Ton Van Den Bogert

06-11-1989, 11:11 PM

Nashwa Abdel Baki writes:

> I'm studying the muscles behaviour under several types of loadings.

>I'm looking for the stress-strain curve and other parameters defining

>the characteristics of muscles. As I know it is defined as a nonlinear

>viscoplastic material. Could any one help me?. I would appreciate any reply.

You do not say whether you are interested in the properties of passive,

or of activated muscles. One way to describe the constitutive behaviour of

activated muscle (which in a certain sense is indeed visco-plastic) is:

F = u(t)f(L)g(dL/dt) + h(L),

with F the force being generated, u(t) the "active state" (normalized between

0 and 1), f(L) the force-length curve with its maximum at the maximal

isometric force and g(dL/dt) the force-velocity curve (Hill's equation), with

a maximum of 1 at dL/dt=0. h(L) represents the elastic properties of the

passive muscle (parallel elastic element). In case of no activity (u(t)=0),

only the second term remains, so this model may be too simplistic if you

are interested in passive muscle properties. Mathematical models for the

functions f,g and h can be found for example in several publications by

H. Hatze (e.g. A myocybernetic control model for skeletal muscle, Biological

Cybernetics 25:103-119 (1977) ).

The model may be further developed by adding a series elastic element,

in which case you obtain a first order differential equation.

Hope this information is helpful. I would also be interested in the opinions

of other BIOMCH-L subscribers.

Ton van den Bogert

Dept. of Veterinary Anatomy,

University of Utrecht, Netherlands.

> I'm studying the muscles behaviour under several types of loadings.

>I'm looking for the stress-strain curve and other parameters defining

>the characteristics of muscles. As I know it is defined as a nonlinear

>viscoplastic material. Could any one help me?. I would appreciate any reply.

You do not say whether you are interested in the properties of passive,

or of activated muscles. One way to describe the constitutive behaviour of

activated muscle (which in a certain sense is indeed visco-plastic) is:

F = u(t)f(L)g(dL/dt) + h(L),

with F the force being generated, u(t) the "active state" (normalized between

0 and 1), f(L) the force-length curve with its maximum at the maximal

isometric force and g(dL/dt) the force-velocity curve (Hill's equation), with

a maximum of 1 at dL/dt=0. h(L) represents the elastic properties of the

passive muscle (parallel elastic element). In case of no activity (u(t)=0),

only the second term remains, so this model may be too simplistic if you

are interested in passive muscle properties. Mathematical models for the

functions f,g and h can be found for example in several publications by

H. Hatze (e.g. A myocybernetic control model for skeletal muscle, Biological

Cybernetics 25:103-119 (1977) ).

The model may be further developed by adding a series elastic element,

in which case you obtain a first order differential equation.

Hope this information is helpful. I would also be interested in the opinions

of other BIOMCH-L subscribers.

Ton van den Bogert

Dept. of Veterinary Anatomy,

University of Utrecht, Netherlands.