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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 50
  3. Calculus of Variations and Partial Differential Equations : Volume 50, Issue 3-4, July 2014
  4. From finite to linear elastic fracture mechanics by scaling
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 50, Issue 3-4, July 2014
On the structure of the quasiconvex hull in planar elasticity
Regularity and uniqueness of a class of biharmonic map heat flows
From finite to linear elastic fracture mechanics by scaling
Bernstein theorems for length and area decreasing minimal maps
Uniqueness of generalized $$p$$ -area minimizers and integrability of a horizontal normal in the Heisenberg group
Homology computation for a class of contact structures on $$T^3$$
Monotonicity formula and $$\varepsilon $$ -regularity of stable solutions to supercritical problems and applications to finite Morse index solutions
Axially symmetric volume constrained anisotropic mean curvature flow
Second eigenvalue of the Yamabe operator and applications
Diffusion by optimal transport in Heisenberg groups
The extremal solution for the fractional Laplacian
On a class of elliptic problems with indefinite nonlinearities
Weighted Hardy inequality with higher dimensional singularity on the boundary
Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
Non-branching geodesics and optimal maps in strong $$CD(K,\infty )$$ -spaces
Classification of finite Morse index solutions for Hénon type elliptic equation $$-\Delta u = |x|^{\alpha } u_{+}^{p}$$
A priori estimates for Donaldson’s equation over compact Hermitian manifolds
The gradient flow for gauged harmonic map in dimension two II
A strong form of the quantitative isoperimetric inequality
A remark on doubly critical elliptic systems
Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited
Calculus of Variations and Partial Differential Equations : Volume 50, Issue 1-2, May 2014
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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From finite to linear elastic fracture mechanics by scaling

Content Provider SpringerLink
Author Negri, M. Zanini, C.
Copyright Year 2013
Abstract In the setting of finite elasticity we study the asymptotic behaviour of a crack that propagates quasi-statically in a brittle material. With a natural scaling of size and boundary conditions we prove that for large domains the evolution with finite elasticity converges to the evolution with linearized elasticity. In the proof the crucial step is the (locally uniform) convergence of the non-linear to the linear energy release rate, which follows from the combination of several ingredients: the $$\Gamma $$ -convergence of re-scaled energies, the strong convergence of minimizers, the Euler–Lagrange equation for non-linear elasticity and the volume integral representation of the energy release.
Ending Page 548
Page Count 24
Starting Page 525
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 50
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2013-06-22
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword $$\Gamma $$ -convergence Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Theories of fracture and damage Linearized elasticity Finite elasticity Quasi-static crack propagation Variational principles of physics
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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