Elastic Solid Model Research Articles

Loading restrictions for the Blatz–Ko hyperelastic model—application to a finite element analysis

In this paper, we consider the Blatz–Ko constitutive model for compressible elastic solids. It is shown that the Cauchy stress tensor leads to a normal loading limitation. This limitation induces slow convergence of the Newton–Raphson algorithm near the maximum authorized normal loading value and divergence if this value is exceeded. In addition, convergence of the Newton–Raphson scheme also depends on ellipticity and strong ellipticity conditions. These various points are discussed in the case of a rectangular specimen subjected to a tensile load and modeled with finite elements.

Modelling of composite sheet forming: a review

Abstract The use of composite materials in sheet forming applications is gaining popularity with the rise of consumer demands and specific mechanical properties. In addition to unidirectional (UD) fibres, the use of textile reinforcements such as woven fabric and knitted fabric has been shown to be feasible in recent years. This paper gives a survey on the modelling of composite sheet forming for both UD fibre and textile composites. Two broad approaches are reviewed here—the mapping approach and the mechanics approach. Mapping approaches for UD fibre composites, woven fabric composites and knitted fabric composites are elucidated on the basis of their fibre geometry. For the mechanics approach both the viscous fluid models and elastic solid models, as a means of describing the constitutive properties, are reviewed. Various updating methods for modelling large deformation found in sheet forming are then described. Finally, a guideline for the choice of modelling techniques for various types of fibre/fabric reinforcements and suggestions for future work are given.

Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials: Part II: a computational environment for adaptive modeling of heterogeneous elastic solids

This paper addresses a classical and largely unsolved problem: given a structural component constructed of a heterogeneous elastic material that is in equilibrium under the action of applied loads, determine local micromechanical features of its response (e.g., local stresses and displacements in or around phase boundaries or in inclusions) to an arbitrary preset level of accuracy, it being understood that the microstructure is a priori unknown, may be randomly distributed, may exist at multiple spatial scales, and may contain millions, even billions, of microscale components. The approach described in this work begins with a mathematical abstraction of this problem in which the material body is modeled as an elastic solid with highly variable, possibly randomly distributed, elastic properties. Information on the actual character of the microstructure of given material bodies is determined by computerized tomography (CT) imaging. A procedure is given for determining the effective material properties from imaging data, using either deterministic or stochastic methods. An algorithm is then described for determining local quantities of interest, such as average stresses on inclusion boundaries, to arbitrary accuracy relative to the fine-scale model. A new computational environment for implementing such analyses is presented which employs parallel, adaptive, hp finite element methods, CT interfaces, automatic meshing procedures, and, effectively, adaptive modeling schemes. Within the basic premises on which the approach is based, results of any specified accuracy can be obtained, independently of the number of microscale components and constituents. The results of several numerical experiments are presented.

Study for Stress Wave in Solid Induced by Shock Wave.

Stress waves induced in elastic solid models by shock waves were studied experimentally and theoretically. For shock-tube experiments, several kinds of solid models were made of transparent acrylic resin and shock waves at approximately Mach 3 were propagated to the models in stationary argon. The schlieren method with a spark light source were employed to visualize shock waves outside and stress waves inside the model. In the schlieren snap-shot photographs, not only shock waves around the models but also stress waves inside the models were observed. Numerical simulations were carried out for shock waves as well as stress waves employing the finite volume method based on the Godunov algorithm. Good agreement was obtained between the experiments and the simulations.

DIPLODEF: A Unified Backcalculation System for Asphalt and Concrete Pavements

The absence of a single backcalculation program that can incorporate all combinations of the four widely used pavement models (elastic layer, plate, elastic solid, and dense liquid) deprives the pavement community of the ability to perform comparative studies. The program DIPLODEF was developed to analyze both asphalt concrete and portland cement concrete pavement systems. The new code was assembled from an existing backcalculation program called WESDEF by replacement of its engine, WESLEA, with DIPLOMAT. In addition to the elastic layer and elastic solid models, DIPLOMAT can accommodate the plate and dense liquid idealizations and can analyze multilayer asphalt and concrete pavement systems with user-defined inputs. DIPLODEF has been thoroughly debugged and tested for consistency and reasonableness. Analyses involving various combinations of elastic layers, plates, and springs were performed. Finally, a rating scheme was devised to standardize the assessment of the precision of backcalculated values and permit consistency in comparisons of results.

Integrated mechanically based CAE system using B-Spline finite elements

In a product development cycle interaction between design and analysis should be very intensive. However, currently existing Computer Aided Engineering systems substantially limit such interaction, since design and analysis are realized in them as two isolated modules. These limitations can be distinguished on two levels: the conceptual and the technical. On the conceptual level a gap exists according to the functionality of each module: the design module is based on purely geometric operations, while the analysis module is based on physical phenomena. On the technical level an environmental gap exists that is characterized by differences in mathematical representation and computational methods. This is partially dictated by the functionality of each module. As a result of these limitations, each iteration between design and analysis and vice versa requires remodeling of the object and conversion of its mathematical representation. In order to overcome these problems, a mechanical B-Spline finite element model is proposed in this work to be used for both geometric design and mechanical analysis. With this approach the target object is modeled as a physical entity from the very beginning of the geometric design stage. Furthermore, both modules utilize the same computational environment—B-Spline finite element, and the same representational environment—B-Spline representation. Therefore, design and analysis are tightly integrated into a completely unified system, and corresponding analysis operations can be performed simultaneously with the geometric design. Technically, this eliminates remodeling and conversion operations between the design and analysis stages of the product development cycle. Conceptually, this allows engineers to substantially shorten the product development cycle time, test many more design variants, tune the final product more finely according to its functionality and reduce the total product development cost. A few examples verifying feasibility and demonstrating performance of the proposed system are presented in the paper. These are developing sculptured surface objects based upon an elastic linear plate model and developing sculptured solid objects based upon an elastic linear solid model.

Determination of the gravimetric factor at the Chandler period from Earth orientation data and superconducting gravimetry observations

Summary We have used more than 8 years’ worth of a combination of superconducting gravimeter (SG) data from the Strasbourg station and Very Long Baseline Interferometry (VLBI) Earth orientation data in order to determine the gravimetric factor at the Chandler period of 435 days. The method presented here takes advantage of the relation between the rotational potential and the gravity variation at the Earth’s surface. The length of the data set is a critical parameter in such a determination but appears to be long enough to separate the annual and Chandler components. Our results are in a good agreement with the long-period theoretical gravimetric factor relative to an elastic solid earth model and a static pole tide in the oceans. We also find that the effect of the atmosphere (computed from a global atmospheric model assuming a static response of the oceans to air-pressure changes) is not negligible and perturbs the amplitude of the Chandler wave observed in the gravimetric data.

The thermodynamic structure and constitutive equations for fluid-saturated compressible and incompressible elastic porous solids

The macroscopic porous media theory consists of the mixture theory, restricted by the volume fraction concept. The incorporation of this concept leads to major difficulties in constructing a consistent macroscopic theory. With the help of thermodynamic restrictions, in addition with the multiplicative decomposition of the deformation gradient as well as experimental observations it will be shown, as to how a consistent phenomenological porous media theory for compressible and incompressible elastic porous solid models filled with an incompressible fluid can be developed which is mathematically and physically well balanced.

Analysis of fiber formation during air‐gap wet spinning

AbstractThe steady formation of fibers in the air‐gap wet‐spinning process is analyzed, in which solidification of the fiber material is brought about by the diffusional exchange of solvent and nonsolvent in a coagulation bath. The concentration profile within the fiber is determined, and a simple model is given for the change of the material behavior with changing concentration. The material behavior of the uncoagulated spinning solution is described by a constitutive model for viscoelastic liquids that allows the incorporation of a relaxation‐time spectrum. The behavior of the solidified fiber is described by a model for rubberlike elastic solids. The effects of variable fiber temperature and skin friction on the fiber motion are also taken into account. The computed velocity profiles are compared to experimental data. These data were obtained by spinning three samples of nominally identical spinning solutions. Even though the theoretically predicted profiles agree well with those obtained with the first two samples, they completely fail to do so for the third. This failure is attributed to the unexpected extreme sensitivity of the model predictions to the width of the dynamic spectrum that is used to infer the relaxation‐time spectrum. It is also found that the velocity profile depends rather strongly on the initial conditions for the stress.

Damage model for brittle elastic solids with unequal tensile and compressive strengths

The paper presents a rate-type constitutive analysis of damage, applicable to brittle materials whose elastic properties degrade during a deformation process. Different tensile and compressive material responses are modeled incorporating positive and negative projections of the stress or strain tensors. Proposed evolution laws for the rate of compliance tensors are consistent with some of the prominent features of brittle material response. A new structure of the damage surface is introduced for a more accurate account of the effects of the hydrostatic states of stress on the overall response. Derived rate constitutive equations provide the explicit representation of the tangent compliance tensor. The proposed model is applied to uniaxial tension and compression to illustrate nonlinear relationships between stress and longitudinal, lateral, and volumetric strains. The proposed model is compared with some of the existing theories.

Residual Stresses in Quenched and Injection Moulded Products

Abstract The differences between residual stress formation mechanisms are studied for several important polymer processes. The most important cases are free quenching (e.g. in extrusion), constrained quenching and constrained quenching with varying applied pressure (injection moulding). A simple, but physically relevant, elastic solid model is assumed (viscous melt and purely elastic solid) yielding Struik's cooling stress model for the free quenching case. In the constrained quenching case, however, the residual stresses are found to vanish. This allowed us to derive a simple analytical expression for the residual stresses in injection moulded products. These stresses were found to be proportional to the maximum melt pressure and are tensile near the surfaces. The predictions compared well with the measured stress distribution. Finally the effects of residual stresses with respect to warpage and environmental stress cracking are discussed.

A microscopic model for stress-strain relations in rock—Part I. Equilibrium equations

The classical microscopic model for elastic solids, based upon bonds between atoms or molecules, is modified to include more general networks and breakage of over-extended bonds. The resulting macroscopic stress-strain relation is non-linear and history dependent. The equilibrium differential equations have multiple solutions. For monotonically increasing compressive stress, it is argued that the physically appropriate solution minimizes a free energy functional. Discontinuous transition between states with different degrees of internal bond breakage can occur. Multiphase mixtures of homogeneous internal states can also occur. Various configurations of broken bonds can be interpreted as cracks.

Acceleration waves in elastic solids near the melting point

By adopting the self-consistent Einstein model for elastic solids and by using the method of singular surface, adiabatic and isothermal acceleration waves in elastic solids in the vicinity of the melting point are studied theoretically. The propagation velocities of the waves are determined and differential equations which govern the variation of amplitudes with time are obtained. It is shown that properties of solid materials near the melting point reflect sensitively on the wave propagations. The following facts are also shown: 1. (1) The variation of amplitudes may have a universal character irrespective of elastic solids. 2. (2) There exist singularities in the temperature dependences of the wave propagations just at the melting point.

Determination of the parameters of a model of a base from engineering-geologic survey data

The authors present a mathematical model that aids in the design of foundations of hydroelectric power plants. The semi-infinite linearly deformable elastic solid model, SIE model, allows calculation of the effect of the shape in plan and rigidity of foundation, the mutual effect of foundations, etc. Engineering-geologic surveys are used to establish analogues for the SIE model.

A continuum theory of thermoelastic solids with diatomic structure

Generalizing the idea of the deformable elastic shell model by Dick and Overhauser [1], a continuum model for thermoelastic diatomic elastic solids is presented. The model used is based on the assumption that a diatomic solid may be considered to consist of two simple and initially overlapping elastic media interacting with each other. Based on this assumption, the kinematics, balance laws and the appropriate constitutive relations for heat conducting diatomic elastic solids with multiple temperature are presented. For the illustration of the theory, the propagation of time-harmonic thermal waves in elastically rigid heat-conducting diatomic solids is studied and some particular cases are discussed.

On the thermodynamics of deformable solid surfaces

The system of thermodynamic fundamental equations for bulk phases and interfaces has been studied within the frames of the completely elastic solid model. The dependence of surface properties on strains has been considered. The deformation of a solid surface at incomplete wetting and the possibility of the contact angle anisotropy have been analyzed. The influence of the bulk strains of a solid on wetting has been discussed.