Modeling Of Nonlinear Behavior Research Articles

Error analysis and modelling of non-linear stress-strain behaviour in measuring dynamic mechanical properties of polymers with the Rheovibron

The Rheovibron is widely used for measuring the dynamic mechanical properties of polymers. Poor reproducibility and data variation which have been considered inherent to the Rheovibron operation necessitate both instrument modifications and modelling of the instrument operation for quantitative interpretation of the experimental data. The instrument modifications that have been made in this study include electronic modifications, a new clamp design that eliminates sample mounting and slippage problems, and the design of an environmental chamber, which, along with a nitrogen purge, eliminates moisture condensation on the sample at low temperatures. A previously-developed mathematical model for the instrument has also been extended to account for the effect of the static stress and the stress rate imposed on the sample during measurement. Based on a simple constitutive relation for non-linear stress-strain behaviour of polymers, this model has been applied to a number of polymeric materials including polyethylene, polyimide, poly (ethylene terephthalate), and polypropylene, among others. The instrument modifications and modelling of the influence of static stress and the stress rate imposed on the sample during dynamic mechanical testing allows for reproducible (within 5%) and accurate use of the Rheovibron.

Adaptive filtering through detection of isolated transient errors in rainfall‐runoff models

Real‐time river discharge forecasting models operate under widely different wet and dry regimes, producing sequences of highly nonstationary prediction residuals. Errors in the mean areal precipitation estimation are often magnified due to model approximations and nonlinear behavior and result in significant effective input errors which propagate as transient signals through the system. Normal operation of a feedback scheme based on the Kalman filter with stationary error statistics cannot account for such discrepancies leading to local divergence between expected and observed prediction residuals. An adaptive filtering methodology which explicitly accounts for transient errors in the prediction due to errors in the estimation of the effective rainfall is presented. The filter operates normally under the assumption of only stationary or slowly varying noise, while a generalized likelihood ratio test is used to detect the presence of transient errors. When such errors are detected, estimates of their timing and magnitude are obtained, and the forecasts are appropriately corrected. An illustrative example of the procedure operation is given.

Numerical modelling of nonlinear behaviour of soft biological materials

This paper deals with the formulation of rigorous numerical methods for the stress analysis, at finite strains, of soft biological materials that can be characterized as incompressible nonlinear elastic solids.

Endochronic model for nonlinear triaxial behavior of concrete

A gradual accumulation of inelastic strain can be most conveniently described in terms of the so-called intrinsic time, whose increment depends on the time increment as well as the strain increments, and was originally developed for metals and was extended in a previous paper by Z.P. Bažant to concrete. In that previous paper it had been demonstrated that the proposed model predicts quite closely: (1) Stress-strain diagrams for concretes of different strength; (2) uniaxial, biaxial and triaxial stress-strain diagrams and failure envelopes; (3) failure envelopes for combined torsion and compression: (4) lateral strains and volume expansion in uniaxial and biaxial tests; (5) the behavior of spirally confined concrete; (6) hysteresis loops for repeated high compression: (7) cyclic creep up to 10 6 cycles; (8) the strain rate effect; (9) the decrease of long time strength: and (10) the increase of short-time strength due to low stress creep. The present paper presents a refinement of the endochronic theory of concrete which consists mainly in taking into account; (a) the inelastic strains due to hydrostatic compression; (b) improved descriptions of strain-softening behavior, (c) cyclic loading in strain-softening range, and (d) volume change in strain-softening range; (e) the differences between proportional and standard triaxial tests; (f) triaxial failure envelopes; and (g) dependence of material parameters on strength. The formulation consists fully of continuous functions, and for numerical analysis it has the advantage that it contains no inequalities. The present expressions are, admittedly, rather complicated and contain many parameters. However, for computer calculations this is not an insurmountable drawback. The agreement with test data is far superior to any other constitutive law found this far — virtually all currently known basic properties are modeled. The value of all material parameters are given, their dependence on concrete strength is identified, and a broad range of normal weight concrete is covered.

Material Models for Nonlinear Deformation of Graphite

ATJ-S graphite is a transversely isotropic granular composite material with different nonlinear stress-strain behavior under tension loading than under compression loading. A model for nonlinear deformation behavior is extended from initial loading under biaxial tension stresses to initial loading under mixed tension and compression stresses. The principal basis of the model is that the material properties are expressed as a function of the strain energy of an equivalent elastic material. Thus, interaction between the various components of a multiaxial stress state is accounted for. Different moduli in tension and compression are excited and are included in the analysis. Both the Jones weighted compliance matrix (WCM) material model and the Isabekian and Khachatryan restricted compliance matrix (RCM) material model are extended to nonlinear deformation.

Constrained and Shear Moduli for Finite Elements

The stress-strain matrix used in finite element analyses has been reformulated in terms of constrained and shear moduli. The new formulation partially uncouples shear and compression and is relatively independent of the relationships of elasticity. Simple hyperbolic functions have been proposed to define equivalent elastic compression and shear moduli for modeling nonlinear soil behavior. Straightforward procedures are provided to determine the parameters for the hyperbolic equations from conventional one-dimensional compression and simple shear tests. In some cases, compression and shear wave propagation velocities measured in situ may also be used. For compatibility with many existing nonlinear finite element programs, either secant or tangent moduli may be developed. Several examples are given for the determination of the hyperbolic parameters from actual soil test data.