Recently, Arumugam et al. (2023) developed a constitutive relation for the response of isotropic inhomogeneous compressible elastic solids
in order to describe the response of the trabecular bone. Since porous solids such as bones, cement concrete, rocks, metallic alloys, etc., are
anisotropic, in this short note we develop a constitutive relation for such bodies that exhibit transverse isotropy and also having two preferred
directions of symmetry. Another characteristic of bones is that they exhibit different response characteristics in tension and compression, and
hence any constitutive relation that is developed has to be capable of describing this. Also, the material moduli depend on both the density and
the mean value of the stress (mechanical pressure), as is to be expected in a porous solid. In the constitutive relation that is developed in this
paper, though the stress and the linearized strain appear linearly in the constitutive relation, the relationship is nonlinear. We also derive the
response of such solids when undergoing uniaxial extension and compression, simple shear and torsion.
more »
« less
This content will become publicly available on April 1, 2025
Residual stress and material symmetry
There seems to be a basic misconception in several recent papers concerning the material
symmetry of bodies in configurations that are pre-stressed. In this short paper we point to
the source of the error and show that the material symmetry that is possible depends on the
nature of the pre-stress. We also extend the results for material symmetry which have been well known
within the context of simple elastic solids to the general class of simple materials. This
generalization has relevance to the material symmetry of biological solids that are viscoelastic.
more »
« less
- Award ID(s):
- 2307562
- NSF-PAR ID:
- 10529059
- Publisher / Repository:
- IJES_RajWineman_24
- Date Published:
- Journal Name:
- International Journal of Engineering Science
- Volume:
- 197
- Issue:
- C
- ISSN:
- 0020-7225
- Page Range / eLocation ID:
- 104013
- Subject(s) / Keyword(s):
- Material symmetry Pre-stress Residual stress Elastic materials Viscoelastic materials
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
For a given class of materials, universal displacements are those displacements that can be maintained for any member of the class by applying only boundary tractions. In this paper, we study universal displacements in compressible anisotropic linear elastic solids reinforced by a family of inextensible fibers. For each symmetry class and for a uniform distribution of straight fibers respecting the corresponding symmetry, we characterize the respective universal displacements. A goal of this paper is to investigate how an internal constraint affects the set of universal displacements. We have observed that other than the triclinic and cubic solids in the other five classes (a fiber-reinforced solid with straight fibers cannot be isotropic), the presence of inextensible fibers enlarges the set of universal displacements.
-
Abstract For a given class of materials, universal deformations are those that can be maintained in the absence of body forces by applying only boundary tractions. Universal deformations play a crucial role in nonlinear elasticity. To date, their classification has been accomplished for homogeneous isotropic solids following Ericksen’s seminal work, and homogeneous anisotropic solids and inhomogeneous isotropic solids in our recent works. In this paper we study universal deformations for inhomogeneous anisotropic solids defined as materials whose energy function depends on position. We consider both compressible and incompressible transversely isotropic, orthotropic, and monoclinic solids. We show that the universality constraints —the constraints that are dictated by the equilibrium equations and the arbitrariness of the energy function—for inhomogeneous anisotropic solids include those of inhomogeneous isotropic and homogeneous anisotropic solids. For compressible solids, universal deformations are homogeneous and the material preferred directions are uniform. For each of the three classes of anisotropic solids we find the corresponding universal inhomogeneities —those inhomogeneities that are consistent with the universality constraints. For incompressible anisotropic solids we find the universal inhomogeneities for each of the six known families of universal deformations. This work provides a systematic approach to study analytically functionally-graded fiber-reinforced elastic solids.more » « less
-
Designing materials to have three unique but predictable thermal expansion axes represents a major challenge. Inorganic materials and hybrid frameworks tend to crystallize in high-symmetry space groups, which necessarily limits this by affording isotropic behavior. On the other hand, molecular organic materials tend to crystallize in lower-symmetry space groups, offering significant opportunity to achieve anisotropic properties. The challenge arises in self-assembling the organic components into a predictable arrangement to afford predictable thermal expansion properties. Here, we demonstrate a design strategy for engineering organic solid-state materials that exhibit anisotropic thermomechanical behaviors. Presented are a series of multicomponent solids wherein one component features a BODPIY core strategically decorated with orthogonal hydrogen- and halogen-bond donor groups. A series of size-matched halogen-bond acceptors are used as the second component in each solid. By matching the molecular dimensions with the interaction strength, we obtained good control over the anisotropic thermal expansion of the molecular materials. Moreover, using shape-size mimicry and propensity for molecular motion, a rare ternary molecular system that is isostructural to the two binary solids was successfully achieved. The diiodo-functionalized BODIPY core in this study has been previously used in photocatalysts, and halogen bonding was hypothesized as a driving force; here, we provide corroborating solution and solid-state evidence of intermolecular halogen bonding in multicomponent solids featuring a 2,6-diiodo BODIPY.more » « less
-
null (Ed.)Amorphous solids lack long-range order. Therefore identifying structural defects—akin to dislocations in crystalline solids—that carry plastic flow in these systems remains a daunting challenge. By comparing many different structural indicators in computational models of glasses, under a variety of conditions we carefully assess which of these indicators are able to robustly identify the structural defects responsible for plastic flow in amorphous solids. We further demonstrate that the density of defects changes as a function of material preparation and strain in a manner that is highly correlated with the macroscopic material response. Our work represents an important step towards predicting how and when an amorphous solid will fail from its microscopic structure.more » « less
