Finite element implementation of nonlinear constitutive models for piezoceramic materials

Thermoplastic pipes are being used increasingly for water supply lines, storm sewers, and leachate collection systems in landfills. To facilitate limit states design for buried polymer pipes, nonlinear constitutive models have recently been developed to characterize the highly nonlinear and time-dependent material behavior of high-density polyethylene (HDPE). These models have been implemented in a finite element program to permit structural analysis for buried HDPE pipes and to provide information regarding performance limits of the structures. Predictions of HDPE pipe response under parallel plate loading and hoop compression in a soil cell are reported and compared with pipe response measured in laboratory tests. Effects on the structural performance of pipe material nonlinearity, geometrical nonlinearity, and backfill soil properties were investigated. Good correlations were found between the finite element predictions and the experimental measurements. The models can be used to predict pipe response under many different load histories (not just relaxation or creep). Work is ongoing to develop nonlinear constitutive models for polyvinylchloride and polypropylene to extend the predictive capability of the finite element model to these materials.

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A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications

Archive of Mechanical Engineering ◽

10.2478/v10180-011-0021-7 ◽

2011 ◽

Vol 58 (3) ◽

pp. 319-346 ◽

Cited By ~ 16

Author(s):

Cyprian Suchocki

Keyword(s):

Finite Element ◽

Energy Function ◽

Function Theory ◽

Constitutive Models ◽

Elasticity Tensor ◽

Stored Energy ◽

Energy Potential ◽

Hyperelastic Materials ◽

Finite Element Implementation ◽

Living Tissues

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications This paper contains the full way of implementing a user-defined hyperelastic constitutive model into the finite element method (FEM) through defining an appropriate elasticity tensor. The Knowles stored-energy potential has been chosen to illustrate the implementation, as this particular potential function proved to be very effective in modeling nonlinear elasticity within moderate deformations. Thus, the Knowles stored-energy potential allows for appropriate modeling of thermoplastics, resins, polymeric composites and living tissues, such as bone for example. The decoupling of volumetric and isochoric behavior within a hyperelastic constitutive equation has been extensively discussed. An analytical elasticity tensor, corresponding to the Knowles stored-energy potential, has been derived. To the best of author's knowledge, this tensor has not been presented in the literature yet. The way of deriving analytical elasticity tensors for hyperelastic materials has been discussed in detail. The analytical elasticity tensor may be further used to develop visco-hyperelastic, nonlinear viscoelastic or viscoplastic constitutive models. A FORTRAN 77 code has been written in order to implement the Knowles hyperelastic model into a FEM system. The performance of the developed code is examined using an exemplary problem.

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