Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem | Paper Citation Record

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Large isotropic elastic deformations: on a comprehensive model to correlate the theory and experiments for incompressible rubber-like materials

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Unresolved cited work

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This paper cites Lemma 3.4.Letf= (f 1,...,f n):M⊂R n →R n be symmetric.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Lemma 3.4.Letf= (f 1,...,f n):M⊂R n →R n be symmetric

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This paper cites Of course, stress tensors can be defined which are not conjugate to any strain measure in the present sense. One such is Cauchy stress for a compressible solid,.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Of course, stress tensors can be defined which are not conjugate to any strain measure in the present sense. One such is Cauchy stress for a compressible solid,

Reference 4

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This paper cites Convexity conditions and existence theorems in nonlinear elasticity.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Convexity conditions and existence theorems in nonlinear elasticity

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This paper cites Hyperelastic stability landscape: A check for Hill stability of isotropic, incompressible hyperelasticity depending on material parameters.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Hyperelastic stability landscape: A check for Hill stability of isotropic, incompressible hyperelasticity depending on material parameters

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This paper cites Inequalities restricting the form of the stress-deformation relations for isotropic elastic solids and Reiner-Rivlin fluids.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Inequalities restricting the form of the stress-deformation relations for isotropic elastic solids and Reiner-Rivlin fluids

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Three observations on linear algebra

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Hyperbolic polynomials and convex analysis

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Bhatia.Matrix Analysis

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This paper cites Analysis of intrinsic stability criteria for isotropic third-order Green elastic and compressible Neo-Hookean solids.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Analysis of intrinsic stability criteria for isotropic third-order Green elastic and compressible Neo-Hookean solids

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Constitutive models of rubber elasticity: a review

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This paper cites A theorem of tensor calculus and its application to isotropic elasticity.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem A theorem of tensor calculus and its application to isotropic elasticity

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This paper cites All convex invariant functions of hermitian matrices.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem All convex invariant functions of hermitian matrices

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem On the thermostatics of continuous media

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This paper cites A constitutive condition for idealized isotropic Cauchy elasticity involving the logarithmic strain.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem A constitutive condition for idealized isotropic Cauchy elasticity involving the logarithmic strain

Reference 16

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This paper cites ¨Uber die Abgrenzung der Eigenwerte einer Matrix.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem ¨Uber die Abgrenzung der Eigenwerte einer Matrix

Reference 17

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This paper cites Elastic materials of coaxial type and inequalities sufficient to ensure strong ellipticity.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Elastic materials of coaxial type and inequalities sufficient to ensure strong ellipticity

Reference 18

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Convex spectral functions

Reference 19

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This paper cites A generalization of the Chandler Davis convexity theorem.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem A generalization of the Chandler Davis convexity theorem

Reference 20

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This paper cites Polyconvexity implies Hill’s inequality in SL (2).

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Polyconvexity implies Hill’s inequality in SL (2)

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Lower bounds for the Helmholtz function

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Unresolved cited work

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Application of a new constitutive model for the description of rubber-like materials under monotonic loading

Reference 24

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Unresolved cited work

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Unresolved cited work

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This paper cites Constitutive inequalities for isotropic elastic solids under finite strain.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Constitutive inequalities for isotropic elastic solids under finite strain

Reference 27

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem On constitutive inequalities for simple materials—I

Reference 28

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Polyconvexity does not imply true-stress-true-strain monotonicity in the incompressible three-dimensional case

Reference 29

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This paper cites Conditions for the onset of elastic and material instabilities in hyperelastic materials.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Conditions for the onset of elastic and material instabilities in hyperelastic materials

Reference 30

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Large strain viscoelastic constitutive models for rubber, part I: Formulations

Reference 31

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem On the convexity of the functionC→f(detC) on positive definite matrices

Reference 32

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Sur les fonctions de matrices convexes et isotropes

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem A constitutive inequality for hyperelastic materials in finite strain

Reference 34

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Eigenvalue optimization

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Convex analysis on the Hermitian matrices

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem The mathematics of eigenvalue optimization

Reference 37

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Isotropie et convexit´ e dans l’espace des tenseurs symˆ etriques

Reference 38

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Derivatives of spectral functions

Reference 39

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Group invariance and convex matrix analysis

Reference 40

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem On the trace of matrix products

Reference 41

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This paper cites Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices

Reference 42

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This paper cites 6 It reads TSTS-M+ :⟨σ(logV)−σ(log V),logV−log V⟩>0, V̸= V∈Sym ++(3).(2.36) 3Also sometimes written as⟨dσ,dε⟩>0 or⟨˙σ,˙ε⟩>0 and referred to asDrucker-stabilitycondition.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem 6 It reads TSTS-M+ :⟨σ(logV)−σ(log V),logV−log V⟩>0, V̸= V∈Sym ++(3).(2.36) 3Also sometimes written as⟨dσ,dε⟩>0 or⟨˙σ,˙ε⟩>0 and referred to asDrucker-stabilitycondition

Reference 43

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This paper cites How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

Reference 44

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This paper cites Geometry of logarithmic strain measures in solid mechanics.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Geometry of logarithmic strain measures in solid mechanics

Reference 45

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This paper cites The exponentiated Hencky-logarithmic strain energy. Part I: Constitutive issues and rank-one convexity.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem The exponentiated Hencky-logarithmic strain energy. Part I: Constitutive issues and rank-one convexity

Reference 46

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This paper cites Hypo-elasticity, Cauchy-elasticity, corotational stability and monotonicity in the logarithmic strain.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Hypo-elasticity, Cauchy-elasticity, corotational stability and monotonicity in the logarithmic strain

Reference 47

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This paper cites On Grioli’s minimum property and its relation to Cauchy’s polar decomposition.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem On Grioli’s minimum property and its relation to Cauchy’s polar decomposition

Reference 48

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This paper cites A logarithmic minimization property of the unitary polar factor in the spectral and Frobenius norms.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem A logarithmic minimization property of the unitary polar factor in the spectral and Frobenius norms

Reference 49

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This paper cites Some matrix inequalities and metrization of matrix space.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Some matrix inequalities and metrization of matrix space

Reference 50

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This paper cites A certain zero-sum two-person game equivalent to the optimal assignment problem.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem A certain zero-sum two-person game equivalent to the optimal assignment problem

Reference 51

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This paper cites Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids

Reference 52

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This paper cites Inequalities associated with the inversion of elastic stress-deformation relations and their implications.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Inequalities associated with the inversion of elastic stress-deformation relations and their implications

Reference 53

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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Unresolved cited work

Reference 54

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This paper cites Das isotrope Elastizit¨ atsgesetz.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Das isotrope Elastizit¨ atsgesetz

Reference 55

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This paper cites Zur Absch¨ atzung von Matrizennormen.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Zur Absch¨ atzung von Matrizennormen

Reference 56

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This paper cites Another Simple Proof of a Theorem of Chandler Davis.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Another Simple Proof of a Theorem of Chandler Davis

Reference 57

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This paper cites Golden-Thompson from Davis.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Golden-Thompson from Davis

Reference 58

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This paper cites Stress-deformation relations for isotropic materials.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Stress-deformation relations for isotropic materials

Reference 59

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This paper cites The convexity ofCtoh(detC).

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem The convexity ofCtoh(detC)

Reference 60

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This paper cites Silhavy.The Mechanics and Thermodynamics of Continuous Media.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Silhavy.The Mechanics and Thermodynamics of Continuous Media

Reference 61

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This paper cites A note on the convexity of C7→h(detC).

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem A note on the convexity of C7→h(detC)

Reference 62

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This paper cites An inequality for the trace of the product of two symmetric matrices.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem An inequality for the trace of the product of two symmetric matrices

Reference 63

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This paper cites Do we need Truesdell's empirical inequalities? On the coaxiality of stress and stretch.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Do we need Truesdell's empirical inequalities? On the coaxiality of stress and stretch

Reference 64

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This paper cites Inequality with applications in statistical mechanics.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Inequality with applications in statistical mechanics

Reference 65

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This paper cites Inequalities sufficient to ensure semi-invertibility of isotropic functions.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Inequalities sufficient to ensure semi-invertibility of isotropic functions

Reference 66

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This paper cites Wang and C.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Wang and C

Reference 67

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This paper cites Davis’ convexity theorem and extremal ellipsoids.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Davis’ convexity theorem and extremal ellipsoids

Reference 68

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This paper cites In search of constitutive conditions in isotropic hyperelasticity: polycon- vexity versus true-stress-true-strain monotonicity.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem In search of constitutive conditions in isotropic hyperelasticity: polycon- vexity versus true-stress-true-strain monotonicity

Reference 69

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This paper cites Concurrent enforcement of polyconvexity and true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity: application to neural network constitutive models.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem Concurrent enforcement of polyconvexity and true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity: application to neural network constitutive models

Reference 70

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This paper cites We can compute a simple 15Here, the tensorsεand εare representatives of some nonlinear strain tensors, i.e.ε= logVorε=V−1.

Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem We can compute a simple 15Here, the tensorsεand εare representatives of some nonlinear strain tensors, i.e.ε= logVorε=V−1

Reference 71

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