Finite-strain Poynting–Thomson model: Existence and linearization

IF 1.7 4区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY
Andrea Chiesa, Martin Kružìk, Ulisse Stefanelli
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引用次数: 0

Abstract

We analyze the finite-strain Poynting–Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to the serial connection of an elastic spring and a Kelvin–Voigt viscoelastic element. In the finite-strain case, the total deformation of the body results from the composition of two maps, describing the deformation of the viscoelastic element and the elastic one, respectively. We prove the existence of suitably weak solutions by a time-discretization approach based on incremental minimization. Moreover, we prove a rigorous linx earization result, showing that the corresponding small-strain model is indeed recovered in the small-loading limit.
有限应变 Poynting-Thomson 模型:存在与线性化
我们分析了有限应变 Poynting-Thomson 粘弹性模型。在其线性化小变形极限中,这相当于弹性弹簧和开尔文-伏依格粘弹性元件的串联。在有限应变情况下,物体的总变形由两个映射组成,分别描述粘弹性元素和弹性元件的变形。我们通过基于增量最小化的时间离散化方法证明了适当弱解的存在。此外,我们还证明了一个严格的线性耳化结果,表明相应的小应变模型在小载荷极限下确实可以恢复。
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来源期刊
Mathematics and Mechanics of Solids
Mathematics and Mechanics of Solids 工程技术-材料科学:综合
CiteScore
4.80
自引率
19.20%
发文量
159
审稿时长
1 months
期刊介绍: Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science. The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
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