Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour

Engelen, R.A.B.; Geers, M.G.D.; Baaijens, F.P.T.

doi:10.1016/s0749-6419(01)00042-0

Cited by 295 publications

(190 citation statements)

References 21 publications

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“…In practice, we are concerned with steady granular flows; however, reducing (21) to the steadystate case is not as simple as setting the left-hand side to zero, since the stability of g-solutions depends on the sign of (µ s − µ). Denoting the steady solution of (21) in the absence of spatial gradients as g loc , for µ < µ s , the stable solution is g loc = 0, while for µ > µ s , the stable solution…”

Section: Summary Of the Modelmentioning

confidence: 99%

A finite element implementation of the nonlocal granular rheology

Henann¹,

Kamrin²

2016

Numerical Meth Engineering

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SUMMARYInhomogeneous flows involving dense particulate media display clear size effects, in which the particle length scale has an important effect on flow fields. Hence, nonlocal constitutive relations must be used in order to predict these flows. Recently, a class of nonlocal fluidity models have been developed for emulsions and subsequently adapted to granular materials. These models have successfully provided a quantitative description of experimental flows in many different flow configurations. In this work, we present a finiteelement-based numerical approach for solving the nonlocal constitutive equations for granular materials, which involve an additional, non-standard nodal degree-of-freedom -the granular fluidity, which is a scalar state parameter describing the susceptibility of a granular element to flow. Our implementation is applied to three canonical inhomogeneous flow configurations: (i) linear shear with gravity, (ii) annular shear flow without gravity, and (iii) annular shear flow with gravity. We verify our implementation, demonstrate convergence, and show that our results are mesh-independent.

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Section: Summary Of the Modelmentioning

confidence: 99%

A finite element implementation of the nonlocal granular rheology

Henann¹,

Kamrin²

2016

Numerical Meth Engineering

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“…This problem is not purely numerical since the mesh dependence is the direct consequence of ill-posedness of the underlying mathematical problem, i.e. the boundary value problem loses ellipticity in statics or hyperbolicity in dynamics (Engelen et al, 2003). Many non-local models have been proposed not only to address this numerical deficiency, but also to represent a physical behavior, see e.g.…”

Section: Introductionmentioning

confidence: 99%

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Nguyễn

Lani

Pardoen

et al. 2016

International Journal of Solids and Structures

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A large strain hyperelastic phenomenological constitutive model is proposed to model the highly nonlinear, rate-dependent mechanical behavior of amorphous glassy polymers under isothermal conditions. A corotational formulation is used through the total Lagrange formalism. At small strains, the viscoelastic behavior is captured using the generalized Maxwell model. At large strains beyond a viscoelastic limit characterized by a pressure-sensitive yield function, which is extended from the Drucker-Prager one, a viscoplastic region follows. The viscoplastic flow is governed by a non-associated Perzyna-type flow rule incorporating this pressure-sensitive yield function and a quadratic flow potential in order to capture the volumetric deformation during the plastic process. The stress reduction phenomena arising from the post-peak plateau and during the failure stage are considered in the context of a continuum damage mechanics approach.The post-peak softening is modeled by an internal scalar, so-called softening variable, whose evolution is governed by a saturation law. When the softening variable is saturated, the rehardening stage is naturally obtained since the isotropic and kinematic hardening phenomena are still developing. Beyond the onset of failure characterized by a pressure-sensitive failure criterion, the damage process leading to the total failure is controlled by a second internal scalar, so-called failure variable. The final failure occurs when the failure variable reaches its critical value. To avoid the loss of solution uniqueness when dealing with the continuum damage mechanics formalism, a non-local implicit gradient formulation is used for both the softening and failure variables, leading to a multi-mechanism non-local damage continuum. The pressure sensitivity considered in both the yield and failure conditions allows for the distinction under compression and tension loading conditions. It is shown through experimental comparisons that the proposed constitutive model has the ability to capture the complex behavior of amorphous glassy polymers, including their failure.

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“…For this reason, we will restrict our attention to two widely popular families of models, referred to as explicit and implicit. Explicit gradient models have their origins in the pioneering work of Aifantis [1], while implicit gradient models found inspiration in the implicit gradient damage model [10] and for plasticity were first proposed by Geers and coworkers [7,5,6]. In each family, we will investigate the basic version and one of its modifications:…”

Section: One-dimensional Localization Problemmentioning

confidence: 99%

“…The usual formulation of implicit gradient plasticity, developed by Geers and coworkers [7,5,6] and considered in the previous section, imposes the homogeneous Neumann boundary condition at the physical boundary of the body of interest. In a recent study focusing on applications to beam bending, Challamel [4] proposed to impose that condition on the boundary of the plastic zone.…”

Section: Implicit Gradient Plasticity With Modified Boundary Conditionsmentioning

confidence: 99%

Softening Gradient Plasticity: Analytical Study of Localization under Nonuniform Stress

Jirásek

Zeman

Vondřejc

2010

Int J Mult Comp Eng

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Localization of plastic strain induced by softening can be objectively described by a regularized plasticity model that postulates a dependence of the current yield stress on a nonlocal softening variable defined by a differential (gradient) expression. This paper presents analytical solutions of the one-dimensional localization problem under certain special nonuniform stress distributions. The one-dimensional problem can be interpreted as describing either a tensile bar with variable cross section, or a beam subjected to a nonuniform bending moment. Explicit as well as implicit gradient formulations are considered. The evolution of the plastic strain profile and the shape of the load-displacement diagram are investigated. It is shown that even if the local constitutive law exhibits softening right from the onset of yielding, the global loaddisplacement diagram has a hardening part. The interplay between the internal length scales characterizing the material and the geometry is discussed.

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Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour

Cited by 295 publications

References 21 publications

A finite element implementation of the nonlocal granular rheology

A finite element implementation of the nonlocal granular rheology

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Softening Gradient Plasticity: Analytical Study of Localization under Nonuniform Stress

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