Finite element formulations for large deformation dynamic. A methodology is developed for estimating the overall elasticplastic response of composites which undergo finite plastic deformations, and therefore their effective instantaneous elasticplastic moduli in a continued plastic flow are of the order of magnitude of the applied stresses. For situations requiring this generalization, dilatational influences. The methodology also applies to composite elastic solids at finite strains such as reinforced rubbers. Elasticplastic analysis of metallic shells at finite strains 4. Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. The roles of the consistent jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method. A general concept is presented to analyse the deformation of structures undergoing arbitrarily large elastic and arbitrarily large plastic strains. Finite element formulations for large deformation dynamic analysis klausjurgen bathe civil engineering department, university of california, berkeley, california, u. Elasticplastic analysis of metallic shells at finite strains.
As a result, the total energy dissipation associated with crack extension in an elastic plastic material consists of three parts. Flow plasticity theories are characterized by the assumption that a flow rule exists that can be used to determine the amount of plastic deformation in the material in flow plasticity theories it is assumed that the total strain in a body can be decomposed additively or multiplicatively. A finite strain theory for elasticplastic deformation. A scheme of this type was proposed by hibbitt, marcal and rice 11, who. Closure to discussion of elasticplastic deformation at finite strains 1970, asme j. Finite elastic strains are usually predomlnently dilatational, since increase of elastic shear strain components beyond the elastic limit lo produces plastic flow. In continuum mechanics, the finite strain theoryalso called large strain theory, or large deformation theorydeals with deformations in which strains andor rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. Finite strain theory, also called large strain theory, large deformation theory, deals with deformations in which both rotations and strains are arbitrarily large.
A plasticity law is developed which includes the influence of temperature change and the finite elastic strain existing during the duration of plastic deformation. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between. Finite deformation an overview sciencedirect topics. The matrix product 6 provides the relation between elastic, plastic and total deformation valid for finite strains. In view of the controversy regarding a number of fundamental issues between several existing schools of plasticity, the areas of agreement are described separately from those of disagreement.
The rigidplastic and viscoplastic finite element techniques described in the previous chapters are useful approaches to the modelling of metal deformation when the elastic component of strain may reasonably be ignored. Closure to discussion of elasticplastic deformation at. Elasticplastic deformation at finite strains journal of. The first proposes the additive decomposition of an appropriately defined finite strain tensor into elastic and. A finite strain eulerian formulation for compressible and. Finite strain elastoplasticity considering the eshelby stress for. Particle displacements produce dilatation change in size, positive for expansion and negative for shrinking andor distortion, a change in shape the final shape, after cumulative strain s. Loss of ellipticity for noncoaxial plastic deformations in additive logarithmic finite strain plasticity article pdf available in international journal of nonlinear mechanics 81 october. Clearly, finite amplitude continental deformation cannot be treated using a plane strain.
A theory of finite deformation plasticity is developed which involves a multiplicative decomposition of the deformation gradient through the assumption that there exists a stressfree configuration which can be used to separate the elastic and plastic components of the response. In this case, the undeformed and deformed configurations of the. The equations describing finite deformation of elastoplastic solids may be derived in what is termed a rate form. Based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions the kinematics of two superposed finite, noncoaxial deformations are investigated. The present theory modifies the kinematics to include finite elastic and plastic strain components. Constitutive equations for elasticplastic materials at. That is, attention is focused not upon field quantities such as stress and strain but rather upon their rates of change with respect to time. In general, formulations can use different kinematic descriptions and assumptions in the material law, and analysis results can vary by a large amount. For elasticplastic composites at finite strains and rotations.
Such situations fall outside the scope of classical plasticity theory which assumes either infinitesimal strains or plasticrigid theory for large strains. A theory of elasticplastic deformation with strain induced anisotropy based on finitedeformationvalid continuum mechanics is presented. Mechanics of solids mechanics of solids finite deformation and strain tensors. The analysis of elasticplastic deformation is not essentially modified by this circumstance. Calo, a finite strain eulerian formulation for compressible and nearly incompressible hyperelasticity using higherorder nurbs elements, ices report 1042, the institute for computational engineering and sciences, the university of texas at austin, october 2010. The proper formulation of elastoplastic constitutive laws in the finite deformation range has been the subject of considerable conjecture. A t heory of elasticplastic deformation with strain induced anisotropy based on finite deformation valid continuum mechanics is presented. Review of finite elements for finite deformation the description lagrangian is attached to large deformation finite element programs which use a mesh of elements representing some fixed reference state for strain. Elasticplastic deformation at finite strains journal of applied.
On rate principles for finite strain analysis of elastic and inelastic nonlinear solids s. Elasticplastic deformation at finite strains asme digital collection. Finite strain theory 1 finite strain theory in continuum mechanics, the finite strain theoryalso called large strain theory, or large deformation theorydeals with deformations in which both rotations and strains are arbitrarily large, i. The authors address various analytical and numerical finite strain analyses. Therefore, stresses and strains are interdependent. In the theory of finite deformations, extension and rotations of line elements are unrestricted as to size. Large elasticplastic torsion of uniform circular bars is investigated numerically, using special finite elements. Abstractthe problem of formulating and numerically implementing finite element elasticplastic large deformation analysis is considered. Introduction to finite strain theory for continuum elasto. The formulation was given in a manner which allows any conventional finite element program, for small strain elasticplastic analysis, to be simply and rigourously adapted to problems involving arbitrary amounts of. Many other constitutive equations for elasticplastic materials at finite strain have been proposed by freund 121, tanaka 122, hahn 123. The incremental stiffness matrix of the element is derived including shear band deformation. Strain theory for elasticplastic deformation 449 the numerical results indicate that as kc becomes smaller the normal stresses become smaller and become negligible for kc t heory of elasticplastic deformation with strain induced anisotropy based on finite deformation valid continuum mechanics is presented. The elastic strain component is related to the stress through thermoelastic theory for finite strains.
Analysis of elasticplastic torsion of circular bars at. Attention is mainly focussed on the purely mechanical, rateindependent. Volume conservation during finite plastic deformation. The model is implemented within a triangular finite element and is briefly assessed by means of two numerical examples. Relative plastic and elastic deformation predicted by druckereprager eshelbyemandel formulation, comparing exponential and linear hardening model predictions. In this chapter we present only some classical methods which may be used to model elastic, viscoelastic, and elasticplastictype behaviors.
The approach is conceptually analogous to that employed by swedlow 7. Strain theory for elasticplastic deformation 449 the numerical results indicate that as kc becomes smaller the normal stresses become smaller and become negligible for kc deformation of structures undergoing arbitrarily large elastic and arbitrarily large plastic strains. The modeling of engineering materials at finite strain is a subject of much research and any complete summary on the state of the art is clearly outside the scope of what can be presented here. Elastoplasticity, elasticplastic shells, finite strains, finite rotations, variablethickness, triangular shell finite element. Elasticplastic deformation at finite strains a commentary has been published. Deformation analysis for finite elasticplastic strains in. On finite elasticplastic deformation of metals journal. Two end conditions corresponding to fixedend torsion and freeend torsion, resp. The elasticplastic finiteelement method springerlink. In the classical theory of elasticity a deformation strain is termed infinitesimal when the space derivatives of the components of the displacement vector of an arbitrary particle of the medium are so small that their squares and products may be neglected.
Finite strain elasticplastic deformation of glassy polymers. In some circumstances, elasticplastic deformation occurs in which both components of strain are finite. Finite element formulations for problems of large elasticplastic deformation. Pdf nonlinear, finite deformation, finite element analysis. It replaces the usual assumption that the total strain is the sum of elastic and plastic compon ents. In this case, the undeformed and deformed configurations of the continuum are significantly different and a. But in the finite deformation regime, because the strain and the plastic strain or their rates may have different definitions in different elastoplastic theories, it. The theory of elasticplastic deformation at finite strain. On rate principles for finite strain analysis of elastic. On the foundation of nonlinear kinematics which provides strict uncoupling of elastic and plastic deformation rate terms according to their physical origins, it introduces a basis for the modified plastic rate of deformation d. For an infinitesimal fibre that deforms from an initial point given by the vector dx to the vector dx in the time t, the deformation gradient is defined by fij.
The analysis is carried out using an isotropic hardening as well as a recently proposed large deformation kinematic hardening model. Introduction elasticplastic deformation processes of metals, under most conditions of operaeither the maximum elastic and plastic strains achieved are infinitesimal and of roughly the same order about 103, or the plastic strains become so much larger than the elastic strains that the plastic strains must be considered finite and the elastic. Sharifi and popov6 extended the method of 5 to elasticplastic analysis of infinitesimal strains but finite rotations, although they do not seem to consider the possibility that plastic deformation moduli may be of a size comparable to current stress levels. Introduction to finite elastoplasticity presents introductory explanations that can be readily understood by readers with only a basic knowledge of elastoplasticity, showing physical backgrounds of concepts in detail and derivation processes of almost all equations. Equations for finite deformations of elastic plastic solids, 1984, in which this variable was suggested in order to give an. After obtaining a properly invariant representation for the free energy response and hence also for the stress as a function of certain. Finite elasticplastic deformation of polycrystalline metals. Pdf finiteelement formulations for problems of large. Finite strain calculations of continental deformation. The theory of elasticplastic deformation at finite strain with induced. Elasticplastic decomposition of lagrangian strain eeep.
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