Identification of plastic material parameters with error estimation

In recent years, inverse analysis has become a common approach to typical engineering problems such as model identification. In this contribution, the inverse problem is discussed in light of taking experimental uncertainties into account. This involves in particular the propagation of experimental errors and the analysis of the sensitivity of the model response to variations in the model parameters to be determined. The method is applied to an elasto-viscoplastic material model which is used in the context of electromagnetic high-speed forming. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ultrasonic determination of the stiffness characteristics of an orthotropic material with imperfect elasticity

The propagation parameters of ultrasonic vibrations in an orthotropic material with imperfect elasticity have been measured. The results of the measurements are used to calculate the complex stiffness characteristics, and the correspondence between the nature of the anisotropy and the adopted model is examined. The anisotropy of the inelastic properties is investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 195–206, March–April, 1973.     

Configurational forces on material defects

In micromechanical applications, the behaviour of material defects has been a great subject of interest. In this paper, the idea of Eshelby's energy momentum tensor is briefly reconsidered with respect to problems in solid mechanics. The derived configurational force balance is used to obtain the thermodynamic driving forces acting on centers of dilatation, dislocations, crack tips and interfaces of misfitting precipitates.     

Estimating the parameters of fatigue curve of a composite material

By using the method of maximum likelihood, the parameters of two versions of a mathematical model for fatigue damage accumulation in a laminate are estimated. The models, which are founded on the Markov chain theory, are very simple: they do not take into account the specific structural features of a composite and therefore cannot provide numerical coincidence with experimental fatigue test data, but they can be used for a nonlinear regression analysis of fatigue curves. A simple method is offered for approximately estimating model parameters, some of which characterize the distribution of the local static strength. By using such models, we can predict the relative changes in fatigue curves from known relative variations in the parameters of static strength and also predict the distribution function of fatigue life in program fatigue tests.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 109–120, January–February, 2005.     

Relating DEM contact parameters to macroscopic material parameters

Although the Discrete Element Method (DEM) is already widely applied in several fields of applications, one main challenge remains to define contact parameters that lead to realistic material behaviour. Here, it is shown how potentials can be defined on the contact level and from these a correlation to the macroscopic continuum parameters can be established. The analytically formed predictions are then compared to the results of discrete element simulations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of the moduli of elasticity and tensile strength of oriented glass-reinforced plastics on the basis of a nondestructive determination of their composition and structural parameters

The theoretical basis of the nondestructive determination of the modulus of elasticity and tensile strength of oriented glass-reinforced plastics in the direction of the principal axes of anisotropy from the resin content and porosity of the finished product is examined. The results of an experimental verification are presented.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 332–341, March–April, 1969.     

Obtaining Cosserat material parameters by homogenization of a Cauchy continuum

An increasing importance of composites with sandwich architecture and fibre-reinforced components is recognizable especially in aerospace and light weight industry. Due to the inner structure such materials often exhibit a complex behavior. If the ratio of micro- and macroscopic length scales, l and L, violates the condition l/L ≪ 1, a higher order continuum should be used to describe the macroscopic material behavior correctly. The numerical simulation requires reliable material constants, for which the experimental determination is laborious and sometimes impossible. Alternatively homogenization methods can be used for the numerical identification of overall material parameters. A short introduction to the linear Cosserat theory is followed by an extended homogenization procedure to derive the macroscopic material constants of a linear Cosserat continuum. The parameters obtained with a heterogeneous cell are used to simulate different bending load cases. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extraction of effective material parameters with application to sandwich structures

In this contribution we present a first-order numerical homogenization approach which allows for extracting effective linear elastic properties of heterogeneous materials. The approach is based on the window or self consistency method where a representative microscopic subdomain is embedded into a window of effective properties. Since these properties are not known in advance they have to be determined iteratively. For the discretization of the micro structures we use the Finite Cell Method, which is a fictitious domain method of higher-order. It is very well suited for efficiently discretizing complicated geometries stemming, for example, from tomography (CT-scans). In the numerical examples we will investigate a bending test of a sandwich plate which is composed of a polymeric core with thin faceplates made of Aluminum. Firstly, effective properties of the core are extracted and then applied to a macroscopic numerical model. The numerical results are validated by experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zero-moment laminated cylindrical shells with variable elasticity parameters obtained by the continuous winding method

Conclusions The general solution in the displacements of the problem of thermal-force loading of a zero-moment laminated cylindrical shell with variable elasticity parameters has been obtained in analytic form. Boundary-value problems for the practically important and often realized boundary conditions which arise in tests of samples, models, and natural structures have been discussed.Presented at the Fifth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, October, 1983).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 493–502, May–June, 1984.     

Investigation of Cosserat material parameters obtained by homogenization of a Cauchy continuum

If a higher order continuum theory is used in a numerical simulation, the material parameters have to be derived. The experimental determination is laborious and sometimes impossible. Alternatively homogenization methods can be used for the numerical identification of overall material parameters. A short introduction to the micropolar continuum and the homogenization approach is followed by the discussion of the identified properties. Therefore some parameter studies are presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of a member with variable modulus of elasticity

The problem of the optimal (from the weight standpoint) law of longitudinal variation of the modulus of elasticity is considered with reference to a member in axial compression when the limit state is reached as a result of loss of stability. Constraints are imposed on the modulus of elasticity. The problem is solved with the aid of the apparatus of the generalized maximum principle.     

Optimization of elastic material parameters of sheet metal with FEMU and DIC

In this paper a deep-drawing sheet steel is characterized through tensile tests with samples taken in different angles to the rolling direction. The displacement field is recorded with an optical full-field measurement system and the deformation field is calculated by Digital Image Correlation (DIC). The orthotropic elastic material parameters are identified through an iterative parameter optimization via Finite Element Model Updating (FEMU). In this procedure the material parameters are modified in every iteration so that the numerically computed deformation field and forces match the measured values as well as possible. Depending on the objective function and the input values used in the optimization routine, global or only local minima exist. To show the convergence of the applied technique, two different optimization algorithms, one gradient-based and one gradient-free with different initial starting points were used. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Camouflage devices with simplified material parameters based on conformal transformation acoustics

Owing to the recent fascinating advances in transformation acoustics, it is possible to design the distribution of refractive index of attractive devices that can manipulate acoustic waves in almost any manner. Furthermore, if the transformation is conformal, the resultant devices can be made with ordinary isotropic materials instead of exotic anisotropic metamaterials. In this paper, we use conformal transformation acoustics to design camouflage devices with layered homogeneous structures, which can acoustically generate illusions of objects. We demonstrate two devices: one is called shifter that makes an object appearing at different places from the actual location; another is called combiner that makes two objects at separated locations looking like only one object.     

Mathematical analysis of successive linear approximation for Mooney-Rivlin material model in finite elasticity

For calculating large deformations of solid bodies, we have proposed a method of successive linear approximation, by considering the relative Lagrangian formulation. In this article we briefly describe this method, which is applied for nearly incompressible Mooney-Rivlin materials. We prove the existence and uniqueness of weak solutions for associated boundary value problems that arise in each step of the method. In our analysis we consider also a non-standard case, where the coefficients present in the constitutive function of Mooney-Rivlin materials do not satisfy the usual E-inequalities.     

The elasticity of elasticity

In this note we assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrates our thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, the development of a hierarchy of approximations wherein, while the strains are infinitesimal the relationship between the stress and the linearized strain is non-linear. Such approximations would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity that are currently popular.