Identification of elastic property and loading fields from full-field displacement measurements

A method is introduced to identify simultaneously elastic properties and loading fields from a measured displacement field. Since the mechanical behavior of micro-electro-mechanical systems (MEMS) is governed by surface effects, this type of identification tool is thought to be of major interest. However, increasing the number of parameters to retrieve affects the redundancy necessary for an accurate identification. A finite-element formulation of a distance between measured and statically admissible (SA) displacement fields is shown to be equivalent to a standard least-squares distance to kinematically admissible (KA) fields if the used modeling is suitable. Any deviation from this equivalence is then the signature of a modeling error. Balancing the distance to KA and SA displacement fields allows one to retrieve unknown modeling parameters. This method is detailed on heterogeneous Euler–Bernoulli beams submitted to an unknown loading field and applied to experimental displacement fields of micro-cantilevers obtained with an electrostatic set-up. An elastic property field and a parameterized loading field are then identified, and the quality of the identification is assessed.     

Learning material law from displacement fields by artificial neural network

The recently developed data-driven approach can establish the material law for nonlinear elastic composite materials(especially newly developed materials) by the generated stress-strain data under different loading paths(Computational Mechanics, 2019). Generally, the displacement(or strain) fields can be obtained relatively easier using digital image correlation(DIC) technique experimentally, but the stress field is hard to be measured. This situation limits the applicability of the proposed data-driven approach. In this paper, a method based on artificial neural network(ANN) to identify stress fields and further obtain the material law of nonlinear elastic materials is presented, which can make the proposed data-driven approach more practical. A numerical example is given to prove the validity of the method. The limitations of the proposed approach are also discussed.     

Stress and displacement fields in soft cylindrical multilayers

Multilayered gels play an important role in biomedical engineering as drug delivery vehicles, replacement tissues and bio-mimetic substrates for cell cultures. It has been established that the gel elasticity strongly influences the intended functionalities. In view of this, second-order elastic solutions for the stresses and displacements in cylindrical multilayered hydrogels subjected to various dilatation profiles are developed in this paper. The results emphasize the importance of nonlinearity in gel mechanics, and suggest the possibility of a rational selection of layer elasticities, layer thicknesses and dilatation profiles for improved mechanical responses such as maximum/minimum swelling and multiaxial stress states.     

Transient displacement fields in hexagonal crystals and transversally isotropic media

The structure of the disturbed region and the geometry of the wave front is investigated under the condition that a concentrated source of the instantaneous-pulse type is acting in an unbounded transversally isotropic medium. The regions of permissible values of the anisotropy coefficient introduced in [1] for transversally isotropic media on the basis of conditions of the elastic energy's positive-definiteness and hyperbolicity conditions are determined. It is suggested that motion of the medium occurs under conditions of plane deformation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 153–160, March–April, 1976.The author expresses his thanks to S. A. Khristianovich for his attention to this work.     

Determination of displacement and strain fields using dual-beam holographic-moiré interferometry

A procedure is described to determine the surface strains of objects of arbitrary shape using the same setup. The shape of the object is determined by contouring holography. The displacements are determined by holographic-moiré in the form of contour-line maps for the displacement components inx, y andz direction. From these maps, the so called basic strains' are derived as if the object were flat. Formulas are given to transform these basic strains' into surface strains.     

Biaxial stress effects on the elastic-plastic crack-tip displacement fields

Summary A plane stress, finite element analysis of the monotonic loading of a Mode I stationary crack under small scale yielding using a boundary layer approach is presented. A small-strain,J ₂ plasticity theory is used in conjunction with a linear hardening material model. The effects due to the inclusion of the non-singular elastic T-stress in the asymptotic boundary conditions on the elastic-plastic fields near the tip are investigated. This parameter, which accounts for the inherent biaxial stress state at a crack tip, is found to control extension and state of deformation of the plastic zone. The full-field numerical solutions are also used to simulate moirè interferometric fringe patterns in order to assess earlier detailed experimental observations.

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Sommario Viene presentato uno studio agli elementi finiti con un approccio allo strato limite del caricamento monotono seconda il Modo I di una fessura stazionaria in condizioni di stato di tensione piana e plasticità contenuta. Viene esaminata in particolare l'influenza che la componente tensionale elastica trasversale nonsingolare (i.e. T-stress) delle condizioni al contorno ha sullo stato di sollecitazione elasto-plastica all'apice della fessura. Si osserva che questo parametro dello stato di biassialità all'apice di fessure controlla sia l'estensione della zona plastica che lo stato deformativo al suo interno. Le soluzioni numeriche vengono inoltre impiegate per simulare sistemi di frange moirè interferometriche fornendo così un utile strumento di confronto con precedenti risultati sperimentali.

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Portions of this paper are included in the Proceedings of 9.th Congress of AIMETA, Bari, 1988.     

Dynamic simulation of stress and displacement fields for tsinghaitibet plateau lithosphere

Tsinghai-Tibet Plateau becomes an important research topic of global tectonics, because of its marvelous thickness and rapid uplifting since Quaternary. By using finite element method, the numerical simulation is carried our for the movement of structural lithosphere. The deformable elements are employed to simulate structural zones, and the frictional mechanism is introduced to illustrate the characteristic of a zone with a contact crack surface. The boundary conditions are prescribed by the displacements around the plateau. As a result, the stress and displacement distributions are obtained, which are consistent with P axial orientations of the earthquake focus mechanism and the measured principal stress direction. Analysis and estimate are also made for the evolution of historical process and present situation of the plateau lithosphere.     

Time domain modeling of damping using anelastic displacement fields and fractional calculus

A fractional derivative model of linear viscoelasticity based on the decomposition of the displacement field into an anelastic part and elastic part is developed. The evolution equation for the anelastic part is then a differential equation of fractional order in time. By using a fractional order evolution equation for the anelastic strain the present model becomes very flexible for describing the weak frequency dependence of damping characteristics. To illustrate the modeling capability, the model parameters are fit to available frequency domain data for a high damping polymer. By studying the relaxation modulus and the relaxation spectrum the material parameters of the present viscoelastic model are given physical meaning. The use of this viscoelastic model in structural modeling is discussed and the corresponding finite element equations are outlined, including the treatment of boundary conditions. The anelastic displacement field is mathematically coupled to the total displacement field through a convolution integral with a kernel of Mittag–Leffler function type. Finally a time step algorithm for solving the finite element equations are developed and some numerical examples are presented.     

Meso-mechanical investigation of the three-dimensional displacement fields around a crack tip

Experimental Techniques -     

Simultaneous on-line measurement of orthogonal displacement fields by Moiré interferometry

Experimental Techniques - A modified four-beam optical arrangement for moiré interferometry provides simultaneous determination of the in-plane U and V displacement fields, and is suitable for...     

Uniqueness theorems for displacement fields with locally finite energy in linear elastostatics

Uniquencess theorems are proved for the fundamental boundary value problems of linear elastostatics in bodies of arbitrary shape. The displacement fields are required to have finite strain energy in bounded portions of the bodies and satisfy the principle of virtual work. For bounded bodies, the total strain energy is finite and uniquencess is proved without additional hypotheses. In particular, no restrictions other than the energy condition are placed on the field singularities that may occur at sharp edges and corners. For unbounded bodies, uniqueness can be proved as in the bounded case if the total strain energy is finite. Sufficient conditions for this are shown to be the finiteness of the strain energy in bounded portions of the body together with the growth restriction % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqef0uAJj3BZ9Mz0bYu% H52CGmvzYLMzaerbd9wDYLwzYbItLDharqqr1ngBPrgifHhDYfgasa% acOqpw0xe9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% GabaqaaiGacaGaamqadaabaeaafiaakeaadaWdraqaaiaabwhadaWg% aaWcbaGaaeyAaaqabaGccaGGOaGaaeiEaiaacMcacaqG1bWaaSbaaS% qaaiaabMgaaeqaaOGaaiikaiaabIhacaGGPaGaaeizaiaabIhacaqG% 9aGaaGimaiaacIcacaqGYbGaaiykaiaacYcacaqGYbGaeyOKH4Qaey% OhIukaleaacqGHPoWvdaWgaaadbaGaaeOCaiaacYcacqaH0oazaeqa% aaWcbeqdcqGHRiI8aaaa!5E73!\[\int_{\Omega _{{\text{r}},\delta } } {{\text{u}}_{\text{i}} ({\text{x}}){\text{u}}_{\text{i}} ({\text{x}}){\text{dx = }}0({\text{r}}),{\text{r}} \to \infty } \] on the displacement fieldu _i , where _r, is the portion of the body that lies between concentric spheres with radiir andr+ and >0.This research was supported by the Air Force Office of Scientific Research. Reproduction in whole or part is permitted for any purpose of the United States Government.Prepared under Contract No. F 49620-77-C-0053 for Air Force Office of Scientific Research.     

Theorme of the uniqueness of displacement and stress fields of line-loaded integral equation method

According to Fredholm’s theorem, this paper proves that due to the virtual fundaemental loods which satisfy the boundary conditions and being distributed outside the elastic body occupied region the displacement and stress fields in the elastic body occupied region are unique. This theorem forms a theoretical basis of the applications of the line-loaded integral equation method.     

Producing and transferring low-spatial-frequency grids for measuring displacement fields with moiré and grid methods

Experimental Techniques -     

An in-situ determination of virgin compression line parameters for predicting soil displacement resulting from agricultural tire passes

This paper demonstrates the determination of the virgin compression line parameters from initial soil density, contact pressure and resulting rut depth in uniform soil conditions for which a constant soil density change to a depth of 500 mm was obtained in soil bin experiments (whereby total soil depth was 750 mm). The density change was determined with a “non-invasive” technique determining soil displacement (strain) by placing talcum powder lines into the soil during preparation of the soil bin and measuring the change in their relative position. The soil compaction model COMPSOIL with these parameters predicted wheel rut depth to within ±5%, from which in turn an absolute soil density increase can be determined to within ±3%. The model was successfully validated against data for uniform initial densities of 1.2 g/cm³ and 1.6 g/cm³ and a simulated layered field condition. The estimation of the virgin compression line was validated in the field as well. The parameters of the virgin compression line were estimated using soil density change data for the corresponding average contact pressures of different tires with loads of 4.5–10.5 t.     

On the representation of elastic displacement fields in terms of three harmonic functions

In this paper the representation of displacement fields in linear elasticity in terms of harmonic functions is considered. In the original work of Papkovich and Neuber four harmonic functions were presented with a subsequent reduction to three on the grounds that only three are sufficient for the representation of displacements fields. This reduction is unsubstantiated and several authors have investigated the generality of the Papkovich-Neuber solutions. The paper derives by simple means the conditions under which it is possible to omit one of the four harmonic functions and considers the significance of the subsequent three function form.     

Effective strength parameters of composites in coupled physicomechanical fields

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 124–130, July–August, 1992.     

Determination of impact parameters by optical measurement of the impactor displacement

In dynamic materials research, high precision impact displacement, velocity and force measurements are often required. In lower velocity testing apparatus, impact force histories are most often obtained through strain gage, piezoelectric force transducer or accelerometer signals. Velocity and displacement histories are then obtained by integration. Non-contact measurement systems have a number of advantages over these more common mechanical contact methods, and can generally be used at higher impact speeds. In this paper a relatively simple optical technique is presented for recording the impactor displacement history, from which the impact velocity and force histories can be readily obtained for a (quasi-) rigid impactor. The technique is based on the relative displacement of two moiré line gratings: one grating attached to the impacting body and the other serving as stationary reference grating. The technique has proven to be useful for impact speeds of a few m/s to well over 200 m/s. Results of transverse impact experiments on composite laminates are presented.     

Measuring displacement fields of curved surface by moire interferometry of partial coherent light

This paper presents a method to measure the in-plane displacement fields of curved surface by moire interferometry of partial coherent light. The method has the following advantages: simple optical system, no requirement on vibration isolation, high sensitivity, large measuring range, high contrast of interference fringes and availability to in situ structural testing. the present paper also gives theoretical analysis of the method and the formulas of light intensity and displacement field, and introduces a replication technique to form a high frequency reflectance grating on the curved surface. The expriments achieved the measurement of the surface displacement field of a cylindrical shell— the simultaneous circumferential, axial and 45° displacement fields. The torsional test data for surface displacement of a circular bar agree well with the theoretical result. The project supported by National Natural Science Foundation of China.     

Measurement of two-dimensional velocity fields in porous media by particle image displacement velocimetry

Local measurements of the phase function and of two components of the velocity can be performed in transparent porous media by means of particle image displacement velocimetry (P.I.D.V.). Some preliminary results are presented and discussed.     

A weight function for the single edge crack based on approximative displacement fields

Weight functions for the calculation of stress intensity factors can simply be determined by using an extension of the Petroski-Achenbach method. The procedure is demonstrated for an edge crack in a strip of finite width. The resulting weight function is compared with solutions available in the literature.