On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations

By Javier Oliver. 2000

203 citations recorded by the source corpus.

On the basis of continuum constitutive models (stress vs. strain), the introduction of strong discontinuity kinematics (considering jumps in the displacement fields across a discontinuity interface) induces projected discrete constitutive models (traction-displacement jumps) in a consistent manner. Therefore, this projection provides possible links between the classical continuum strain-localization analysis and the non-linear (decohesive) fracture mechanics techniques. The strong discontinuity analysis shows that (bandwidth based) regularization of the hardening/softening parameter is the crucial modification to be done on the continuum model to achieve such a projection, and it also provides the strong discontinuity conditions that set restrictions on the stress state compatible with bifurcations in a strong discontinuity format. The methodology is illustrated on the basis of two classical families of non-linear constitutive models (scalar continuum damage and elasto-plasticity) for which the corresponding discrete constitutive models and the strong discontinuity conditions are derived.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9a27385aa7356b56fcdfac7c4e10ca175dcdf35c

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Modeling 3D crack propagation in unreinforced concrete using PUFEM (2005, unknown): “Recently, it was shown that every continuum constitutive model includes a discrete model in a consistent manner [36,38].”
On the strong discontinuity approach in finite deformation settings (2003, methodology): “For comparison purposes the results using the in nitesimal strain counterpart of the continuum model (23) and the SDA for in nitesimal strains settings given in [17] are used.”
A phantom node formulation with mixed mode cohesive law for splitting in laminates (2009, methodology): “3.1 Damage law We start from a discrete rigid-damage law (Oliver 2000), written as t = 1 − ω ω T u (19) in which ω is a damage variable that evolves from 0 to 1 during crack opening and T is a stiffness parameter.”
Continuum approach to material failure in strong discontinuity settings (2004, background): “In fact it can be shown [19], that the introduction of strong discontinuity kinematics in a continuum medium, ruled by continuum (stress-strain) constitutive equations equipped with strain softening, induces the fulfillment of specific traction-separation constitutive laws at a discrete set of propa”
Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach (2006, background): “Implicit integration of the rate equations (5) and (9) leads to the following solutions, at time 1 + n t , for the internal variables 1 + n r , 1 + n q and the stress 1 + n σ in terms of the current strains 1 + n ε (see [19]):”
Continuum approach to the numerical simulation of material failure in concrete (2004, methodology): “An isotropic damage constitutive model, taken from Reference [9], has been adopted in all cases as non-linear continuum material to model the continuum and discontinuum behaviour of concrete.”
On three-dimensional modelling of crack growth using partition of unity methods (2010, background): “Embedded elements [50,100–103] can handle arbitrary crack paths without remeshing.”
Smeared crack approach: back to the original track (2006, background): “In this way, the decohesion law relating tractions with displacement jumps can be interpreted as the projection onto S of a strain-softening constitutive law relating (certain components of the) stress with (certain components of the) strain, defining the strain tensor in S as ε =∇u, in a distributi”
Theoretical and computational issues in modelling material failure in strong discontinuity scenarios (2004, background): “(b) As the strong discontinuity kinematics (1) is activated, the original continuum constitutive equation (2) is projected into a discrete constitutive model (relating the traction at the failure interface T 1⁄4 rS n with the displacement jump 1⁄21⁄2u ) that is automatically fulfilled at that failur”
3D Crack propagation in unreinforced concrete. A two-step algorithm for tracking 3D crack paths (2006, result): “Note, however, that it was recently shown that every continuum constitutive model linked to strong discontinuity kinematics includes a discrete model in a consistent manner [ 32 ,36].”
A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM (2006, background): “H ðq Þ¼ kH ðqÞ ð13Þ in terms of a discrete softening modulus H , considered a material property available from the mechanical and fracturing properties of the material (peak stress ru, Young modulus E, and fracture energy Gf; see [ 21 ,27] for additional details).”