Search results for "Hyperelastic material"
showing 10 items of 11 documents
G. Herglotz’ Behandlung von Beschleunigungswellen in seiner Vorlesung «Mechanik der Kontinua» angewandt auf die Stosswellen von Christoffel
1981
Following a lecture delivered by Herglotz in 1925/26 we briefly treat acceleration waves in hyperelastic materials. Our main result is a divergence equation for the squared Euclidean norm of the so-called ‘wave vector’. We then apply Herglotz’ method (devised for acceleration waves) to the propagation of such first order discontinuities in elastic bodies as were treated by Christoffel in [1].
A symmetric Galerkin boundary/domain element method for finite elastic deformations
2000
Abstract The Symmetric Galerkin Boundary Element Method (SGBEM) is reformulated for problems of finite elasticity with hyperelastic material and incompressibility, using fundamental solutions related to a (fictitious) homogeneous isotropic and compressible linear elastic material. The proposed formulation contains, besides the standard boundary integrals, domain integrals which account for the problem's nonlinearities through some (fictitious) initial strain and stress fields required to satisfy appropriate “consistency” equations. The boundary/domain integral equation problem so obtained is shown to admit a stationarity principle (a consequence of the Hu-Washizu one), which covers a number…
A new hyperelastic model for anisotropic hyperelastic materials with one fiber family
2016
International audience; The main goal of this study is to propose a practical application of a new family of transverse anisotropic invariants by designing a strain energy function (SEF) for incompressible fiber-reinforced materials. In order to validate the usability and creativeness of the proposed model, two different fiber-reinforced rubber materials under uniaxial and shear testing are considered. For each kind of material, numerical simulations based on the proposed model are consistent with experimental results and provide information about the effect of the new family of invariants in the construction of the SEF.
From fracture to damage mechanics: a behavior law for microcracked composites using the concept of crack opening mode
2010
International audience; Many studies have been carried out in order to build a coherent macroscopic behavior law for a composite containing microcracks. All of them are only partially coherent and none of them is complete. This study proposes a hyperelastic behavior law for a microcracked composite, respecting all the conditions associated with the damage activation/deactivation, stress/strain relation continuity, induced anisotropy and the Clausius–Duhem inequality. This approach is based on the definition of the Crack Opening Mode for Damage Mechanics as it exists in Fracture Mechanics.
A theoretical approach to pneumatic muscle mechanics
2013
The mechanical response of pneumatic artificial muscles is analyzed assuming the inextensibility of the sheathing braids and taking into account the stress field inside the rubber bladder, which is regarded as a Mooney-Rivlin hyperelastic material. The end effects are simulated by heuristically profiling the meridian section. After estimating the constitutive parameters by traction tests on rubber specimens, the theoretical results are compared with experiments and a satisfactory accordance may be detected.
Can biomechanical analysis shed some light on aneurysmal pathophysiology? Preliminary study on ex vivo cerebral arterial walls
2019
Abstract Background The pathophysiology of cerebral aneurysm is complex and poorly understood, and it can have the most catastrophic clinical presentation. Flow dynamics is a key player in the initiation and progression of aneurysm. Better understanding the interaction between hemodynamic loading and biomechanical wall responses can help to add the missing piece on aneurysmal pathophysiology. In this laboratory study we aimed to analyze the effect of the application of a mechanical force to cerebral arterial walls. Methods Displacement control tests were performed on five porcine cerebral arteries. The test machine was the T150 Nanotensile. The stiffness variation with the increment of the …
Historischer Überblick zur mathematischen Theorie von Unstetigkeitswellen seit Riemann und Christoffel
1981
We give a brief historical account of the development of the mathematical theory of propagation of discontinuities in gases, fluids or elastic materials. The theory was initiated by Riemann who investigated the propagation of shocks in one-dimensional isentropic gas flow. Riemann’s results were used by Christoffel to treat, more generally, the propagation of (first order) discontinuity surfaces in three-dimensional flows of perfect fluids. Subsequently Christoffel applied his general theory to first order waves in certain elastic materials. Independently of Riemann and Christoffel significant contributions were made by Hugoniot. The theory was completed in Hadamard’s celebrated monograph [3…
A constructive approach of invariants of behavior laws with respect to an infinite symmetry group – Application to a biological anisotropic hyperelas…
2014
Abstract In this paper, six new invariants associated with an anisotropic material made of one fiber family are calculated by presenting a systematic constructive and original approach. This approach is based on the development of mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Definition of the generalized Reynolds Operator. • Calculation of an integrity basis for invariant polynomials. • Comparison between the new (constructed) invariants and the classical ones.
A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families
2013
Abstract In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Analytical calculation of a set of generators using the Noether’s theorem. • Analytical calculation of an integrity basis. • Comparison between the proposed invariants and the classical ones.
Investigation on the indentation behavior of sandwich beams using crushable and hyperelastic foam cores
2010
In this work the indentation behaviour of sandwich beams is studied adopting the classical approach representing the core material as a Winkler-type foundation. It is shown how most of the proposed theories can be derived from a general fourth order linear differential equation expressing the equilibrium of the indented beam skin. Different assumptions on the supporting boundary constraints and materials constitutive behaviour, lead to simplifications of the general equation and to the prediction of different indentation features. An extension of the Segment-Wise approach recently proposed in the literature is in particular presented with potential to better simulate foam cores with markedl…