Non–convex potentials and microstructures in finite–strain plasticity

By Carsten Carstensen, Klaus Hackl, Alexander Mielke. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2002

388 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c3447b742e69088a29c9bbd494773ad1c6372d29

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In Biomedical Engineering

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Citations in the corpus

Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, background): “Such variational principles aim at recasting the constitutive equations into equivalent minimization problems (Comi et al., 1991; Ortiz and Stainier, 1999; Carstensen et al., 2002; Miehe, 2002).”
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids (2006, methodology): “For instance, time-discretization has been employed to formulate incremental minimum principles for plasticity that establish a connection between non-attainment and the formation of microstructures (Ortiz and Repetto, 1999; Ortiz et al., 2000; Carstensen et al., 2002; Aubry and Ortiz, 2003 ).”
A Vanishing Viscosity Approach to Quasistatic Evolution in Plasticity with Softening (2006, background): “Other rate-independent problems with nonconvex energy have been studied in [3],[16], and [12].”
Energetic formulation of multiplicative elasto-plasticity using dissipation distances (2003, methodology): “quasiconvexity [ CHM02 ,HH01]) or failure via fracture or localization, see Sect.”
Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, background): “In many situations the above described model is intractable, either because the suitable tools are not yet developed or because the model is badly behaved resulting in the formation of microstructure, see [6], [7], [28], [29], [33], [39].”
Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions (2017, background): “Like in structures, instability at the material level stems from non-(quasi)convex energy landscapes [44,45]; here, however, instability is not tied to multiple stable or metastable structural deformation modes but involves multiple stable microstructural configurations such as those in phase transi”
Existence results for energetic models for rate-independent systems (2005, positive): “The purpose of this work is to provide an abstract framework for constructing solutions to (S) & (E) without relying on any underlying linear structures in Y = F ◊ Z. Thus, we hope to provide a basis for applications in genuinely nonlinear mechanical models such as elasto-plasticity with finite stra”
On the implementation of rate-independent standard dissipative solids at finite strain – Variational constitutive updates (2010, methodology): “In the present paper, an enhanced constitutive update for so-called standard dissipative solids obeying the postulate of maximum dissipation, in line with [19, 20, 22–25, 28, 29], is elaborated.”
A finite-strain elastic–plastic Cosserat theory for polycrystals with grain rotations (2006, background): “However, the very feasibility of a timeental variational formulation [15,75,97] depends on this potential structure.”
Modeling Dislocations and Disclinations With Finite Micropolar Elastoplasticity (2006, background): “Possible sources of instability or nonconvexity of the strain energy density of single crystals, from the perspective of continuum plasticity theory, include geometrical softening and strong latent hardening (Ortiz and Repetto, 1999; Sedláček et al., 2001; Carstensen et al., 2002).”
Variationally consistent modeling of finite strain plasticity theory with non-linear kinematic hardening (2010, methodology): “Also, such methods allows to analyze the existence of solutions by using nowadays standard tools such as those known from hyperelasticty [22,23,20], and they can be applied as a canonical basis for error estimation, cf.”