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.

最近，Arumugam 等人。(2023) 开发了各向同性非均匀可压缩弹性固体响应的本构关系，以描述小梁骨的响应。由于多孔固体（例如骨头、水泥混凝土、岩石、金属合金等）是各向异性的，因此在这篇简短的说明中，我们为此类具有横向各向同性且具有两个优选对称方向的物体开发了本构关系。骨骼的另一个特征是它们在拉伸和压缩方面表现出不同的响应特征，因此开发的任何本构关系都必须能够描述这一点。此外，材料模量取决于密度和应力平均值（机械压力），正如多孔固体中所预期的那样。在本文提出的本构关系中，虽然应力和线性化应变在本构关系中呈线性出现，但该关系是非线性的。我们还推导了此类固体在经历单轴拉伸和压缩、简单剪切和扭转时的响应。