A return map algorithm for general isotropic elasto/visco‐plastic materials in principal space

SUMMARYThis paper presents alternative forms of hyperelastic-plastic constitutive equations and their integration algorithms for isotropic-hardening materials at large strain, which are established in two-point tensor field, namely between the first Piola-Kirchhoff stress tensor and deformation gradient. The eigenvalue problems for symmetric and non-symmetric tensors are applied to kinematics of multiplicative plasticity, which imply the transformation relationships of eigenvectors in current, intermediate and initial configurations. Based on the principle of plastic maximum dissipation, the two-point hyperelastic stress-strain relationships and the evolution equations are achieved, in which it is considered that the plastic spin vanishes for isotropic plasticity. On the computational side, the exponential algorithm is used to integrate the plastic evolution equation. The return-mapping procedure in principal axes, with respect to logarithmic elastic strain, possesses the same structure as infinitesimal deformation theory. Then, the theory of derivatives of non-symmetric tensor functions is applied to derive the two-point closed-form consistent tangent modulus, which is useful for Newton's iterative solution of boundary value problem. Finally, the numerical simulation illustrates the application of the proposed formulations.

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“…This result is identical to both the spatial and material return-mapping algorithms for finite elastoplasticity [9,12,14,24].…”

Section: Plastic Corrector: Return Mappingsupporting

confidence: 74%

“…The spatial description provides the possibilities to simplify numerical implementation [9,24,25]. However, for space-curved membrane shells, material description is more suitable [12,14].…”

Section: Constitutive Equations Based On Nominal Stress P and Deformamentioning

confidence: 99%

Two‐point constitutive equations and integration algorithms for isotropic‐hardening rate‐independent elastoplastic materials in large deformation

Wang

Dui

2008

Numerical Meth Engineering

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“…Suppose a i is the ith eigenvalue, and a i the corresponding eigenvector ofC, then we have (see [43]),…”

Section: Derivation For J2 Deformation Plasticity Modelmentioning

confidence: 99%

A semi-numerical algorithm for instability of compressible multilayered structures

et al. 2015

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A computational method is proposed for the analysis and prediction of instability (wrinkling or necking) of multilayered compressible plates and sheets made by metals or polymers under plane strain conditions. In previous works, a basic assumption (or a physical argument) that has been frequently made is that materials are incompressible to simplify mathematical derivations. To account for the compressibility of metals and polymers (the lower Poisson's ratio leads to the more compressible material), we propose a combined semi-numerical algorithm and finite element method for instability analysis. Our proposed algorithm is herein verified by comparing its predictions with published results in literature for thin films with polymer/metal substrates and for polymer/metal systems. The new combined method is then used to predict the effects of compressibility on instability behaviors. Results suggest potential utility for compressibility in the design of multilayered structures.

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“…• Determine if (S k+1 , C n , q n ) 0 using Equation (18), where q n represents all the internal variables at the time t = t n . If yes, the response is instantaneously elastic.…”

Section: Algorithmmentioning

confidence: 99%

Stress and strain‐driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

Jog

Bayadi

2009

Numerical Meth Engineering

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SUMMARYThis work deals with the formulation and implementation of finite deformation viscoplasticity within the framework of stress-based hybrid finite element methods. Hybrid elements, which are based on a twofield variational formulation, are much less susceptible to locking than conventional displacement-based elements. The conventional return-mapping scheme cannot be used in the context of hybrid stress methods since the stress is known, and the strain and the internal plastic variables have to be recovered using this known stress field. We discuss the formulation and implementation of the consistent tangent tensor, and the return-mapping algorithm within the context of the hybrid method. We demonstrate the efficacy of the algorithm on a wide range of problems.

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A return map algorithm for general isotropic elasto/visco‐plastic materials in principal space

Cited by 36 publications

References 57 publications

Two‐point constitutive equations and integration algorithms for isotropic‐hardening rate‐independent elastoplastic materials in large deformation

Two‐point constitutive equations and integration algorithms for isotropic‐hardening rate‐independent elastoplastic materials in large deformation

A semi-numerical algorithm for instability of compressible multilayered structures

Stress and strain‐driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

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