The Experts below are selected from a list of 4155 Experts worldwide ranked by ideXlab platform
A. Rezgui - One of the best experts on this subject based on the ideXlab platform.
-
Directional model for isotropic hyperelastic rubber-like materials
Mechanics of Materials, 2004Co-Authors: Julie Diani, Mathias Brieu, J.m. Vacherand, A. RezguiAbstract:A material direction-dependent constitutive model has been formulated for large deformations for isotropic and anisotropic rubber-like materials. Although such materials are usually isotropic, anisotropic behavior has been observed in calendered plates of filled rubbers. Strain energy density function characterizing rubber-like materials is usually dependent on Principal Stretch ratios and thus is unable to account for anisotropy, whereas the proposed strain energy density depends on material directions and accounts for anisotropy. The material directions have simply been chosen using regular solid geometry. The strain energy density is given as the sum, over all material directions, of elementary directional strain energy densities. Then the elementary strain energy form is phenomenologically determined to account for the state of strain dependence of the material response. The model response is compared to uniaxial tension experimental data for anisotropic hyperelastic rubber-like materials and to uniaxial and biaxial tension for isotropic rubber-like materials.
-
Directional model for anisotropic hyperelastic rubber-like materials
Journal of Physics IV, 2003Co-Authors: Julie Diani, Mathias Brieu, J.m. Vacherand, A. RezguiAbstract:A material direction-dependent constitutive model has been formulated for large deformation of anisotropic rubber-like materials. Anisotropic behavior has been observed in calendered plates of filled elastomers. Strain energy density functions characterizing rubber-like material behavior are usually dependent on the Principal Stretch ratios and are unable to take into account anisotropy. The proposed strain energy density depends on material directions and accounts for anisotropy. Model material directions have simply been chosen using existing macromolecular model chains geometry. The material strain energy density is given as the sum, over all material directions, of the elementary directional strain energy density. This elementary strain energy is determined by analogy with chain entropy of macromolecular models using the Langevin statistics. To evaluate the effectiveness of the proposed model, it is compared to uniaxial tension experimental data of anisotropic hyperelastic rubber-like materials.
J G Loughran - One of the best experts on this subject based on the ideXlab platform.
-
numerical aspects associated with the implementation of a finite strain elasto viscoelastic viscoplastic constitutive theory in Principal Stretches
International Journal for Numerical Methods in Engineering, 2010Co-Authors: David W Holmes, J G LoughranAbstract:This paper treats the numerical implementation of a finite strain, elasto-viscoelastic-viscoplastic constitutive model for semi-crystalline polymers, written in Principal Stretches. A parallel configuration of the three model elements is used that enables the decoupled algorithmic treatment of each response within a stress update numerical scheme. The numerical aspects associated with the use of Principal Stretch constitutive expressions in a tensor space numerical environment are initially developed for the general cases of any elastic or inelastic constitutive element. Included is the formulation of the closed-form, consistent tangential modulus tensor. The Principal space algorithmic treatments of the elastic, viscoelastic and viscoplastic elements are then used as specific examples. Of particular importance is the development of a Principal space, closest point projection return mapping algorithm for viscoplasticity including isotropic strain hardening. Preliminary numerical examples are presented to illustrate the versatility of the model.
-
Numerical aspects associated with the implementation of a finite strain, elasto‐viscoelastic–viscoplastic constitutive theory in Principal Stretches
International Journal for Numerical Methods in Engineering, 2010Co-Authors: David W Holmes, J G LoughranAbstract:This paper treats the numerical implementation of a finite strain, elasto-viscoelastic-viscoplastic constitutive model for semi-crystalline polymers, written in Principal Stretches. A parallel configuration of the three model elements is used that enables the decoupled algorithmic treatment of each response within a stress update numerical scheme. The numerical aspects associated with the use of Principal Stretch constitutive expressions in a tensor space numerical environment are initially developed for the general cases of any elastic or inelastic constitutive element. Included is the formulation of the closed-form, consistent tangential modulus tensor. The Principal space algorithmic treatments of the elastic, viscoelastic and viscoplastic elements are then used as specific examples. Of particular importance is the development of a Principal space, closest point projection return mapping algorithm for viscoplasticity including isotropic strain hardening. Preliminary numerical examples are presented to illustrate the versatility of the model.
Julie Diani - One of the best experts on this subject based on the ideXlab platform.
-
Directional model for isotropic hyperelastic rubber-like materials
Mechanics of Materials, 2004Co-Authors: Julie Diani, Mathias Brieu, J.m. Vacherand, A. RezguiAbstract:A material direction-dependent constitutive model has been formulated for large deformations for isotropic and anisotropic rubber-like materials. Although such materials are usually isotropic, anisotropic behavior has been observed in calendered plates of filled rubbers. Strain energy density function characterizing rubber-like materials is usually dependent on Principal Stretch ratios and thus is unable to account for anisotropy, whereas the proposed strain energy density depends on material directions and accounts for anisotropy. The material directions have simply been chosen using regular solid geometry. The strain energy density is given as the sum, over all material directions, of elementary directional strain energy densities. Then the elementary strain energy form is phenomenologically determined to account for the state of strain dependence of the material response. The model response is compared to uniaxial tension experimental data for anisotropic hyperelastic rubber-like materials and to uniaxial and biaxial tension for isotropic rubber-like materials.
-
Directional model for anisotropic hyperelastic rubber-like materials
Journal of Physics IV, 2003Co-Authors: Julie Diani, Mathias Brieu, J.m. Vacherand, A. RezguiAbstract:A material direction-dependent constitutive model has been formulated for large deformation of anisotropic rubber-like materials. Anisotropic behavior has been observed in calendered plates of filled elastomers. Strain energy density functions characterizing rubber-like material behavior are usually dependent on the Principal Stretch ratios and are unable to take into account anisotropy. The proposed strain energy density depends on material directions and accounts for anisotropy. Model material directions have simply been chosen using existing macromolecular model chains geometry. The material strain energy density is given as the sum, over all material directions, of the elementary directional strain energy density. This elementary strain energy is determined by analogy with chain entropy of macromolecular models using the Langevin statistics. To evaluate the effectiveness of the proposed model, it is compared to uniaxial tension experimental data of anisotropic hyperelastic rubber-like materials.
David W Holmes - One of the best experts on this subject based on the ideXlab platform.
-
numerical aspects associated with the implementation of a finite strain elasto viscoelastic viscoplastic constitutive theory in Principal Stretches
International Journal for Numerical Methods in Engineering, 2010Co-Authors: David W Holmes, J G LoughranAbstract:This paper treats the numerical implementation of a finite strain, elasto-viscoelastic-viscoplastic constitutive model for semi-crystalline polymers, written in Principal Stretches. A parallel configuration of the three model elements is used that enables the decoupled algorithmic treatment of each response within a stress update numerical scheme. The numerical aspects associated with the use of Principal Stretch constitutive expressions in a tensor space numerical environment are initially developed for the general cases of any elastic or inelastic constitutive element. Included is the formulation of the closed-form, consistent tangential modulus tensor. The Principal space algorithmic treatments of the elastic, viscoelastic and viscoplastic elements are then used as specific examples. Of particular importance is the development of a Principal space, closest point projection return mapping algorithm for viscoplasticity including isotropic strain hardening. Preliminary numerical examples are presented to illustrate the versatility of the model.
-
Numerical aspects associated with the implementation of a finite strain, elasto‐viscoelastic–viscoplastic constitutive theory in Principal Stretches
International Journal for Numerical Methods in Engineering, 2010Co-Authors: David W Holmes, J G LoughranAbstract:This paper treats the numerical implementation of a finite strain, elasto-viscoelastic-viscoplastic constitutive model for semi-crystalline polymers, written in Principal Stretches. A parallel configuration of the three model elements is used that enables the decoupled algorithmic treatment of each response within a stress update numerical scheme. The numerical aspects associated with the use of Principal Stretch constitutive expressions in a tensor space numerical environment are initially developed for the general cases of any elastic or inelastic constitutive element. Included is the formulation of the closed-form, consistent tangential modulus tensor. The Principal space algorithmic treatments of the elastic, viscoelastic and viscoplastic elements are then used as specific examples. Of particular importance is the development of a Principal space, closest point projection return mapping algorithm for viscoplasticity including isotropic strain hardening. Preliminary numerical examples are presented to illustrate the versatility of the model.
Ryszard Staroszczyk - One of the best experts on this subject based on the ideXlab platform.
-
Stress and strain-rate formulations for fabric evolution in polar ice
Continuum Mechanics and Thermodynamics, 2003Co-Authors: Leslie Morland, Ryszard StaroszczykAbstract:Re-orientation of individual crystal glide planes, as isotropic surface ice is deformed during its passage to depth in an ice sheet, creates a fabric and associated anisotropy. We re-examine an orthotropic viscous law which was developed to reflect the induced anisotropy arising from the mean rotation of crystal axes during deformation. This expresses the deviatoric stress, the stress formulation, in terms of the strain-rate, strain, and three structure tensors based on the Principal Stretch axes, and involves two fabric response coefficient functions which determine the strength of the anisotropy. A validity condition implicitly relates the two response functions, so the model law has only one independent fabric response function. A modified formulation is now presented in which the two fabric response coefficients are expressed as functions of different invariant arguments, and the validity condition becomes an explicit algebraic relation between the two functions. The response can therefore be described explicitly in terms of a single fabric response function. An analogous orthotropic viscous law for the strain-rate, the strain-rate formulation, akin to the conventional “flow law” for isotropic ice, expressed in terms of the deviatoric stresss, strain and the three structure tensors, is also constructed. Correlations with complete (idealised) uni-axial compression and shearing responses are made for the stress formulation, to determine the fabric response function which would yield these responses. Ice core samples taken from depth in an ice sheet reveal strong fabrics, shown by significant alignment of initially randomly distributed c-axes of individual crystals, and consequent substantial differences in shear viscosities in different planes. The macroscopic viscous law for the shear stress proposed by Morland and Staroszczyk [1] was motivated by a simple picture of lattice rotation by basal slip in which the angle between individual crystal glide planes, material planes, and planes normal to Principal axes of compression, decreases, and the angle between individual crystal glide planes and planes normal to Principal axes of extension, increase. These three planes, with normals the Principal Stretch axes, are described as the Principal Stretch planes. The instantaneous viscous response at each stage of the deformation has reflexional symmetry in these planes; that is, the instantaneous viscous response is orthotropic with respect to the current Principal Stretch planes. It is further assumed that the directional strengths of the response depend only on the current deformation, which is an assumption that the generated fabric and subsequent response are independent of the deformation path, which is a questionable restriction. The orthotropic viscous law is then a frame indifferent relation between deviatoric stress, strainrate, deformation, and the three structure tensors defined by the outer products of the three orthogonal unit vectors along the Principal Stretch axes. The simple Morland and Staroszczyk [1] model, a stress formulation in which the deviatoric stress is expressed in terms of the other tensors, involved one set of tensor generators with one coefficient, described as a fabric response function. Subsequently, a set of equalities and inequalities on the instantaneous directional viscosities derived from the rotation concepts by Staroszczyk and Morland
-
Strain-rate formulation of ice fabric evolution
Annals of Glaciology, 2003Co-Authors: Leslie Morland, Ryszard StaroszczykAbstract:AbstractReorientation of individual crystal-glide planes as isotropic surface ice is deformed during its passage to depth in an ice sheet, lattice rotation, creates a fabric and associated anisotropy. A simple macroscopic description is that these material glide planes are rotated towards planes normal to an axis of compression, and away from planes normal to an axis of extension, inducing an instantaneous orthotropic viscous response with reflexional symmetries in the planes orthogonal to the current Principal Stretch axes. An orthotropic viscous law is presented for the strain rate expressed in terms of the deviatoric stress, the deformation, and three structure tensors based on the Principal Stretch axes. This anisotropic relation is expressed in terms of a single fabric response function in addition to the isotropic ice viscosity. The predicted responses in uniaxial compression and simple shear are determined. While the uniaxial response yields an explicit relation between the axial strain rate and stress, it is found that the shear response is governed by three, complicated, coupled relations between the shear strain rate and three deviatoricstress components. The new result derived here is the solution of this system: an explicit relation between the shear strain rate and shear stress. Correlation of these relations with idealized uniaxial and shear responses is then used to determine the required fabric function in the model law.
-
Orthotropic viscous response of polar ice
Journal of Engineering Mathematics, 2000Co-Authors: Ryszard Staroszczyk, Leslie MorlandAbstract:Re-orientation of individual crystal glide planes as isotropic surface ice is deformed during its passage to depth in an ice sheet creates a fabric and associated anisotropy. A simple macroscopic description is that these material glide planes are rotated towards planes normal to an axis of compression, and away from planes normal to an axis of extension, inducing an instantaneous orthotropic viscous response with reflexional symmetries in the planes orthogonal to the current Principal Stretch axes. An associated orthotropic viscous law expresses the stress in terms of the strain-rate, strain, and three structure tensors based on the Principal Stretch axes. The fabric induced during differential Stretchings along fixed Principal axes, and the subsequent instantaneous viscous shear response in different planes due to the frozen fabric when the axial stress and strain-rate are removed, define a set of instantaneous directional viscosities in terms of the frozen Principal Stretches and the material response coefficients. Various inequalities and equalities between these viscosities are derived from the original rotation concepts, which, together with observed enhancement factors at large Stretch and shearing, impose restrictions on the permitted response coefficients. It is shown how a simple viscous law can meet all these requirements, and such a law is illustrated for continued axial Stretchings and shearing.
-
Viscous Response of Polar Ice with Evolving Fabric
Continuum Mechanics and Thermodynamics, 1998Co-Authors: Leslie Morland, Ryszard StaroszczykAbstract:Re-orientation of individual crystal glide planes as isotropic surface ice is deformed during its passage to depth in an ice sheet creates a fabric and associated anisotropy. A simple macroscopic description is that these material glide planes are rotated towards planes normal to an axis of compression, and away from planes normal to an axis of extension, inducing an instantaneous orthotropic viscous response with reflexional symmetries in the planes orthogonal to the current Principal Stretch axes. An associated orthotropic viscous law expresses the stress in terms of the strain-rate, deformation, and three structure tensors based on the Principal Stretch axes. General frame indifferent forms are analysed to determine the fabric induced during differential Stretchings along fixed Principal axes. Then, freezing the fabric by removal of the stress, and hence strain-rate, the instantaneous simple shear responses in different planes are determined and compared. The corresponding instantaneous viscosities are expressed in terms of the response coefficients of the constitutive model. A simple model is adopted to illustrate the evolution of the viscosities during axial Stretchings and shearing.