scholarly journals Linearized Elasticity as Γ-Limit of Finite Elasticity in the Case of Cracks

PAMM ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 351-352
Author(s):  
Pascal Gussmann
Keyword(s):  
Finite Elasticity ◽  
Linearized Elasticity

scholarly journals Variational linearization of pure traction problems in incompressible elasticity

2020 ◽  
Vol 71 (5) ◽  
Author(s):  
Edoardo Mainini ◽  
Danilo Percivale
Keyword(s):  
Finite Elasticity ◽  
Linearized Elasticity ◽  
Incompressible Elasticity ◽  
External Loads ◽  
Variational Limit

Abstract We consider pure traction problems, and we show that incompressible linearized elasticity can be obtained as variational limit of incompressible finite elasticity under suitable conditions on external loads.

Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks

2020 ◽  
Vol 13 (1) ◽  
pp. 33-52
Author(s):  
Pascal Gussmann ◽  
Alexander Mielke
Keyword(s):  
Elastic Energy ◽  
Finite Elasticity ◽  
Small Deformation ◽  
Local Constraint ◽  
Deformation Limit ◽  
Linearized Elasticity ◽  
Global Injectivity

AbstractThe small-deformation limit of finite elasticity is considered in presence of a given crack. The rescaled finite energies with the constraint of global injectivity are shown to Γ-converge to the linearized elastic energy with a local constraint of non-interpenetration along the crack.

An Appraisal of the Paper by O'Carrol et al. (1990)

1995 ◽  
Vol 209 (3) ◽  
pp. 203-205 ◽  
Author(s):  
A Strozzi ◽  
A Unsworth
Keyword(s):  
Finite Element ◽  
Finite Elasticity ◽  
Experimental Measurements ◽  
Linear Elastic ◽  
Numerical Predictions ◽  
Elasticity Effects

The paper by O'Carrol et al. (1), which addresses the problem of an elastomeric disc indented by a spherical punch, has been evaluated. The sources of disagreement between linear elastic numerical predictions and experimental measurements noted in this paper have been critically examined in the light of finite element forecasts obtained with a package which incorporates finite elasticity effects and incompressibility.

scholarly journals From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions

2014 ◽  
Vol 25 (01) ◽  
pp. 1-38 ◽  
Author(s):  
V. Agostiniani ◽  
T. Blass ◽  
K. Koumatos
Keyword(s):  
Coercivity Conditions ◽  
Coercivity Condition ◽  
Nematic Elastomers ◽  
Linearized Elasticity ◽  
Γ Convergence

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.

scholarly journals A Systematic Review of Continuum Modeling of Skeletal Muscles: Current Trends, Limitations, and Recommendations

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Tien Tuan Dao ◽  
Marie-Christine Ho Ba Tho
Keyword(s):  
Systematic Review ◽  
Skeletal Muscle ◽  
Parameter Identification ◽  
Skeletal Muscles ◽  
Finite Elasticity ◽  
Data Uncertainty ◽  
Continuum Models ◽  
Holistic View ◽  
Muscle Modeling ◽  
Passive Muscle

Finite elasticity theory has been commonly used to model skeletal muscle. A very large range of heterogeneous constitutive laws has been proposed. In this review, the most widely used continuum models of skeletal muscles were synthetized and discussed. Trends and limitations of these laws were highlighted to propose new recommendations for future researches. A systematic review process was performed using two reliable search engines as PubMed and ScienceDirect. 40 representative studies (13 passive muscle materials and 27 active muscle materials) were included into this review. Note that exclusion criteria include tendon models, analytical models, 1D geometrical models, supplement papers, and indexed conference papers. Trends of current skeletal muscle modeling relate to 3D accurate muscle representation, parameter identification in passive muscle modeling, and the integration of coupled biophysical phenomena. Parameter identification for active materials, assumed fiber distribution, data assumption, and model validation are current drawbacks. New recommendations deal with the incorporation of multimodal data derived from medical imaging, the integration of more biophysical phenomena, and model reproducibility. Accounting for data uncertainty in skeletal muscle modeling will be also a challenging issue. This review provides, for the first time, a holistic view of current continuum models of skeletal muscles to identify potential gaps of current models according to the physiology of skeletal muscle. This opens new avenues for improving skeletal muscle modeling in the framework of in silico medicine.

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