Finite Deformation and Nonlinear Elastic Behavior of Flexible Composites

1988 ◽  
Vol 55 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Shen-Yi Luo ◽  
Tsu-Wei Chou
Keyword(s):  
Present Theory ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Flexible Composites ◽  
Elastomeric Matrix ◽  
Eulerian Description ◽  
Stress Strain Relation ◽  
Nonlinear Stress ◽  
Material Nonlinear ◽  
Nonlinear Elastic

The flexible composites discussed in this paper are composed of continuous fibers in an elastomeric matrix. The usable range of deformation of these composites is much larger than that of conventional rigid composites. Due to the material as well as geometric factors, the stress-strain relations for these composites are generally nonlinear under finite deformations. A constitutive model has been developed based upon the Eulerian description. The material nonlinear stress-strain relation is derived by using the stress energy density referring to the deformed volume. The stretching-shear coupling and the effects of the in-plane reorientation of fibers are also considered in the theoretical analysis. Comparisons are made between predictions of the present theory and experimental data for tirecord/rubber and Kevlar/silicone-elastomer flexible composite laminae; very good correlations have been found.

Nonlinear Elastic Behavior of Unidirectional Composites With Fiber Waviness Under Compressive Loading

1996 ◽  
Vol 118 (4) ◽  
pp. 561-570 ◽  
Author(s):  
H. M. Hsiao ◽  
I. M. Daniel
Keyword(s):  
Constitutive Relations ◽  
Compressive Loading ◽  
Nonlinear Material ◽  
Elastic Behavior ◽  
Compression Tests ◽  
Fiber Waviness ◽  
Unidirectional Composites ◽  
Nonlinear Stress ◽  
Material Nonlinear ◽  
Nonlinear Elastic

Nonlinear elastic behavior of unidirectional composites with fiber waviness under compressive loading was investigated theoretically and experimentally. Unidirectional carbon/epoxy composites with uniform, graded, and localized fiber waviness were studied. Complementary strain energy was used to derive the material nonlinear stress-strain relations. Nonlinear material properties obtained from shear and longitudinal and transverse compression tests were incorporated into the analysis. Compression tests of specimens with known fiber waviness were conducted to verify the constitutive relations. Experimental results were in good agreement with predictions based on the constitutive model.

scholarly journals Black rubber and the non-linear elastic response of scale invariant solids

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Matteo Baggioli ◽  
Víctor Cáncer Castillo ◽  
Oriol Pujolàs
Keyword(s):  
Strain Curve ◽  
Effective Field ◽  
Elastic Response ◽  
Elastic Behaviour ◽  
Scale Invariant ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Hyper Elastic ◽  
Simple Class ◽  
Nonlinear Elastic

Abstract We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

Parametric Variational Principle for Bi-Modulus Materials and Its Application to Nacreous Bio-Composites

2016 ◽  
Vol 08 (06) ◽  
pp. 1650082 ◽  
Author(s):  
Liang Zhang ◽  
Huiting Zhang ◽  
Jian Wu ◽  
Bo Yan ◽  
Mengkai Lu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Variational Principle ◽  
Principal Stress ◽  
Stress Strain ◽  
Element Analysis ◽  
Parametric Variational Principle ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Nonlinear Stress

Bi-modulus materials have different moduli in tension and compression and the stress–strain relation depends on principal stress that is unknown before displacement is determined. Establishment of variational principle is important for mechanical analysis of materials. First, parametric variational principle (PVP) is proposed for static analysis of bi-modulus materials and structures. A parametric variable indicating state of principal stress is included in the potential energy formulation and the nonlinear stress–strain relation is evolved into a linear complementarity constraint. Convergence of finite element analysis is thus improved. Then the proposed variational principle is extended to a dynamic problem and the dynamic equation can be derived based on Hamilton’s principle. Finite element analysis of nacreous bio-composites is performed, in which a unilateral contact behavior between two hard mineral bricks is modeled using the bi-modulus stress–strain relation. Effective modulus of composites can be determined numerically and stress mechanism of “tension–shear chain” in nacre is revealed. A delayed effect on stress propagation is found around the “gaps” between mineral bricks, when a tension force is loaded to nacreous bio-composites dynamically.

Effects of Nonlinear Stress-Strain Rate Relation on Deformation and Fracture of Materials in Creep Range

1979 ◽  
Vol 101 (4) ◽  
pp. 369-373 ◽  
Author(s):  
Ryuichi Ohtani ◽  
Shuji Taira
Keyword(s):  
High Temperature ◽  
Industrial Development ◽  
Practical Investigations ◽  
High Temperature Strength ◽  
Stress Strain ◽  
Stress Strain Relation ◽  
Deformation And Fracture ◽  
Nonlinear Stress ◽  
Fracture Of Materials ◽  
Rate Relation

Fundamental and practical investigations on high-temperature strength of materials have made significant contributions to industrial development for the last twenty-five years. However, an additional effort is required to make clear the effects of dominant factors on the deformation and fracture of materials, since the knowledge obtained to date are not enough to explain the overall phenomena of high temperature strength. In this paper the importance of the effects of nonlinearlity and time-dependence of stress-strain relation on the well-known creep behaviors are reviewed and reexamined on the basis of our laboratory study conducted over the last twenty years.

Inelastic Strain Accumulation in Cortical Bone During Rapid Transient Tensile Loading

1999 ◽  
Vol 121 (6) ◽  
pp. 616-621 ◽  
Author(s):  
M. T. Fondrk ◽  
E. H. Bahniuk ◽  
D. T. Davy
Keyword(s):  
Cortical Bone ◽  
Axial Strain ◽  
Human Bone ◽  
Elastic Behavior ◽  
Transverse Strain ◽  
Bovine Bone ◽  
Stress Strain ◽  
Nonlinear Strain ◽  
Strain Behavior ◽  
Nonlinear Stress

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of ±420 MPa/s. Loads were reversed at pre-selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.

Anisotropic Mechanics of Cellular Substrate Under Finite Deformation

2018 ◽  
Vol 85 (7) ◽  
Author(s):  
Feng Zhu ◽  
Hanbin Xiao ◽  
Yeguang Xue ◽  
Xue Feng ◽  
Yonggang Huang ◽  
...  
Keyword(s):  
Cell Walls ◽  
Constitutive Models ◽  
Applied Strain ◽  
Stretchable Electronics ◽  
Stress Strain ◽  
Element Analysis ◽  
Natural Motion ◽  
Nonlinear Stress ◽  
Comparison Of The Results ◽  
Nonlinear Elastic

The use of cellular substrates for stretchable electronics minimizes not only disruptions to the natural diffusive or convective flow of bio-fluids, but also the constraints on the natural motion of the skin. The existing analytic constitutive models for the equivalent medium of the cellular substrate under finite stretching are only applicable for stretching along the cell walls. This paper aims at establishing an analytic constitutive model for the anisotropic equivalent medium of the cellular substrate under finite stretching along any direction. The model gives the nonlinear stress–strain curves of the cellular substrate that agree very well with the finite element analysis (FEA) without any parameter fitting. For the applied strain <10%, the stress–strain curves are the same for different directions of stretching, but their differences become significant as the applied strain increases, displaying the deformation-induced anisotropy. Comparison of the results for linear and nonlinear elastic cell walls clearly suggests that the nonlinear stress–strain curves of the cellular substrate mainly result from the finite rotation of cell walls.

Effect of Fiber Waviness on the Nonlinear Elastic Behavior of Flexible Composites

1988 ◽  
Vol 22 (11) ◽  
pp. 1004-1025 ◽  
Author(s):  
Chen-Ming Kuo ◽  
Kiyohisa Takahashi ◽  
Tsu-Wei Chou
Keyword(s):  
Elastic Behavior ◽  
Fiber Waviness ◽  
Flexible Composites ◽  
Nonlinear Elastic
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