925:, an extracellular protein that accounts for approximately 75% of its dry weight. The pliability of skin is a parameter of interest that represents its firmness and extensibility, encompassing characteristics such as elasticity, stiffness, and adherence. These factors are of functional significance to patients. This is of significance to patients with traumatic injuries to the skin, whereby the pliability can be reduced due to the formation and replacement of healthy skin tissue by a pathological
929:. This can be evaluated both subjectively, or objectively using a device such as the Cutometer. The Cutometer applies a vacuum to the skin and measures the extent to which it can be vertically distended. These measurements are able to distinguish between healthy skin, normal scarring, and pathological scarring, and the method has been applied within clinical and industrial settings to monitor both pathophysiological sequelae, and the effects of treatments on skin.
408:
38:
340:
must be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or
352:
For a body with multiple DOF, to calculate a particular direct-related stiffness (the diagonal terms), the corresponding DOF is left free while the remaining should be constrained. Under such a condition, the above equation can obtain the direct-related stiffness for the degree of unconstrained
638:
of a material is not the same as the stiffness of a component made from that material. Elastic modulus is a property of the constituent material; stiffness is a property of a structure or component of a structure, and hence it is dependent upon various physical dimensions that describe that
348:
It is noted that for a body with multiple DOF, the equation above generally does not apply since the applied force generates not only the deflection along its direction (or degree of freedom) but also those along with other directions.
283:(or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of six DOF at a point). For example, a point on a horizontal
1133:
V. GOPALAKRISHNAN and CHARLES F. ZUKOSKI; "Delayed flow in thermo-reversible colloidal gels"; Journal of
Rheology; Society of Rheology, U.S.A.; July/August 2007; 51 (4): pp. 623–644.
818:
696:
534:
174:
335:
62:
582:
429:
219:
270:
501:
475:
452:
137:
85:
867:
841:
771:
745:
719:
557:
309:
197:
1118:
1084:
1233:
Nedelec, Bernadette; Correa, José; de
Oliveira, Ana; LaSalle, Leo; Perrault, Isabelle (2014). "Longitudinal burn scar quantification".
644:
640:
284:
1100:
784:
662:
140:
506:
146:
237:
899:
is often one of the primary properties considered when selecting a material. A high modulus of elasticity is sought when
1284:
1279:
1274:
31:
353:
freedom. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses.
139:
of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single
363:
A single spring may intentionally be designed to have variable (non-linear) stiffness throughout its displacement.
225:
produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring)
900:
748:
280:
1005:
94:
656:
372:
896:
288:
222:
981:
951:
907:
337:
945:
652:
622:
230:
966: – Any of several imaging modalities that map degrees of soft-tissue elasticity and stiffness
895:
The stiffness of a structure is of principal importance in many engineering applications, so the
392:
388:
1023:
881:
722:
341:
different points) or the same degree of freedom at two different points. In industry, the term
314:
1250:
1215:
1174:
1114:
1080:
987:
954: – Physical property when materials or objects return to original shape after deformation
939:
357:
44:
567:
414:
204:
1242:
1205:
1192:
Graham, Helen K; McConnell, James C; Limbert, Georges; Sherratt, Michael J (February 2019).
1164:
1156:
1106:
1054:
1014:
870:
844:
560:
37:
1110:
877:
Note that the torsional stiffness has dimensions * / , so that its SI units are N*m/rad.
999:
993:
957:
921:
biology. The skin maintains its structure due to its intrinsic tension, contributed to by
903:
is undesirable, while a low modulus of elasticity is required when flexibility is needed.
635:
20:
990: – Scalar measure of the rotational inertia with respect to a fixed axis of rotation
247:
483:
457:
434:
119:
67:
1169:
1144:
975:
852:
826:
756:
730:
704:
604:
542:
407:
294:
182:
24:
1058:
1268:
600:
396:
273:
241:
143:(DOF) (for example, stretching or compression of a rod), the stiffness is defined as
978: – Physical law: force needed to deform a spring scales linearly with distance
963:
615:
589:
1246:
360:
is a generalization that describes all possible stretch and shear parameters.
911:
1254:
1219:
1178:
972: – Measure of a material's resistance to localized plastic deformation
1045:
Baumgart F. (2000). "Stiffness--an unknown world of mechanical science?".
969:
922:
610:
Further measures of stiffness are derived on a similar basis, including:
384:
948: – Mechanism which transmits force through elastic body deformation
1026: – Mechanical property that measures stiffness of a solid material
910:
is important for guiding the migration of cells in a phenomenon called
880:
For the special case of unconstrained uniaxial tension or compression,
23:. For the term regarding the stability of a differential equation, see
1210:
1193:
1160:
599:
In the SAE system, rotational stiffness is typically measured in inch-
774:
593:
108:
or pliability: the more flexible an object is, the less stiff it is.
651:
its shape and boundary conditions. For example, for an element in
406:
98:
36:
926:
918:
588:
In the SI system, rotational stiffness is typically measured in
291:
and a rotation relative to its undeformed axis. When there are
960: – Physical property that measures stiffness of material
395:, and so take the units of reciprocal stress, for example, 1/
1008: – Differential equation exhibiting unusual instability
887:
be thought of as a measure of the stiffness of a structure.
781:
Similarly, the torsional stiffness of a straight section is
1017: – Stress-strain relation in a linear elastic material
272:). In Imperial units, stiffness is typically measured in
984: – Relationship between harmonic force and velocity
19:
For pain and/or loss of range of motion of a joint, see
1019:
Pages displaying short descriptions of redirect targets
1010:
Pages displaying short descriptions of redirect targets
383:, typically measured in units of metres per newton. In
345:
is sometimes used to refer to the coupling stiffness.
855:
829:
787:
759:
733:
707:
665:
643:
of the material; stiffness, on the other hand, is an
570:
545:
509:
486:
460:
437:
417:
317:
297:
250:
207:
185:
149:
122:
70:
47:
1002: – Elastic object that stores mechanical energy
647:
of the solid body that is dependent on the material
1075:Martin Wenham (2001), "Stiffness and flexibility",
861:
835:
812:
765:
739:
713:
690:
576:
551:
528:
495:
469:
446:
423:
329:
303:
264:
213:
191:
168:
131:
79:
56:
30:"Flexibility" redirects here. For other uses, see
917:Another application of stiffness finds itself in
1145:"Collagen-Based Biomaterials for Wound Healing"
16:Resistance to deformation in response to force
1143:Chattopadhyay, S.; Raines, R. (August 2014).
1077:200 science investigations for young students
480:A body may also have a rotational stiffness,
8:
621:torsional stiffness - the ratio of applied
1063:"Stiffness" = "Stress" divided by "strain"
1209:
1168:
854:
828:
800:
786:
758:
732:
706:
678:
664:
569:
544:
516:
508:
485:
459:
436:
416:
316:
296:
254:
249:
206:
184:
156:
148:
121:
93:is the extent to which an object resists
69:
46:
1105:(2 ed.). Oxford University Press.
1099:Escudier, Marcel; Atkins, Tony (2019).
1037:
813:{\displaystyle k=G\cdot {\frac {J}{L}}}
691:{\displaystyle k=E\cdot {\frac {A}{L}}}
639:component. That is, the modulus is an
614:shear stiffness - the ratio of applied
233:, but sometimes under dynamic loading.
1102:A Dictionary of Mechanical Engineering
529:{\displaystyle k={\frac {M}{\theta }}}
169:{\displaystyle k={\frac {F}{\delta }}}
721:is the (tensile) elastic modulus (or
240:, stiffness is typically measured in
7:
1111:10.1093/acref/9780198832102.001.0001
387:, it may be defined as the ratio of
229:Stiffness is usually defined under
1079:, SAGE Publications, p. 126,
431:of a cylindrical bar, with length
14:
906:In biology, the stiffness of the
996: – Hardness-testing device
1:
1059:10.1016/S0020-1383(00)80040-6
238:International System of Units
104:The complementary concept is
625:moment to the angle of twist
287:can undergo both a vertical
41:Extension of a coil spring,
32:Flexibility (disambiguation)
1247:10.1016/j.burns.2014.03.002
942: – Continuum mechanics
454:caused by an axial moment,
1301:
630:Relationship to elasticity
618:force to shear deformation
97:in response to an applied
64:caused by an axial force,
29:
18:
659:, the axial stiffness is
330:{\displaystyle M\times M}
1198:Experimental Dermatology
199:is the force on the body
57:{\displaystyle \delta ,}
1006:Stiffness (mathematics)
577:{\displaystyle \theta }
424:{\displaystyle \alpha }
231:quasi-static conditions
214:{\displaystyle \delta }
863:
837:
814:
767:
741:
715:
692:
578:
553:
530:
497:
477:
471:
448:
425:
331:
305:
266:
215:
193:
170:
133:
87:
81:
58:
897:modulus of elasticity
864:
838:
815:
768:
742:
716:
693:
584:is the rotation angle
579:
554:
531:
498:
472:
449:
426:
410:
343:influence coefficient
332:
311:degrees of freedom a
306:
267:
216:
194:
171:
134:
82:
59:
40:
1194:"How stiff is skin?"
982:Mechanical impedance
952:Elasticity (physics)
908:extracellular matrix
853:
827:
785:
757:
749:cross-sectional area
731:
705:
663:
568:
543:
507:
484:
458:
435:
415:
403:Rotational stiffness
315:
295:
279:Generally speaking,
248:
205:
183:
147:
120:
68:
45:
1285:Structural analysis
1280:Continuum mechanics
1275:Physical quantities
1053:. Elsevier: 14–84.
946:Compliant mechanism
265:{\displaystyle N/m}
859:
833:
810:
763:
737:
711:
688:
645:extensive property
641:intensive property
574:
549:
526:
496:{\displaystyle k,}
493:
478:
470:{\displaystyle M.}
467:
447:{\displaystyle L,}
444:
421:
327:
301:
262:
211:
189:
166:
132:{\displaystyle k,}
129:
88:
80:{\displaystyle F.}
77:
54:
1211:10.1111/exd.13826
1161:10.1002/bip.22486
1120:978-0-19-883210-2
1086:978-0-7619-6349-3
988:Moment of inertia
940:Bending stiffness
862:{\displaystyle J}
836:{\displaystyle G}
808:
766:{\displaystyle L}
740:{\displaystyle A}
714:{\displaystyle E}
686:
552:{\displaystyle M}
524:
358:elasticity tensor
304:{\displaystyle M}
192:{\displaystyle F}
164:
141:degree of freedom
1292:
1259:
1258:
1241:(8): 1504–1512.
1230:
1224:
1223:
1213:
1189:
1183:
1182:
1172:
1140:
1134:
1131:
1125:
1124:
1096:
1090:
1089:
1072:
1066:
1065:
1042:
1020:
1015:Stiffness tensor
1011:
873:for the section.
871:torsion constant
868:
866:
865:
860:
847:of the material,
845:rigidity modulus
842:
840:
839:
834:
819:
817:
816:
811:
809:
801:
772:
770:
769:
764:
746:
744:
743:
738:
720:
718:
717:
712:
697:
695:
694:
689:
687:
679:
583:
581:
580:
575:
558:
556:
555:
550:
535:
533:
532:
527:
525:
517:
502:
500:
499:
494:
476:
474:
473:
468:
453:
451:
450:
445:
430:
428:
427:
422:
411:Twist, by angle
375:of stiffness is
336:
334:
333:
328:
310:
308:
307:
302:
276:(lbs) per inch.
271:
269:
268:
263:
258:
220:
218:
217:
212:
198:
196:
195:
190:
175:
173:
172:
167:
165:
157:
138:
136:
135:
130:
86:
84:
83:
78:
63:
61:
60:
55:
1300:
1299:
1295:
1294:
1293:
1291:
1290:
1289:
1265:
1264:
1263:
1262:
1232:
1231:
1227:
1191:
1190:
1186:
1142:
1141:
1137:
1132:
1128:
1121:
1098:
1097:
1093:
1087:
1074:
1073:
1069:
1044:
1043:
1039:
1034:
1029:
1024:Young's modulus
1018:
1009:
1000:Spring (device)
994:Shore durometer
958:Elastic modulus
935:
893:
882:Young's modulus
851:
850:
825:
824:
783:
782:
777:of the element.
755:
754:
729:
728:
723:Young's modulus
703:
702:
661:
660:
636:elastic modulus
632:
566:
565:
559:is the applied
541:
540:
505:
504:
482:
481:
456:
455:
433:
432:
413:
412:
405:
369:
313:
312:
293:
292:
246:
245:
203:
202:
181:
180:
145:
144:
118:
117:
116:The stiffness,
114:
66:
65:
43:
42:
35:
28:
21:joint stiffness
17:
12:
11:
5:
1298:
1296:
1288:
1287:
1282:
1277:
1267:
1266:
1261:
1260:
1225:
1184:
1155:(8): 821–833.
1135:
1126:
1119:
1091:
1085:
1067:
1036:
1035:
1033:
1030:
1028:
1027:
1021:
1012:
1003:
997:
991:
985:
979:
973:
967:
961:
955:
949:
943:
936:
934:
931:
892:
889:
886:
875:
874:
858:
848:
832:
807:
804:
799:
796:
793:
790:
779:
778:
762:
752:
736:
726:
710:
685:
682:
677:
674:
671:
668:
650:
631:
628:
627:
626:
619:
586:
585:
573:
563:
548:
523:
520:
515:
512:
492:
489:
466:
463:
443:
440:
420:
404:
401:
382:
378:
368:
365:
326:
323:
320:
300:
261:
257:
253:
227:
226:
210:
200:
188:
163:
160:
155:
152:
128:
125:
113:
110:
76:
73:
53:
50:
25:stiff equation
15:
13:
10:
9:
6:
4:
3:
2:
1297:
1286:
1283:
1281:
1278:
1276:
1273:
1272:
1270:
1256:
1252:
1248:
1244:
1240:
1236:
1229:
1226:
1221:
1217:
1212:
1207:
1203:
1199:
1195:
1188:
1185:
1180:
1176:
1171:
1166:
1162:
1158:
1154:
1150:
1146:
1139:
1136:
1130:
1127:
1122:
1116:
1112:
1108:
1104:
1103:
1095:
1092:
1088:
1082:
1078:
1071:
1068:
1064:
1060:
1056:
1052:
1048:
1041:
1038:
1031:
1025:
1022:
1016:
1013:
1007:
1004:
1001:
998:
995:
992:
989:
986:
983:
980:
977:
974:
971:
968:
965:
962:
959:
956:
953:
950:
947:
944:
941:
938:
937:
932:
930:
928:
924:
920:
915:
913:
909:
904:
902:
898:
890:
888:
884:
883:
878:
872:
856:
849:
846:
830:
823:
822:
821:
805:
802:
797:
794:
791:
788:
776:
760:
753:
750:
734:
727:
724:
708:
701:
700:
699:
683:
680:
675:
672:
669:
666:
658:
654:
648:
646:
642:
637:
629:
624:
620:
617:
613:
612:
611:
608:
606:
602:
597:
595:
591:
590:newton-metres
571:
564:
562:
546:
539:
538:
537:
521:
518:
513:
510:
490:
487:
464:
461:
441:
438:
418:
409:
402:
400:
398:
394:
390:
386:
380:
376:
374:
366:
364:
361:
359:
354:
350:
346:
344:
339:
324:
321:
318:
298:
290:
286:
282:
277:
275:
259:
255:
251:
243:
239:
234:
232:
224:
208:
201:
186:
179:
178:
177:
161:
158:
153:
150:
142:
126:
123:
111:
109:
107:
102:
100:
96:
92:
74:
71:
51:
48:
39:
33:
26:
22:
1238:
1234:
1228:
1201:
1197:
1187:
1152:
1148:
1138:
1129:
1101:
1094:
1076:
1070:
1062:
1050:
1046:
1040:
964:Elastography
916:
905:
894:
891:Applications
879:
876:
780:
633:
609:
598:
587:
479:
370:
362:
355:
351:
347:
342:
289:displacement
278:
235:
228:
223:displacement
115:
112:Calculations
105:
103:
90:
89:
1149:Biopolymers
976:Hooke's law
657:compression
377:flexibility
281:deflections
244:per meter (
106:flexibility
95:deformation
1269:Categories
1032:References
901:deflection
381:compliance
367:Compliance
912:durotaxis
798:⋅
676:⋅
572:θ
522:θ
503:given by
419:α
322:×
209:δ
162:δ
91:Stiffness
49:δ
1255:24703337
1220:30698873
1179:24633807
970:Hardness
933:See also
923:collagen
385:rheology
1204:: 4–9.
1170:4203321
869:is the
843:is the
773:is the
747:is the
653:tension
623:torsion
373:inverse
242:newtons
236:In the
221:is the
176:where,
1253:
1218:
1177:
1167:
1117:
1083:
1047:Injury
820:where
775:length
698:where
605:degree
601:pounds
594:radian
561:moment
536:where
393:stress
389:strain
338:matrix
274:pounds
1235:Burns
616:shear
99:force
1251:PMID
1216:PMID
1175:PMID
1115:ISBN
1081:ISBN
927:scar
919:skin
634:The
603:per
592:per
371:The
356:The
285:beam
1243:doi
1206:doi
1165:PMC
1157:doi
1153:101
1107:doi
1055:doi
885:can
655:or
649:and
391:to
379:or
1271::
1249:.
1239:40
1237:.
1214:.
1202:28
1200:.
1196:.
1173:.
1163:.
1151:.
1147:.
1113:.
1061:.
1051:31
1049:.
914:.
725:),
607:.
596:.
399:.
397:Pa
101:.
1257:.
1245::
1222:.
1208::
1181:.
1159::
1123:.
1109::
1057::
857:J
831:G
806:L
803:J
795:G
792:=
789:k
761:L
751:,
735:A
709:E
684:L
681:A
673:E
670:=
667:k
547:M
519:M
514:=
511:k
491:,
488:k
465:.
462:M
442:,
439:L
325:M
319:M
299:M
260:m
256:/
252:N
187:F
159:F
154:=
151:k
127:,
124:k
75:.
72:F
52:,
34:.
27:.
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