scholarly journals Anisotropic linear elastic parameter estimation using error in the constitutive equation functional

2016 ◽  
Vol 472 (2192) ◽  
pp. 20160213 ◽  
Author(s):  
Shyamal Guchhait ◽  
Biswanath Banerjee
Keyword(s):  
Constitutive Equation ◽  
Elastic Parameter ◽  
Linear Elastic ◽  
Explicit Material ◽  
New Strategy ◽  
Minimization Procedure ◽  
Parameter Identification Problems ◽  
Anisotropic Elastic ◽  
Necessary Constraints ◽  
Constitutive Tensor

A modified error in the constitutive equation-based approach for identification of heterogeneous and linear anisotropic elastic parameters involving static measurements is proposed and explored. Following an alternating minimization procedure associated with the underlying optimization problem, the new strategy results in an explicit material parameter update formula for general anisotropic material. This immediately allows us to derive the necessary constraints on measured data and thus restrictions on physical experimentation to achieve the desired reconstruction. We consider a few common materials to derive such conditions. Then, we exploit the invariant relationships of the anisotropic constitutive tensor to propose an identification procedure for space-dependent material orientations. Finally, we assess the numerical efficacy of the developed tools against a few parameter identification problems of engineering interest.

Small Scale Contact Conditions for the Linear-Elastic Interface Crack

1988 ◽  
Vol 55 (4) ◽  
pp. 814-817 ◽  
Author(s):  
Peter M. Anderson
Keyword(s):  
Interface Crack ◽  
Growth Parameter ◽  
Small Scale ◽  
Elastic Materials ◽  
Small Scale Yielding ◽  
Contact Conditions ◽  
Linear Elastic ◽  
Elastic Interface ◽  
Scale Yielding ◽  
Anisotropic Elastic

Conditions are discussed for which the contact zone at the tip of a two-dimensional interface crack between anisotropic elastic materials is small. For such “small scale contact” conditions combined with small scale yielding conditions, a stress concentration vector uniquely characterizes the near tip field, and may be used as a crack growth parameter. Representative calculations for an interface crack on a representative Cu grain boundary show small contact conditions to prevail, except possibly under large shearing loads.

Assessment of 3D Linear Elastic Masonry-Like Vaulted Structures

2019 ◽  
Vol 817 ◽  
pp. 50-56
Author(s):  
Deborah Briccola ◽  
Matteo Bruggi ◽  
Alberto Taliercio
Keyword(s):  
Material Model ◽  
Equivalent Material ◽  
Technical Literature ◽  
Linear Elastic ◽  
Novel Approach ◽  
Out Of Plane ◽  
Minimization Procedure ◽  
Live Loads ◽  
Historical Masonry ◽  
No Tension Material

A novel approach is adopted to assess the static behavior of vaulted structures, such as cantilevered masonry stairs, assuming a linear elastic no-tension material model. Masonry is substituted by an equivalent orthotropic material whose elastic properties vary locally and with a negligible stiffness where tensile strain occurs. In order to recover a tension-free state of stress, an energy-based minimization procedure is carried out to establish the distribution and the orientation of the equivalent material for a given compatible load. The capability of the approach in defining purely compressive stress solutions in masonry walls under dead load and both in-plane and out-of-plane live loads has already been assessed. A meaningful application to a cantilevered masonry stair is here presented; the results are in good agreement with those available in the technical literature on historical masonry constructions.

scholarly journals Effect of Process Orientation on the Mechanical Behavior and Piezoelectricity of Electroactive Paper

Materials ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 204
Author(s):  
Sean Yoon ◽  
Jung Woong Kim ◽  
Hyun Chan Kim ◽  
Jaehwan Kim
Keyword(s):  
Mechanical Behavior ◽  
Process Orientation ◽  
Linear Elastic ◽  
Strong Shear ◽  
Performance Deterioration ◽  
Alignment Angle ◽  
Anisotropic Elastic ◽  
Stretching Ratio ◽  
Orientation Dependency ◽  
Piezoelectric Charge

This paper reports the effect of process orientation on the mechanical behavior and piezoelectricity of electroactive paper (EAPap) made from natural cotton pulp. EAPap is fabricated by a casting and wet drawing of cellulose film after dissolving cotton with LiCl and DMAc solvent. During the fabrication, permanent wrinkles, a possible factor for performance deterioration, were found in the films. Finite element method was introduced to identify the formation mechanism behind the wrinkles. The simulation results show that the wrinkles were caused by buckling and are inevitable under any conditions. The tensile and piezoelectric tests show that the orientation dependency of the stretched EAPap gives the anisotropic characteristics on both mechanical and piezoelectric properties. In this research, the anisotropic elastic moduli and Poisson’s ratios are reported. The piezoelectric charge constant of EAPap in the linear elastic is calculated. The piezoelectric charge constants of EAPap are associated with the alignment angle in the order of 45° > 0° > 90° due to the strong shear effect. The higher stretching ratio gives the higher piezoelectricity due to the alignment of the molecular chains and the microstructure in EAPap. The highest piezoelectric charge constant is found to be 12 pC/N at a stretching ratio of 1.6 and aligning angle of 45°.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

scholarly journals Study on Quasi-Static Uniaxial Compression Properties and Constitutive Equation of Spherical Cell Porous Aluminum-Polyurethane Composites

Materials ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1261 ◽  
Author(s):  
Haiying Bao ◽  
Aiqun Li
Keyword(s):  
Constitutive Equation ◽  
Relative Density ◽  
Uniaxial Compression ◽  
Spherical Cell ◽  
Plateau Stress ◽  
Porous Aluminum ◽  
Linear Elastic ◽  
Compression Properties ◽  
Three Stages ◽  
Polyurethane Composites

Quasi-static uniaxial compression properties and the constitutive equation of spherical cell porous aluminum-polyurethane composites (SCPA-PU composites) were investigated in this paper. The effects of relative density on the densification strain, plateau stress and energy absorption properties of the SCPA-PU composites were analyzed. It is found that the stress-strain curves of SCPA-PU composites consist of three stages: The linear elastic part, longer plastic plateau segment and densification region. The results also demonstrate that both the plateau stress and the densification strain energy of the SCPA-PU composites can be improved by increasing the relative density of the spherical cell porous aluminum (SCPA), while the densification strain of the SCPA-PU composites shows little dependence on the relative density of the SCPA. Furthermore, the applicability of three representative phenomenological models to the constitutive equations of SCPA-PU composites are verified and compared based on the experimental results. The error analysis result indicates that the Avalle model is the best model to characterize the uniaxial compression constitutive equation of SCPA-PU composites.

Microstructural Constitutive Equation for Sprain Analysis

2008 ◽  
Author(s):  
Zheying Guo ◽  
Raffaella De Vita
Keyword(s):  
Experimental Data ◽  
Probability Density Function ◽  
Constitutive Equation ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Damage Evolution ◽  
Linear Elastic ◽  
Proposed Model ◽  
Collagenous Tissues

A new constitutive equation is presented to describe the damage evolution process in parallel fibered collagenous tissues such as ligaments and tendons. The model is formulated by accounting for the fibrous structure of the tissues. The tissue’s stress is defined as the average of the collagen fiber’s stresses. The fibers are assumed to be undulated and straighten out at different stretches that are defined by a Weibull probability density function. After becoming straight each fiber is assumed to be linear elastic. Its waviness is defined by a Weibull distribution. Tissue’s damage is assumed to occur at the fiber level and is defined as a reduction in the fiber’s stiffness. The proposed model is validated by using experimental data published in the biomechanics literature by Provenzano et al. [1].

A 3D Masonry-Like Model with Bounded Shear Stress

2017 ◽  
Vol 747 ◽  
pp. 20-27 ◽  
Author(s):  
Massimiliano Lucchesi ◽  
Barbara Pintucchi ◽  
Nicola Zani
Keyword(s):  
Shear Stress ◽  
Constitutive Equation ◽  
Convex Subset ◽  
Numerical Results ◽  
Stress Range ◽  
Symmetric Tensors ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Non Linear

This paper deals with non linear elastic materials for which not all the stresses are admis-sible but only those which belong to the stress range, i.e. a closed and convex subset of the spaceof all symmetric tensors. The constitutive equation that has been formulated and explicitly solved issufficiently general to include, besides the so-called masonry-like materials, many others whose stressrange is obtained experimentally or is theoretically defined. The model, implemented into the finiteelement code MADY, has been used to analyze a masonry panel under a bi-directional monotonicallyincremental load and the obtained numerical results have been discussed.

Wave-front singularities for two-dimensional anisotropic elastic waves

1972 ◽  
Vol 72 (1) ◽  
pp. 105-116 ◽  
Author(s):  
Robert G. Payton
Keyword(s):  
Point Source ◽  
Wave Front ◽  
Elastic Waves ◽  
Elastic Solid ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Anisotropic Elastic

AbstractWave-front singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d–½ where d measures distance away from the front. However, in certain exceptional cases singularities of order d–-n where n = ¼, ⅔, ¾, may be encountered.

1303 Anisotropic Elastic Constitutive Equation of Drawn Polymers

2005 ◽  
Vol 2005.18 (0) ◽  
pp. 499-500
Author(s):  
Yukio Sanomura ◽  
Kunio Hayakawa ◽  
Mamoru Mizuno
Keyword(s):  
Constitutive Equation ◽  
Anisotropic Elastic
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