P. Ariza, S. Conti, A. Garroni and M. Ortiz Variational modeling of dislocations in crystals in the line-tension limit In V. Mehrmann and M. Skutella, editor, European Congress of Mathematics, Berlin, 2016
page 583-598.
Publisher: EMS
2018 10.4171/176-1/27
Sergio Conti, Stefan Müller and Michael Ortiz Data-driven problems in elasticity Arch. Ration. Mech. Anal., 229: 79-123 2018 10.1007/s00205-017-1214-0
Celia Reina, Landry Fokoua Djodom, Michael Ortiz and Sergio Conti Kinematics of elasto-plasticity: Validity and limits of applicability of $F=F_eF_p$ for general three-dimensional deformations Journal of the Mechanics and Physics of Solids, 121: 99--113 2018 10.1016/j.jmps.2018.07.006
W. Schill, S. Heyden, S. Conti and M. Ortiz The anomalous yield behavior of fused silica glass Journal of the Mechanics and Physics of Solids, 113: 105 - 125 2018 10.1016/j.jmps.2018.01.004
2016
Sergio Conti and Michael Ortiz Optimal Scaling in Solids Undergoing Ductile Fracture by Crazing Arch. Rat. Mech. Anal., 219(2): 607-636 2016 http://dx.doi.org/10.1007/s00205-015-0901-y
Abstract: We derive optimal scaling laws for the macroscopic fracture energy of polymers failing by crazing. We assume that the effective deformation-theoretical free-energy density is additive in the first and fractional deformation-gradients, with zero growth in the former and linear growth in the latter. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. For this particular geometry, we derive optimal scaling laws for the dependence of the specific fracture energy on cross-sectional area, micromechanical parameters, opening displacement and intrinsic length of the material. In particular, the upper bound is obtained by means of a construction of the crazing type.
2015
Sergio Conti, Adriana Garroni and Michael Ortiz The line-tension approximation as the dilute limit of linear-elastic dislocations Arch. Ration. Mech. Anal., 218(2): 699-755 2015 http://dx.doi.org/10.1007/s00205-015-0869-7
Abstract: We prove that the classical line-tension approximation for dislocations in crystals, i.e., the approximation that neglects interactions at a distance between dislocation segments and accords dislocations energy in proportion to their length, follows as the $\Gamma$-limit of regularized linear-elasticity as the lattice parameter becomes increasingly small or, equivalently, as the dislocation measure becomes increasingly dilute. We consider two regularizations of the theory of linear-elastic dislocations: a core-cutoff and a mollification of the dislocation measure. We show that both regularizations give the same energy in the limit, namely, an energy defined on matrix-valued divergence-free measures concentrated on lines. The corresponding self-energy per unit length $\psi(b,t)$, which depends on the local Burgers vector and orientation of the dislocation, does not, however, necessarily coincide with the self-energy per unit length $\psi_0(b,t)$ obtained from the classical theory of the prelogarithmic factor of linear-elastic straight dislocations. Indeed, microstructure can occur at small scales resulting in a further relaxation the classical energy down to its $\calH^1$-elliptic envelope.
Stefanie Heyden, Bo Li, Kerstin Weinberg, Sergio Conti and Michael Ortiz A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity J. Mech. Phys. Solids, 74: 175-195 2015 http://dx.doi.org/10.1016/j.jmps.2014.08.005
Abstract: We derive and numerically verify scaling laws for the macroscopic fracture energy of poly- mers undergoing crazing from a micromechanical model of damage. The model posits a local energy density that generalizes the classical network theory of polymers so as to account for chain failure and a nonlocal regularization based on strain-gradient elasticity. We specifically consider periodic deformations of a slab subject to prescribed opening dis- placements on its surfaces. Based on the growth properties of the energy densities, scaling relations for the local and nonlocal energies and for the specific fracture energy are derived. We present finite-element calculations that bear out the heuristic scaling relations.
Brandon Runnels, Irene Beyerlein, Sergio Conti and Michael Ortiz A relaxation method for the energy and morphology of grain boundaries and interfaces J. Mech. Phys. Solids 2015 http://dx.doi.org/10.1016/j.jmps.2015.11.007
2014
Landry Fokoua Djodom, Sergio Conti and Michael Ortiz Optimal Scaling in Solids undergoing Ductile Fracture by Void Sheet Formation Arch. Ration. Mech. Anal., 212(1): 331-357 2014 http://dx.doi.org/10.1007/s00205-013-0687-8
Abstract: This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, that is, it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material.
Landry Fokoua Djodom, Sergio Conti and Michael Ortiz Optimal scaling laws for ductile fracture derived from strain-gradient microplasticity J. Mech. Phys. Solids, 62: 295-311 2014 http://dx.doi.org/10.1016/j.jmps.2013.11.002
Abstract: This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, that is, it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material.