Generalization of one‐dimensional material models for the finite element method

Abstract

The concept of representative directions is intended to generalize one‐dimensional material models for uniaxial tension to complete three‐dimensional constitutive models for the finite element method. The concept is applicable to any model which is able to describe uniaxial loadings, even to those for inelastic material behavior without knowing the free energy. The typical characteristics of the respected material class are generalized in a remarkable similarity to the input model. The algorithm has already been implemented into the finite element systems ABAQUS and MSC.MARC considering several methods to increase the numerical efficiency. The implementation enables finite element simulations of inhomogeneous stress conditions within technical components, though the input model predicts uniaxial material behavior only.

On the simulation of nonlinear hardening in metallic materials using the concept of representative directions

“…Then, the yield stress is detected for 16 loading directions in the ( √ 3τ, σ)-stress space. 2 The material is supposed to yield when the plastic equivalent strain (as a measure of deviation from linear material response) exceeds the given strain offset.…”

“…A somewhat different generalization approach is considered in the current work. This approach is based on the concept of representative directions [2], which is a further development of the technique proposed in [4]. The concept of representative directions is similar (but not identical) to the micro-sphere approach (see [3] and references therein).…”

“…In order to construct a new constitutive law, the material model [5] was reduced to the case of uniaxial isochoric tension-/compression. After that, the uniaxial constitutive relations were generalized using the concept of representative directions presented in [2].…”

Constitutive Generalization of a Microstructure‐Based Model for Filled Elastomers

“…The uniaxial formulation can be generalized to a fully three-dimensional stress/strain relation, utilizing the concept of representative directions. [18] This 3D generalization of the dynamic flocculation model has been implemented into the finite element method (FEM).…”

Simulation of a chassis bushing with regard to strain induced softening of filled rubber

“…The theory of a strain amplification factor is applied (Mullins & Tobin [4]), which decreases with increasing prestrain controlled by a two-parameter formulation and hereby causes strain induced softening. The generalization of the model for simulation of arbitrary spatial deformation processes is done applying the concept of representative directions proposed by Freund & Ihlemann [2]. The concept utilizes the evaluation of the uniaxial material model in several equally distributed directions and numerical integration in order to obtain a tensorial model for FE simulations.…”