Rate-independent Elastoplastic Model Research Articles

Fractional-order uniaxial visco-elasto-plastic models for structural analysis

We propose two fractional-order models for uniaxial large strains and visco-elasto-plastic behavior of materials in structural analysis. Fractional modeling seamlessly interpolates between the standard elasto-plastic and visco-elasto-plastic models, taking into account the history (memory) effects of the accumulated plastic strain to specify the state of stress. To this end, we develop two models, namely M1 and M2, corresponding to visco-elasto-plasticity considering a rate-dependent yield function and visco-plastic regularization, respectively. Specifically, we employ a fractional-order constitutive law that relates the Kirchhoff stress to the Caputo time-fractional derivative of the strain with order β∈(0,1). When β→0 the standard rate-independent elasto-plastic model with linear isotropic hardening is recovered by the models for general loading, and when β→1, the corresponding classical visco-plastic model of Duvaut–Lions (Perzyna) type is recovered by the model M2 for monotonic loading. Since the material behavior is path-dependent, the evolution of the plastic strain is achieved by fractional-order time integration of the plastic strain rate with respect to time. The plastic strain rate is then obtained by means of the corresponding plastic slip and proper consistency conditions. Finally, we develop the so called fractional return-mapping algorithm for solving the nonlinear system of the equilibrium equations developed for each model. This algorithm seamlessly generalizes the standard return-mapping algorithm to its fractional counterpart. We test both models for convergence subject to prescribed strain rates, and subsequently we implement the models in a finite element truss code and solve for a two-dimensional snap-through instability problem. The simulation results demonstrate the flexibility of fractional-order modeling using the Caputo derivative to account for rate-dependent hardening and viscous dissipation, and its potential to effectively describe complex constitutive laws of engineering materials and especially biological tissues.

Modeling of the Cyclic Behavior of Loose Sand by an Elasto-Plastic Fuzzy Set Model

The paper focuses on the development of a cyclic plasticity model based on the fuzzy set theory, which is implemented as a computational tool in order to simplify the computer programming of the constitutive driver. The constitutive model is a rate independent elasto-plastic model which is capable of describing repeated load cycles, dilatancy, material memory, and critical state soil mechanics features. Also, with the aid of membership function, the validity of the constitutive model is enhanced by comparing the theoretical output with a set of experimental data obtained from a variety of cyclic triaxial tests of loose sand.

Global spatial regularity for a regularized elasto‐plastic model

AbstractIn this note the spatial regularity of weak solutions for a class of elasto‐viscoplastic evolution models is studied for nonsmooth domains. The considered class comprises models which are obtained through a Yosida regularization from classical, rate‐independent elasto‐plastic models. The corresponding evolution model consists of an elliptic PDE for the (generalized) displacements which is coupled with an ordinary differential equation with a Lipschitz continuous nonlinearity describing the evolution of the internal variable. It is shown that the global spatial regularity of the displacements and the inner variables is exactly determined through the mapping properties of the underlying elliptic operator (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computational analysis of PTFE shaft seals

An endochronic viscoplastic approach, derived from the theory of finite viscoplasticity based on material isomorphisms, is presented, in order to describe the nonlinear material behaviour of filled polytetrafluoroethylene (PTFE) in a computational analysis of PTFE shaft seals. The model allows to characterize viscoplastic material behaviour with an equilibrium hysteresis using a rate-independent elastoplastic model (with an endochronic flow rule and a logarithmic elastic law) in parallel connection with a nonlinear Maxwell model. Due to the endochronic flow rule, an elastic range limited by a yield stress is not needed in the present approach. The volumetric stress contribution is assumed to be purely elastic. The proposed model is applied to simulate the mounting process of PTFE shaft seals in an axially symmetric finite element analysis. The numerical results (radial force, pressure in the contact zone) are in fair agreement with the experimental data.

A rate-dependent endochronic approach to thermoplastic materials: temperature and filler volume fraction dependence

An endochronic viscoplastic approach, derived from the theory of finite viscoplasticity based on isomorphisms, is presented. The model allows to characterize viscoplastic material behaviour with equilibrium hysteresis using a rate-independent elastoplastic model with an endochronic flow rule and a logarithmic elastic law in parallel connection with a non-linear Maxwell model. The volumetric strains are assumed to be purely elastic. The proposed model describes the non-linear mechanical behaviour of thermoplastic materials such as filled polytetrafluoroethylene (PTFE). The temperature and filler volume fraction dependencies of the model parameters have been identified by a Levenberg–Marquardt algorithm. In contrast to previous suggestions, the proposed model is capable to describe both the non-linearities during strain controlled loading and the non-linearities during stress controlled unloading in a unified approach. The results of the numerical simulations are in fair agreement with the experimental data.

Endochronic viscoplastic material models for filled PTFE

To describe the nonlinear material behaviour of polytetrafluoroethylene (PTFE), a viscoplastic material model of the overstress type is proposed based on experimental data. The approach starts with a rheological model without an elastic range, using a rate-independent elastoplastic model with an endochronic flow rule and a nonlinear elastic law in parallel connection with a nonlinear Maxwell model. The generalization to three dimensions is possible for both small and finite strains under the assumption that changes of the density are purely elastic. Numerical simulations show that the model can describe the short and long time material behavior of filled PTFE.

An inelastic material model for filled polytetrafluorethylen

This paper presents a viscoplastic model for PTFE designed to simulate numerically PTFE shaft seals. A rate-independent elastoplastic model with an endochronic flow rule is coupled in series with a rate-dependent Kelvin model, which has a highly nonlinear damper. In contrast to previous models for PTFE, this unified approach is suitable for numerical simulation of the loading and the stress relaxation behaviour at ambient temperature.

A general approach to the evaluation of consistent tangent operators for rate-independent elastoplasticity

We present a general approach to the derivation of the explicit expression of tangent operators, consistent with the finite-step integration schemes of the flow rule, for rate-independent elastoplastic models with mixed hardening. By exploiting the model of generalized standard material, we show that the algorithmic tangent operator can be obtained by inverting a suitable positive definite matrix. Use of the Sherman-Morrison-Woodbury formula allows us to reduce to a half the burden associated with such inversion and to derive an expression of the consistent tangent operator prone to computer implementation. The application of the proposed approach to the von Mises yield criterion with linear kinematic and isotropic hardening shows that the closed-form expression of the operator can be obtained by a straightforward procedure.