Large strain field near a notch-tip under tension

This paper considers the plane strain notch-tip filed in a rubber-like material under tension. Based on a new constitutive relation, the asymptotic equations of the near tip field are derived and solved. It is shown that the notch tip field is composed of two narrowing sectors and an expanding sector. The dominant stress and strain near the notch tip are found to be in a state of uniaxial tension.     

An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations

The so-called viscoplastic consistency model, proposed by Wang, Sluys and de Borst, is extended here to the integration of a thermoviscoplastic constitutive equation for J₂ plasticity and adiabatic conditions. The consistency condition in this case includes not only strain rate but also the effect of temperature on the yield function. Using the backward Euler integration scheme to integrate the constitutive equations, an implicit algorithm is proposed, leading to generalized expressions of the classical return mapping algorithm for J₂ plasticity, both for the iterative calculation of the plastic multiplier increment and for the consistent tangent operator when strain rate and temperature are considered also as state variables of the hardening equation. The model was implemented in a commercial finite element code and its performance is demonstrated with the numerical simulation of four Taylor impact tests.     

Shear instability direction at a crack-tip in a thermoviscoplastic body

Deformation fields near a crack tip are analyzed for a thermoviscoplastic body deformed either in an antiplane shear or in plane strain. The effects of inertia forces and heat conduction are considered, but those of material elasticity are neglected. By assuming that a shear band initiating from the crack-tip propagates in the direction of the maximum effective stress. It is found that a shear band propagates along the crack ligament in the body deformed in an antiplane shear. For a body undergoing plane strain deformations, the direction of the propagation of the shear band depends upon the mode-mixity parameter and agrees with that observed by Kalthoff.     

Adiabatic shearing of non-homogeneous thermoviscoplastic materials

In this work we present the role of material non-homogeneities, driven by position-dependent thermomechanical parameters on the emergence, evolution and localization of temperature and strain non-uniformities during the shearing of thermoviscoplastic materials of the rate type. We first present the solution of the quasistatic approximation and show the existence of two stages: the first is characterized by a possible “travelling” of non-uniformities, due to non-homogeneities, while in the second the non-uniformities localize and increase at regions with intense heterogeneities. Moreover, we show that, even under stability conditions, the non-uniformities increase at material regions with inhomogeneities, which affect both their spatial distribution and time evolution. The related strain non-uniformities in the form of shear banding, as well as the comparison with the non-uniformities caused by initial defects or temperature gradient, are presented. Finally, numerical results confirm the analytical findings.     

Finite deformations of Ogden's materials under impact loading

The present paper is devoted to the modeling of finite deformations of a hyperelastic body described by Ogden's model under contact/impact conditions. Frictional contact problems are solved by means of the bi-potential method. The first order algorithm is applied to integrate the equation of motion. The total Lagrangian formulation is adopted to describe the geometrically non-linear behavior. For the finite element implementation, the explicit expression of the tangent operator is derived including the case of repeated eigenvalues. A numerical example is given to illustrate efficiency and accuracy of the method.     

Surface instability of orthotropic laminated materials under compression

The piecewise-homogeneous material model and the three-dimensional linearized theory of stability with the assumption of small subcritical strains are used to study the surface buckling of orthotropic and transtropic laminates. A plane problem is formulated, and characteristic equations are derived. A solution is found for a specific transtropic material with different orientations of the isotropy axis __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 64–72, July 2006.     

Linear stability analysis for a thermoviscoplastic material under cyclic axial loading

Some mechanical properties exhibit a very strong dependence upon temperature; these evolutions can be properly analyzed by the steady state response in cyclic loading. To relate experimental conditions to thermomechanical characteristics, the existence and the stability of steady state solutions are studied for cylinders submitted to cyclic compression. The material, considered as rigid viscoplastic, is modeled by a non-Newtonian temperature dependent viscous law. Closed form solutions are obtained in the framework of a large deformation theory by neglecting thermal expansion and inertia effects. Steady state regime is analyzed. The stress versus strain rate response and the temperature distribution are established as functions of the geometry of the cylinder, the loading characteristics and the material parameters. The stability of steady state solutions is analyzed with use of a linear perturbation scheme.Received: 4 July 2002, Accepted: 5 August 2004, Published online: 24 February 2005PACS: 46.15.Ff, 83.60.St Correspondence to: F. Dinzart     

Properties of rubberlike materials under large deformations explained by self-organizing linkage patterns

The theory of self-organizing linkage patterns is an effort to explain the physical reasons for the complicated behavior of industrial rubber materials, in particular under large deformations. To check the consequences of the theory, calculated data of a Trial Program, especially developed to this purpose, are presented.     

Antiplane deformations of inhomogeneous elastic materials

The system of equations governing antiplane deformations of inhomogeneous elastic media is examined with a view to achieving its reduction to a canonical form associated with the Cauchy-Riemann system.     

Large deformations near a tip of an interface-crack between two Neo-Hookean sheets

This paper contains an asymptotic investigation - within the nonlinear theory of elastostatic plane stress - of the deformations and stresses near the tips of a traction-free interface-crack between two dissimilar semi-infinite Neo-Hookean sheets. The results obtained are free of oscillatory singularities of the kind predicted by the linearized theory, which would require the two deformed faces of an interface-crack to overlap in the vicinity of its tips. Instead, the crack is found to open smoothly near its ends, regardless of the specific loading at infinity.     

Plane deformations of ideal granular materials3

The flow rule based on a double-shearing model developed by A. J. M. Spencer, and M. M. Mehrabadi and S. C. Cowin is intended for use in analyzing fully developed plane flows of rate-independent, isotropic, rigidperfectly plastic frictional and dilatant granular materials. With the view of extending the range of applicability of this physically based flow rule to the prepeak (prelocalization) regime, we systematically introduce isotropic hardening (softening) via the usual consideration of scalar hardening variables in the yield function. However, for this new model to be in accord with some recent experimental observations of I. Vardoulakis on shear-band localizations, it is found that we have to abandon the classical assumption of the coincidence of stress and velocity characteristics.     

Note on a class of controllable deformations of incompressible elastic materials

A controllable deformation is one which is possible in every material by the application of suitable surface tractions. In this note we give a direct complex variable method of obtaining a three parameter family of deformations due to Singh and Pipkin.     

Superposition of finite deformations in Mooney-Rivlin materials

Six controllable states are known to exist for all homogeneous, isotropic, incompressible, elastic bodies. It is shown that certain pairs of these controllable states may be superposed in Mooney-Rivlin materials thereby constructing new controllable states for these materials.

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Zusammenfassung Es gibt sechs kontrollierbare Zustände für alle homogenen, isotropischen, inkompressiblen, elastischen Körper. Es ist gezeigt dass gewisse Paare dieser kontrollierbaren Zustände geschichtet werden können in Mooney-Rivlin Materialen und dadurch neue kontrollierbare Zustände für diese Materialen geschaffen werden.

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This work was carried out while both authors were associated with the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin and was supported by U.S. National Science Foundation Grant GK-37367 to that institution.     

Structure of adiabatic shear bands in thermo-viscoplastic materials

The shear band structure in a thermo-viscoplastic material has been analyzed under quasi-static conditions during the final stage of the localization process. A closed form expression of the bandwidth, of the size of the heat-affected zone and of the failure time has been obtained for a homogeneous material. The analysis is based on the assumption that the strain-rate distribution is steady beyond a certain strain level. Predictions have been compared with experimental measurements.     

Effect of material parameters on shear band spacing in work-hardening gradient dependent thermoviscoplastic materials

We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The effect of material elasticity is neglected but that of work hardening, strain-rate hardening, thermal softening, and strain-rate gradients is considered. The consideration of strain-rate gradients introduces a material characteristic length into the problem. A homogeneous solution of the governing equations is perturbed at different values t₀ of time t, and the growth rate at time t₀ of perturbations of different wavelengths is computed. Following Wright and Ockendon's postulate that the wavelength of the dominant instability mode with the maximum growth rate at time t₀ determines the minimum spacing between shear bands, the shear band spacing is computed. It is found that for the shear band spacing to be positive, either the thermal conductivity or the material characteristic length must be positive. Approximate analytical expressions for locally adiabatic deformations of dipolar (strain-rate gradient-dependent) materials indicate that the shear band spacing is proportional to the square-root of the material charateristic length, and the fourth root of the strain-rate hardening exponent. The shear band spacing increases with an increase in the strain hardening exponent and the thermal conductivity of the material.     

Determination of Mooney material constants for highly nonlinear isotropic incompressible materials under large elastic deformations

Experimental Techniques -