steel pipe internally coated with a thin Corrosion Resistant Alloy (CRA) lining. This CRA layer acts as a barrier against corrosive substance present in the production fluid from offshore Oil & Gas fields, while the high-strength, low-carbon steel outer pipe bears the external loads. Hydroforming expansion stands as the primary method for bonding the liner onto the external carrier pipe. The pursuit of precise and reliable theoretical models is ongoing to improve fabrication efficiency and establish a standard for subsequent failure analysis. The Tresca criterion is traditionally utilized in stress-strain analysis of MLP fabrication due to its mathematical formulation. However, it tends to provide conservative estimations of metallic structure yielding. And comparing the results of theoretical models employing the Tresca yield criterion with the mainstream numerical simulation software relying the von Mises yield criterion poses another difficulty. Hence, its suitability for analyzing MLP fabrication is subject to debate. To enhance accuracy, nonlinear theoretical analysis of MLP incorporating the finite strain theory and the von Mises yield criterion has been performed. Analytical prediction of residual contact pressure is achieved through the circumferential strain compatibility. An axisymmetric Finite Element Model (FEM) is constructed to compare against the theoretical models. Furthermore, the investigation delves into the impact of introducing an appropriate level of carrier pipe plastification on residual contact pressure.

A low-cost space-time finite element for free-surface flows under total Lagrangian description

In this work, we propose a position-based space-time finite element formulation for incompressible Newtonian flows under a total Lagrangian description. This formulation is suggested within the context of finite strain free-surface flows and differs from the traditional finite element approach for fluid dynamics by utilizing current nodal positions as the main variables instead of nodal velocities. In contrast to time-marching methods, space-time formulations involve applying the finite element technique not only to the spatial domain but also to the temporal domain. The proposed approach employs a finite element discretization that can be unstructured or structured in space, but is always structured in time. Thus, the space-time shape functions are expressed as a tensor product of linear shape functions in the spatial direction and specially designed quadratic shape functions in the temporal direction. Consequently, the space-time domain is divided into time slabs that are solved progressively, with the final velocities and positions from the previous time slab serving as initial conditions for the current one, thereby reducing the dimension of the discrete system of equations. The proposed shape functions in the temporal direction yield a system of equations of the same size as standard time-marching methods, but with advantages stemming from the space-time discretization: different stability and high-frequency dissipation can be achieved based on the selection of the time test functions. To solve the incompressible problem stably, we employ mixed equal-order position-pressure finite elements with Petrov-Galerkin/pressure stabilization (PSPG). This formulation possesses several significant features that justify its development: 1) the space-time formulation facilitates dynamic re-meshing by permitting the spatial discretization at the end of one time slab to differ entirely from the spatial discretization at its beginning, thus extending its applicability to flows with undefined distortion and topological changes; 2) by considering positions as variational parameters, it becomes straightforward to couple with Lagrangian hyper-elastic solid solvers, which may also be formulated in terms of positions or displacements in a monolithic way. Numerical examples conducted to validate the formulation demonstrate its robustness and efficiency for finite strain free surface flows, including phenomena such as dam breaks with smooth surfaces and sloshing.

An FFT based chemo-mechanical framework with fracture: Application to mesoscopic electrode degradation

An FFT based method is proposed to simulate chemo-mechanical problems at the microscale including fracture, specially suited to predict crack formation during the intercalation process in batteries. The method involves three fields fully coupled, concentration, deformation gradient and damage. The mechanical problem is set in a finite strain framework and solved using Fourier Galerkin for non-linear problems in finite strains. The damage is modeled with Phase Field Fracture using a stress driving force. This problem is solved in Fourier space using conjugate gradient with an ad-hoc preconditioner. The chemical problem is modeled with the second Fick’s law and physically based chemical potentials, is integrated using backward Euler and is solved by Newton–Raphson combined with a conjugate gradient solver. Buffer layers are introduced to break the periodicity and emulate Neumann boundary conditions for incoming mass flux. The framework is validated against Finite Elements the results of both methods are very close in all the cases. Finally, the framework is used to simulate the fracture of active particles of graphite during ion intercalation. The method is able to solve large problems at a reduced computational cost and reproduces the shape of the cracks observed in real particles.

Axisymmetric forced vibration of the hydro-elastic system consisting of a pre-strained highly elastic plate and compressible viscous fluid

The paper studies the axisymmetric harmonic forced vibration of the hydro-elastic system composed of an initially strained plate made of highly elastic material, a compressible viscous fluid layer, and a rigid wall restricting the fluid flow. It is assumed that the plate is in contact with the fluid layer after the appearance of the finite axisymmetric homogeneous initial strains within which are caused by the stretching of the plate by uniformly distributed radial forces acting at infinity. Also, it is assumed that after this contact, the point located time-harmonic force begins to act on the free-face plane of the plate. Within this framework, the steady-state forced vibration of the hydro-elastic system under consideration is studied by employing the eq. and relations of the so-called three-dimensional linearized theory of elastic waves in bodies with finite initial strains to describe the motion of the plate and by employing the linearized Navier-Stokes eq. to describe the flow of the fluid. The corresponding mathematical problem is solved by employing the Hankel integral transform method, and the originals of the sought values are found numerically by employing the algorithms and PC programs composed by the authors. Numerical results are presented and discussed on the frequency response of the normal stress acting on the interface plane between the plate and fluid layer. According to these discussions, corresponding conclusions on the influence of the problem parameters on the frequency response of the interface stress are made. In particular, it is established that in the axisymmetric forced vibration case, the resonance-type phenomenon appears due to the fluid viscosity.

Training of a physics-based thermo-viscoplasticity model on big data for polypropylene

Research on data-driven constitutive models has demonstrated their outstanding ability to provide highly accurate predictions of the general stress-strain response after learning from data only. Here, we demonstrate that physics-based models can equally benefit from training procedures relying on big data. Specifically, we employ the thermo-mechanically coupled viscoplasticity model [Anand, L., Ames, N.M., Srivastava, V., Chester, S., 2009. A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part 1: Formulation. International Journal of Plasticity] to describe the large deformation response of polypropylene. It combines both mechanism-based evolution equations and high mathematical flexibility. More than 100 constant velocity and strain rate jump experiments are performed on flat tensile specimens extracted from 3 mm thick isotactic polypropylene sheets. The exact cross-sectional area is measured with surround DIC, while an IR camera monitored the surface temperature field. The experiments typically reached true strains greater than 0.8 and cover temperatures and strain rates ranging from 25 to 85 °C and 10–4 to 100s-1, respectively. Training over 100,000 unique random combinations of experiments is performed to identify all model parameters. The effect of the training (and testing) subsets size and composition is carefully analyzed to ensure a high generalization ability. It is found that training based on 26 randomly-selected experiments leads to the most robust parameter estimates. The obtained model performs remarkably well on all our experiments (among which 70 % are unseen during training) with a root mean square error of less than 1.5 MPa. As a byproduct, we also found that there exists a subset of two specific experiments for training that lead to an equally accurate model for polypropylene.

Thermodynamically consistent modeling of viscoelastic solids under finite strain

The present article is concerned with modeling the viscoelastic behavior of Polydimethylsiloxane (PDMS) in large-strain regime. Starting from the basic principles of thermodynamics, an incremental variational formulation is derived. Within this model, the free energy density and dissipation function determine elastic and viscous properties of the solid. The main contribution of this paper is the estimation of the parameters in the proposed phenomenological model from measurements conducted on Sylgard184 samples. This non-linear material model simplifies to a Prony-series representation in frequency domain in case of small deformations. The coefficients of this Prony-series are detected from dynamical temperature mechanical analysis measurements. Time-temperature superposition allows to combine measurements at different temperatures, such that a sufficiently large frequency range is available for subsequent fitting of Prony-parameters. A set of material parameters is thus provided. The incremental variational formulation directly lends itself to finite element discretization, where an efficient and stable choice of elements is proposed for radially symmetric problems. This formulation allows to verify the proposed model against experimental data gained in ball-drop experiments.

Finite strain continuum phenomenological model describing the shape-memory effects in multi-phase semi-crystalline networks

Thermally-driven semi-crystalline polymer networks are capable to achieve both the one-way shape-memory effect and two-way shape-memory effect under stress and stress-free conditions, therefore representing an appealing class of polymers for applications requiring autonomous reversible actuation and shape changes. In these materials, the shape-memory effects are achieved by leveraging the synergistic interaction between one or more crystalline phases and the surrounding amorphous ones that are present within the network itself. The present paper introduces a general framework for the finite strain continuum phenomenological modeling of the thermo-mechanical and shape-memory behavior of multi-phase semi-crystalline polymer networks. Model formulation, including the definition of phase and control variables, kinematic assumptions, and constitutive specifications, is introduced and thoroughly discussed. Theoretical derivations are general and easily adaptable to all cross-linked systems which include two or more crystalline domains or a single crystalline phase with a wide melting range and manifest macroscopically the one-way shape-memory effect and the two-way shape-memory effect under stress and stress-free conditions. Model capabilities are validated against experimental data for copolymer networks with two different crystalline phases characterized by well-separated melting and crystallization transitions. Results demonstrate the accuracy of the proposed model in predicting all the phenomena involved and in furnishing a useful support for future material and application design purposes.

Sound velocities and thermal equation of state of fcc-iron-nickel alloys at high pressure and high temperature: Implications for the cores of Moon and several planets

Fcc-Fe-Ni alloy is believed to be the most dominant solid constitute of moderate-sized terrestrial planetary cores. Investigating the physical properties, especially the density and sound velocity of Fe-Ni alloys and comparing them with seismic observations is an indispensable approach to constructing compositional models for planetary interiors. In this study, we conducted sound velocity measurements on Fe-Ni alloys with 10 wt.% and 20 wt.% Ni up to ∼13.5 GPa and 1073 K, using the ultrasonic interferometry technique in a multi-anvil apparatus in conjunction with synchrotron radiation. By fitting the experimental data to finite strain equations, the bulk and shear moduli and their pressure and temperature derivatives are derived, yielding KS0 =145.8(14) GPa, G0 = 73.2(7) GPa, KS0’ = 5.89(24), G0’ = 2.89(8), (∂KS/∂T)P = -0.0181(12) GPa/K and (∂G/∂T)P = -0.0393(10) GPa/K for fcc-Fe80Ni20. An examination of the density-velocity relationship shows that compressional wave velocity is insensitive to temperature within the current pressure and temperature range, while shear wave velocity exhibits a large reduction with increasing temperature. Extrapolation of the sound velocities following the finite strain theories suggests that much slower Vs should be expected at pressure and temperature conditions corresponding to those of the lunar core. Possible core density and velocity profiles for other moderate planets and satellites, such as Mars, Mercury, and Ganymede are also calculated.

Remeshing in the finite cell method for different types of geometry descriptions

AbstractThe numerical structural analysis of problems with complex geometries can be challenging, especially if standard finite elements are used. In contrast, immersed methods, such as the finite cell method, relieve the mesh generation such that simply shaped elements/cells can be used. Then, the domain boundary is considered during the numerical integration. In finite strain analysis, the elements/cells face large distortions, especially the cells that are intersected by the boundary. When the solution fails, remeshing can be applied to continue the simulation. This process is currently limited to geometries described by a triangulated surface. Therefore, the present work shows an alternative way of describing the deformed geometry by interpolating the displacement field. In this work, the inverse distance approach, and radial basis functions (RBF) with and without a constant extension are applied. It turns out that RBF with constant extension leads to the most robust results compared to the other methods. Moreover, different geometry description types are tested, and the present approach leads to promising results.

Analytical considerations of the load‐deflection behavior in fibers during a filament winding process

AbstractFilament winding is a manufacturing process used in the construction of fiber composite structures, where a thermoset resin impregnated bunch of fibers is deposited on a rotating mandrel. The evolving stress and strain states due to thermal and mechanical loads during the manufacturing process are of particular interest to avoid subsequent failure of the parts. In this first approach, the mechanical load within the fiber, mainly driven by the pre‐stressed fiber tension, is investigated. Thus, the development of the fiber tension and the pressure on the mandrel as a function of the number of windings is examined. Therefore, models based on the theory of large and small deformations are derived under certain assumptions, resulting in a boundary value problem. In case of large deformations, the boundary value problem using a three‐dimensional formulation based on incompressible, isotropic hyperelasticity does not yield a simple solution. Using a small deformation formulation on the basis of a one‐dimensional consideration an analytical solution can be found. The problems are described in curvilinear coordinates. From the derived models, the required quantities including the fiber tension, the pressure on the mandrel, also as a function of the number of windings, and the fiber elongation can be calculated.

Large deformation theory of thin steel cantilever beams under free end load cases

Large deformation theory of thin steel cantilever beams under free end load cases

A continuum magneto-viscoelastic model for isotropic soft magnetorheological elastomers: experiments, theory and numerical implementation

This study deals with the experimental, theoretical and numerical investigation of the nonlinear viscoelastic response of magnetically soft magnetorheological elastomers (commonly known as s-MREs and denoted here simply as MREs) subjected to combined magnetic and simple shear loads. We consider a fairly soft mechanically MRE. The experiments show a strong effect of the magnetic field on the resulting viscosity and hence dissipated energy expanded by the material during a simple shear cycle. Moreover, the effect of frequency on the response is weak indicating strongly nonlinear viscous effects similar to non-Newtonian fluids. An analytical magneto-viscoelastic model is proposed exhibiting magneto-mechanical coupling at both equilibrium and non-equilibrium energies as well as on the dissipation potential. The model is calibrated by solving in a semi-analytical way a simplified boundary value problem (BVP) of an infinite thin MRE strip embedded in an infinite air domain. These simplified solutions are cross-validated by full-field finite element simulations of the experimental setup showing very good agreement between the experimental data and model estimates. This illustrates the validity of the simplified material model for the proposed experimental setup and sets the ground for a more universal experimental protocol to characterize properly the finite strain response of MREs more generally.