BIPHASIC INDENTATION OF ARTICULAR-CARTILAGE .1. THEORETICAL-ANALYSIS
BIPHASIC INDENTATION OF ARTICULAR-CARTILAGE .1. THEORETICAL-ANALYSIS
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DOI：
10.1016/0021-9290(87)90036-4
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发表时间：
1987-01-01
影响因子：
2.4
通讯作者：
MOW, VC
中科院分区：
文献类型：
--
作者：
MAK, AF;LAI, WM;MOW, VC
已经获得了关节软骨的压痕蠕变和应力松弛行为的数学解决方案，其中组织被建模为厚度为 h 的线性 KLM 双相材料层，粘合到不渗透的刚性骨基质上。圆形（半径 = a）、平面端压头被假定为刚性、多孔、自由排水且无摩擦。双拉普拉斯和汉克尔变换技术用于求解偏微分方程。变换后的方程和边界条件产生了 Fredholm 型积分方程，对其进行渐近分析和数值求解。我们的渐近分析表明，线性 KLM 双相材料在 t = O+ 时表现得像不可压缩 (nu. = 0.5) 单相弹性固体；材料的瞬时响应由固体基质的剪切模量 (μs) 控制。线性 KLM 双相材料的行为类似于可压缩弹性固体，其材料属性由固体基质的属性定义，即 (.lambda.s, .mu.s,) 或 (.mu.s, nuws) 作为 t.fwdarw。 .infin.. 该材料的瞬态粘弹性蠕变和应力松弛行为 0 < t < .infin. 由与间隙流体流过多孔渗透固体基质相关的摩擦阻力（与渗透率 k 成反比）控制。对于给定的固体基体泊松比 vs 和纵横比 a/h，其中 a 是压头半径，h 是层厚度，相对于无量纲时间 HAkt/a2 的蠕变行为完全由载荷参数 P2.mu.sa2 控制，应力松弛行为完全由压缩率参数 R0 = kHA/Voh 控制，其中 HA = λs + 2.mu.s 和平衡应变.mu.o/h。该数学解决方案现在可用于描述关节软骨上的压痕实验，以确定组织的固有材料特性，即渗透性 k 和固相的弹性系数 (λs，μs) 或 ((μs，μs)。
A mathematical solution has been obtained for the indentation creep and stress-relaxation behavior of articular cartilage where the tissue is modeled as a layer of linear KLM biphasic material of thickness h bonded to an impervious, rigid bony substrate. The circular (radius = a), plane-ended indenter is assumed to be rigid, porous, free-draining, and frictionless. Double Laplace and Hankel transform techniques were used to solve the partial differential equations. The transformed equations and boundary conditions yielded an integral equation of the Fredholm type which was analyzed asymptotically and solved numerically. Our asymptotic analyses showed that the linear KLM biphasic material behaves like an incompressible (.nu. = 0.5) single-phase elastic solid at t = O+; the instantaneous response of the material is governed by the shear modulus (.mu.s) of the solid matrix. The linear KLM biphasic material behaves like a compressible elastic solid with material properties defined by those of the solid matrix, i.e. (.lambda.s, .mu.s,) or (.mu.s, nuws) as t .fwdarw. .infin.. The transient viscoelastic creep and stress-relaxation behavior, 0 < t < .infin., of this material is controlled by the frictional drag (which is inversely proportional to the permeability k) associated with the flow of the interstitial fluid through the porous-permeable solid matrix. For given values of the Poisson''s ratio of the solid matrix vs and the aspect ratio a/h, where a is the radius of the indenter and h is the thickness of the layer, the creep behavior with respect to the dimensionless time HAkt/a2 is completely controlled by the load parameter P2.mu.sa2 and the stress relaxation behavior is completely controlled by the rate of compression parameter R0 = kHA/Voh where HA = .lambda.s + 2.mu.s and the equilibrium strain .mu.o/h. This mathematical solution may now be used to describe an indentation experiment on articular cartilage to determine the intrinsic material properties of the tissue, i.e. permeability k, and the elastic coefficients of the solid phase (.lambda.s, .mu.s) or ((.mu.s, .nu.s).