Stress-rate-type strain-limiting models for solids resulting from implicit constitutive theory

被引：2

作者：

Duman, Emre ^{[1
]}

Senguel, Yasemin ^{[2
]}

机构：

[1] Sabanci Univ, Fac Engn & Nat Sci, Istanbul, Turkiye

[2] Cardiff Univ, Sch Math, Cardiff CF24 4AG, Wales

来源：

ADVANCES IN CONTINUOUS AND DISCRETE MODELS | 2023年 / 2023卷 / 01期

关键词：

Stress-rate-type models; Strain-limiting theory; Implicit constitutive relation; EXISTENCE;

D O I：

10.1186/s13662-023-03751-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main objective of this work is two-fold. First, we investigate the stress-rate-type implicit constitutive relations for solids within the context of strain-limiting theory of material response. The relations we study are models for generalisations of elastic bodies whose strain depends on the stress and the stress rate. Secondly, we obtain travelling-wave solutions for some special cases that are nonlinear in the stress. These are the first notion of solutions available in the literature for this type of models describing stress-rate-type materials.

引用

页数：15

共 14 条

[1] Stress-rate-type strain-limiting models for solids resulting from implicit constitutive theory
Emre Duman
Yasemin Şengül
Advances in Continuous and Discrete Models, 2023
[2] Existence of solutions for stress-rate type strain-limiting viscoelasticity in Gevrey spaces
Bachmann, L.
De Anna, F.
Schloemerkemper, A.
Senguel, Y.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2023, 381 (2263):
[3] A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity
Erbay, H. A.
Sengul, Y.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2020, 71 (03):
[4] A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity
H. A. Erbay
Y. Şengül
Zeitschrift für angewandte Mathematik und Physik, 2020, 71
[5] Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids
Prusa, Vit
Rajagopal, K. R.
FLUIDS, 2021, 6 (03)
[6] Constitutive Models for Dynamic Strain Aging in Metals: Strain Rate and Temperature Dependences on the Flow Stress
Song, Yooseob
Garcia-Gonzalez, Daniel
Rusinek, Alexis
MATERIALS, 2020, 13 (07)
[7] A thermodynamic basis for implicit rate-type constitutive relations describing the inelastic response of solids undergoing finite deformation
Cichra, David
Prusa, Vita
MATHEMATICS AND MECHANICS OF SOLIDS, 2020, 25 (12) : 2222 - 2230
[8] An implicit constitutive relation in which the stress and the linearized strain appear linearly, for describing the small displacement gradient response of elastic solids
Rajagopal, Kumbakonam R.
arXiv, 2021,
[9] Using constitutive models of the rate type in implicit finite-element calculations: error-controlled stress update and consistent tangent operator
Fellin, W
Ostermann, A
ADVANCED MATHEMATICAL AND COMPUTATIONAL GEOMECHANICS, 2003, 13 : 211 - 237
[10] POINTWISE DISPLACEMENT ERRORS IN LINEAR SHELL THEORY RESULTING FROM ERRORS IN STRESS-STRAIN RELATIONS
SIMMONDS, JG
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1972, 23 (02): : 265 - &

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