Gurson’s Model: ALE Formulation and Strain Localization

IMPLICATIONS OF A CONSTITUTIVE MODEL FOR STRAIN LOCALIZATION

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1988369 ◽

1988 ◽

Vol 49 (C3) ◽

pp. C3-489-C3-496

Author(s):

B. D. COLEMAN ◽

M. L. HODGDON

Keyword(s):

Constitutive Model ◽

Strain Localization

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A Consistent Implementation of Inelastic Material Models into Steady State Rolling

Tire Science and Technology ◽

10.2346/tire.16.440302 ◽

2016 ◽

Vol 44 (3) ◽

pp. 174-190 ◽

Cited By ~ 2

Author(s):

Mario A. Garcia ◽

Michael Kaliske ◽

Jin Wang ◽

Grama Bhashyam

Keyword(s):

Steady State ◽

Numerical Simulations ◽

Viscoelastic Material ◽

Rolling Contact ◽

Arbitrary Lagrangian Eulerian ◽

Ale Formulation ◽

Inelastic Material ◽

Material Formulation ◽

Steady State Rolling ◽

Efficient Alternative

ABSTRACT Rolling contact is an important aspect in tire design, and reliable numerical simulations are required in order to improve the tire layout, performance, and safety. This includes the consideration of as many significant characteristics of the materials as possible. An example is found in the nonlinear and inelastic properties of the rubber compounds. For numerical simulations of tires, steady state rolling is an efficient alternative to standard transient analyses, and this work makes use of an Arbitrary Lagrangian Eulerian (ALE) formulation for the computation of the inertia contribution. Since the reference configuration is neither attached to the material nor fixed in space, handling history variables of inelastic materials becomes a complex task. A standard viscoelastic material approach is implemented. In the inelastic steady state rolling case, one location in the cross-section depends on all material locations on its circumferential ring. A consistent linearization is formulated taking into account the contribution of all finite elements connected in the hoop direction. As an outcome of this approach, the number of nonzero values in the general stiffness matrix increases, producing a more populated matrix that has to be solved. This implementation is done in the commercial finite element code ANSYS. Numerical results confirm the reliability and capabilities of the linearization for the steady state viscoelastic material formulation. A discussion on the results obtained, important remarks, and an outlook on further research conclude this work.

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