Crack occurrence in bodies with gradient polyconvex energies

DOI10.1007/s00332-021-09769-3OpenAlexW3132478893MaRDI QIDQ2073978

Domenico Mucci, Martin Kružík, Paolo Maria Mariano

Publication date: 3 February 2022

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.06641

zbMATH Keywords

calculus of variations ground states geometric measure theory varifolds curvature effects second-neighbor interactions

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Free convection (76R10) PDEs in connection with mechanics of deformable solids (35Q74) Calculus of variations and optimal control; optimization (49-XX)

Cites Work

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On shear bands in ductile materials
Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of \(\mathbf F=\mathbf F^e\mathbf F^p\)
Erratum and addendum to ``Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity
Unilateral problems in nonlinear three-dimensional elasticity
Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
Thermodynamics applied to gradient theories involving the accumulated plastic strain: the theories of Aifantis and Fleck and Hutchinson and their generalization
Geometry and balance of hyperstresses
Physical significance of the curvature varifold-based description of crack nucleation
A variational problem in the mechanics of complex materials
Ground states of simple bodies that may undergo brittle fractures
Continua with latent microstructure
On the thermomechanics of interstitial working
Curvature varifolds with boundary
A gradient flow theory of plasticity for granular materials
On the first variation of a varifold: Boundary behavior
Computational inelasticity
On the axioms of plasticity
A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric
A phenomenological theory for strain gradient effects in plasticity
A new proof of the SBV compactness theorem
Special functions with bounded variation and with weakly differentiable traces on the jump set
Energetic formulation of multiplicative elasto-plasticity using dissipation distances
On the plasticity of single crystals: Free energy, microforces, plastic-strain gradients
A model for the quasi-static growth of brittle fractures: Existence and approximation results
Geometric analysis of hyper-stresses
A unified treatment of strain gradient plasticity
Revisiting brittle fracture as an energy minimization problem
Derivation of \(\mathbf{F} = \mathbf{F}^{\operatorname{e}} \mathbf{F}^{\operatorname{p}}\) as the continuum limit of crystalline slip
Mechanics of dislocations and metadislocations in quasicrystals and their approximants: power invariance and balance
Gradient polyconvexity in evolutionary models of shape-memory alloys
Multiple slip in a strain-gradient plasticity model motivated by a statistical-mechanics description of dislocations
Discrete dislocation plasticity analysis of the wedge indentation of films
A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations
Mechanics of quasi-periodic alloys
Normal and integral currents
On the first variation of a varifold
Dislocation walls in crystals under single slip
A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin
Fundamentals of the Mechanics of Solids
Second-neighbor interactions in classical field theories: invariance of the relative power and covariance
Finite Elastoplasticity Lie Groups and Geodesics on SL(d)
A note on locking materials and gradient polyconvexity
A model of isotropic damage with strain-gradient effects: existence and uniqueness of weak solutions for progressive damage processes
VI. The phenomena of rupture and flow in solids
Mathematical Methods in Continuum Mechanics of Solids
Elastic-Plastic Deformation at Finite Strains
Generalized Elastic-Plastic Decomposition in Defective Crystals
Plastic flow in a composite: A comparison of nonlocal continuum and discrete dislocation predictions

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