An elasto-viscoplastic constitutive model for polymers at finite strains: Formulation and computational aspects

In the present paper a computational algorithmic procedure is presented for modeling the elasto/viscoplastic behavior of solid materials. The effects of different loading programs on the inelastic behavior of rate-sensitive materials are analyzed with specific numerical examples. An appropriate solution scheme and a consistent tangent operator are applied which are capable to be adopted for general computational procedures. Numerical computations and results are reported which illustrate the rate-dependence of the constitutive model in use.

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A Ductile Damage Nonlocal Model of Integral-type at Finite Strains: Formulation and Numerical Issues

International Journal of Damage Mechanics ◽

10.1177/1056789510386850 ◽

2011 ◽

Vol 20 (4) ◽

pp. 515-557 ◽

Cited By ~ 27

Author(s):

F.X.C. Andrade ◽

J.M.A. César de Sá ◽

F.M. Andrade Pires

Keyword(s):

Constitutive Model ◽

Nonlinear Complementarity Problem ◽

Finite Strains ◽

Ductile Damage ◽

Local Theory ◽

Local Form ◽

Nonlocal Model ◽

Numerical Implementation ◽

Integral Type ◽

Classical Formulation

This contribution is devoted to the formulation and numerical implementation of a ductile damage constitutive model enriched with a thermodynamically consistent nonlocal theory of integral type. In order to describe ductile deformation, the model takes finite strains into account. To model elasticity, a Hencky-like hyperelastic free energy potential coupled with nonlocal damage is adopted. The thermodynamic consistency of the model is ensured by applying the first and second thermodynamical principles in the global form and the dissipation inequality can be re-written in a local form by incorporating a nonlocal residual that accounts for energy exchanges between material points of the nonlocal medium. The thermodynamically consistent nonlocal model is compared with its associated classical formulation (in which nonlocality is merely incorporated by averaging the damage variable without resorting to thermodynamic potentials) where the thermodynamical admissibility of the classical formulation is demonstrated. Within the computational scheme, the nonlocal constitutive initial boundary value problem is discretized over pseudo-time where it is shown that well established numerical integration strategies can be straightforwardly extended to the nonlocal integral formulation. A modified Newton-Raphson solution strategy is adopted to solve the nonlinear complementarity problem and its numerical implementation, regarding the proposed nonlocal constitutive model, is presented in detail. The results of two-dimensional finite element analyses show that the model is able to eliminate the pathological mesh dependence inherently present under the softening regime if the local theory is considered.

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Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Applied Mechanics Reviews ◽

10.1115/1.4034024 ◽

2016 ◽

Vol 68 (5) ◽

Cited By ~ 77

Author(s):

Saba Saeb ◽

Paul Steinmann ◽

Ali Javili

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Three Dimensional ◽

Linear Displacement ◽

Computational Homogenization ◽

Finite Strains ◽

Underlying Assumption ◽

Numerical Examples ◽

Various Boundary Conditions ◽

Computational Aspects

The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill–Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two- and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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