TY - JOUR
T1 - Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations
AU - Areias, P.
AU - Rabczuk, T.
AU - César de Sá, J.
AU - Alves, J. L.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelasticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We parametrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complementarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.
AB - A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelasticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We parametrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complementarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.
KW - Constitutive integration
KW - Elasto-plasticity
KW - Finite strains
KW - Newton methods
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U2 - 10.1016/j.engstruct.2016.06.035
DO - 10.1016/j.engstruct.2016.06.035
M3 - Article
AN - SCOPUS:84977136769
VL - 124
SP - 344
EP - 360
JO - Engineering Structures
JF - Engineering Structures
SN - 0141-0296
ER -