Itou Hiromichi, Kovtunenko Victor A, Rajagopal Kumbakonam R
Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku Tokyo, 162-8601 Japan.
Institute for Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstr.36, 8010 Graz, Austria.
J Elast. 2021;144(1):107-118. doi: 10.1007/s10659-021-09831-x. Epub 2021 Apr 14.
We study some mathematical properties of a novel implicit constitutive relation wherein the stress and the linearized strain appear linearly that has been recently put into place to describe elastic response of porous metals as well as materials such as rocks and concrete. In the corresponding mixed variational formulation the displacement, the deviatoric and spherical stress are three independent fields. To treat well-posedness of the quasi-linear elliptic problem, we rely on the one-parameter dependence, regularization of the linear-fractional singularity by thresholding, and applying the Browder-Minty existence theorem for the regularized problem. An analytical solution to the nonlinear problem under constant compression/extension is presented.
我们研究了一种新型隐式本构关系的一些数学性质，其中应力和线性化应变呈线性出现，该本构关系最近已被用于描述多孔金属以及岩石和混凝土等材料的弹性响应。在相应的混合变分公式中，位移、偏应力和球应力是三个独立的场。为了处理拟线性椭圆问题的适定性，我们依赖于单参数依赖性、通过阈值化对线性分式奇异性进行正则化，以及应用正则化问题的布劳德 - 明蒂存在定理。给出了恒压/恒拉情况下非线性问题的解析解。
