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Über dieses Buch

The chicken bone you nibbled yesterday and threw away was a high-tech product! Not only that: it was a superlative light-weight design, functionally adapted to its mechanical requirements. No engineer in the world has, as yet, been able to copy this structural member, which is excellently optimized in its external shape and its internal architecture as regards minimum weight and maximum strength. The tree stem on which you recently carved your initials has also, by life-long care for its body, steadily improved its internal and external structure and adapted optimally to new loads. In the course of its biomechanical self-optimization it will heal up the notch you cut as speedily as possible, in order to repair even the smallest weak point, which might otherwise cost it its life in the next storm. This book is dedicated to the understanding of this biomechanical optimization of shape. It is the synthesis of many years of extensive research using the latest computer methods at the Karlsruhe Research Centre to help understand the mechanism of biological self-optimization (adaptive growth) and to simulate it by computer. The method newly developed for this purpose was called CAO (Computer-Aided Optimization). With this method, it is possible to predict the growth of trees, bones and other biological structures from the tiger's claw to the sea urchin's skeleton.

Inhaltsverzeichnis

Frontmatter

Introduction

Abstract
Anyone wanting to develop a new car today would not delve first into the mysteries of mail-coach design, and then mentally repeat all the main models of old cars in sequence until finally, after great delay, arriving at today’s design problem. Rather, they would study the best types on the market and test how they can be further improved, in order to incorporate such modifications into the chariot of their hopes. Thus they would proceed from the best-known design and measure their product against it.
Claus Mattheck

The Minimum on Mechanics

Abstract
The multiplicity of external loads to which a tree component can be exposed can be divided into forces, bending moments, torsional moments and thermal stresses. If the component is not to be moved, these loads must be countered by a support exerting equally large but opposed reaction loads.
Claus Mattheck

What Is a Good Mechanical Design?

Abstract
Components afflicted with dangerous notches could certainly be redesigned simply by over-dimensioning in order to eliminate the chance of failure. The idea here is to use more material (thicker walls etc.) so as to keep the stress, σ0, acting far away from the notch, at such a low value that the maximum stress σmax. = F ·σ0 caused by the notch is still small enough to exclude crack formation. There is little expertise in such a procedure as the component would be senselessly over-weight, although unfortunately this is sometimes current practice. This solution to the problem is also bad in other ways: the zones far away from the notch are by no means fully loaded and represent unnecessary ballast during the working of the component, which uses up energy, while the zone near the notch with just adequate material leads an uneasy life on the brink of potential fracture.
Claus Mattheck

The Axiom of Uniform Stress and How Computer Methods Derive from It

Abstract
However plausible everything may sound, a generally valid proof for the axiom of uniform stress will hardly be possible, given the rich diversity of species in nature. Still, there will certainly be hardly any real doubt that it does make sense to avoid both weak places and superfluous material, which in the final analysis is just what this uniformity of stress means. In Fig. 12 we have also seen that a notch does not always necessarily cause high notch stresses; its shape is much more important.
Claus Mattheck

The Mechanics of Trees and the Self-Optimization of Tree Shape

Abstract
There are more than just three growth regulators which have been described in detail [35, 37, 39]. The fact that only three of them are discussed here is because they are particularly important. We shall also soon see that the effects of apical dominance and phototropism may even involve mechanical disadvantages for the tree, but are nevertheless necessary for its survival.
Claus Mattheck

The Right Load Distribution: The Axiom of Uniform Stress and Tree Shape

Abstract
The fact that a tree trunk is thick at the bottom and thin at the top may seem so obvious to us that we are unlikely to enquire about a deeper mechanical significance. And yet this tapering of the trunk is probably the simplest and most obvious kind of component optimization which our instructor, the tree, can reveal. As the main loading of the tree is the wind load, acting transversely to the trunk and inducing a bending moment (Fig. 36), it is naturally important whether the crown of a tree is localized high up on the trunk, as is often found in trees in a dense stand (Fig. 36A), whether it increases rather linearly from top to bottom, as is often the case in free-standing conifers (Fig. 36B), or whether, as shown in example (C) in Fig. 36, the foliage is distributed almost uniformly over the length of the trunk. The latter is achieved quite well in Lombardy poplars. In Fig. 36, the relevant lengths are shown as ‘h’, it being assumed here that the distribution of the wind pressure is proportional to the projected crown area. The bending stresses on the trunk surface can be calculated from these distributions with Eq. (3), assuming a circular trunk cross-section. Now, assuming that the tree trunk is a component optimized over millions of years of evolution and satisfies the axiom of uniform stress, we only need to put σmax = σ1 = constant in Eq. (3) and we obtain a relationship D(h), i.e. between diameter and measured distance h, as explained in Fig. 36.
Claus Mattheck

Annual Rings: The Internal Diary as a Consequence of the External Situation

Abstract
Within one growing season the tree lays down some rather more porous earlywood first, and then the often rather denser and stronger latewood. The annual rings are particularly distinct in conifers like Douglas fir, pine and spruce, and are also good in oak, but are less clear in beech.
Claus Mattheck

Wood Fibres and Force Flow: The Fear of Shear Stress

Abstract
The flare figures shown in Fig. 99 do not coincide with the cracks running around the knot. These cracks do however provide very good information on the grain direction around branch holes, knots, inclusions etc. The flare figures are only a consequence of cutting the annual rings (better, annual cylinders) obliquely.
Claus Mattheck

How Does a Tree Break?

Abstract
It is certainly possible in principle to make a tree absolutely safe against failure with even worst-case loading, and thus that tree would be safe against many cases of load which it would never actually experience because of its siting. What a waste of material, what a need for nutrients and energy to prepare this material, and what a competitive disadvantage against the neighbouring tree, which boldly and somewhat light-heartedly grows up tall, dispensing with excessive safety, and leaving the heavyweight safety hypochondriac in the shadow of the dare-devil.
Claus Mattheck

Can Trees Really Not Shrink?

Abstract
Because of competition between trees, light-weight construction is more active, and green parts are essential, in order to utilize the building material as effectively as possible. In contrast to bones, which can actively break down unloaded material in order not to carry the ballast around, trees leave dead material in situ at first. The leading shoot which has died off can remain, just like the dead side branch. And yet some day they will break off. How this happens has already been described in connection with natural pruning. The tree forms a branch-shedding collar in the form of a ring notch around the dead part. After progressive decay has greatly reduced its strength, this fragment breaks off. The tree closes the wound, and smoothes out any unevenness remaining on the surface. It will reveal the history of this loss only to the practised eye, and as the years go by it becomes increasingly difficult to recognize and interpret the details of its body language (Fig. 127). However, the tree will never actively obliterate its history, as bone does.
Claus Mattheck

Bones: Ultra-Light and Very Strong by Continuous Optimization of Shape

Abstract
As mentioned above, as regards our design considerations, bones differ from trees by the possibility of active shrinking, carried out by so-called bone-eating cells (osteoclasts). Bone building is stress-controlled by another building brigade of cells, the osteoblasts (crib: clasts chew, blasts renew!). Muscles relieve bones of tensile loading by bracing, and by active contraction of muscle length they cause the actual movement of the articulated parts of the skeleton (bones) relative to one another. This makes sense, for in contrast to wood, bones have much higher compressive strength than tensile strength.
Claus Mattheck

Bone Design: Selected Examples

Abstract
Figure 128 sketches how the femur is loaded when standing on one leg. The abductor muscles play an important role here, preventing the upper body supported on the ball of the hip joint from tipping inwards (Fig. 128A). Because of the unfavourable lever relationships, the neck of the femur must transmit about 2.5 to 6 times body weight as axial loading (Fig. 128B). These enormous loads can only be coped with by an outstandingly well-adapted design. In the zone near the joint the femur is filled with trabecular bone, also called spongiform bone. This is a micro-framework of very fine small struts of bone which fill the whole head and neck of the femur. Further down they run into the bone-free marrow cavity in the middle, and laterally into the compact bone wall (cortical bone). In the lower region, the femur, which is almost exclusively loaded in bending, is a simple tube with a non-circular cross-section. This is certainly sensible, for we have the highest bending stresses at the edge, and in the middle, i.e. in the marrow cavity where there is no bone, the stresses are correspondingly equal to zero. (A hollow tree is therefore not so bad, for it too has no bending loads in the middle!)
Claus Mattheck

Bony Frameworks and Tree Frameworks Compared

Abstract
The frameworks illustrated in Fig. 138 show trabecular bone (Fig. 138A) and the welded framework of an aerial-rooter (Fig. 138B) from which the host tree has fallen away or rotted. The two components are pleasantly similar in conception, and both certainly satisfy the axiom of uniform stress for their loading. The fact that they have arisen in different ways is unimportant, but the question of what distinguishes the adaptive potential of their design with a possible change of shape must certainly be discussed in this book.
Claus Mattheck

Claws and Thorns: Shape-Optimized by Success in the Lottery of Heredity

Abstract
The experienced finger-wrestler in the pub might think he had a feel for the loads that a good rip-hook has to withstand. Quite wrong! The load in finger-wrestling is a slow quasi-static pull. It is more accurate to imagine jumping up beneath a high washing-line and hooking on to it while swinging freely: a dynamic process which would arouse some self-doubt in even the fittest finger-wrestler. And yet this kind of load is what happens when a tiger lands on the back of a bullock, buffalo etc., claws itself on firmly, is shaken about and finally conquers or is hurled down. A tiger weighs about 200 kp, so just imagine having to hold some swinging sacks full of potatoes with one’s finger nails. As the tiger does not hurt itself in doing this, its claws must be especially well shape-optimized, and the horn material must also exhibit a high tensile strength. The striped predator cannot allow the slightest local excess stress which would mean a design weak point and could have painful consequences for it during the tussle. These few preliminary observations make the tiger’s claw — or the claws of predators in general — an attractive object for study. The FEM and the CAO methods were used in the mechanical analysis [25]. Figure 139 gives an overview of the results of the calculations. The initial design was a hook of `engineered’ shape, consisting of two arcs of a circle. As in all the cases considered previously, here again the circular contour is a design catastrophe with a dangerous stress maximum in the last third of the claw (Fig. 139B), as also emerges from the stress distribution for the non-optimized circular contour. These stresses are reduced and homogenized after using the CAO method. A claw formed as a logarithmic spiral is produced, and this must therefore be the optimum form.
Claus Mattheck

Biological Shells

Abstract
Everyone knows what a plate is. It is a plane component whose thickness is small compared to its other dimensions. Now if this plate has a curvature, it is already a simply curved shell. One example known to us all is the thin-walled tube. If this tube also changes its diameter along a curve in the axial direction, it is a doubly curved shell (Fig. 141).
Claus Mattheck

Bracing: Ultra-Light but Highly Specialized

Abstract
One might criticize the author for introducing this stage of biological light-weight construction with an observation that smacks of a truism. It is, however, necessary to make things digestible for the reader who is less familiar with the theory of the stability of kinking rods.
Claus Mattheck

Shape Optimization by Growth in Engineering Design

Abstract
Light-weight construction can be practised to only a limited extent in technical components, as reliable damage avoidance is usually desired for each product, in contrast to nature. For example, if human life is involved, then we cannot approvingly accept the fracture of some motorcycles in order that this model gets by using less fuel. As already mentioned, nature does not know this scruple. Some of the following examples are industrial commissions and have mostly been built and successfully tested.
Claus Mattheck

Unity in Diversity: Design Target and Realization

Abstract
The aim of improving the chances of survival of a plant or animal species by minimizing the energy requirement is recognizable in all the preceding individual cases examined. The demand for light-weight design with adequate strength is automatically implied. In plants, which do not break down the less heavily loaded zones of the component, the gain is probably only a more economical use of building material. Animals which move about often have the additional possibility of actively breaking down unneeded ballast. In nature, the light-weight principle goes relentlessly on, to the extent that some individuals are readily sacrificed for it. Safety factors in design are kept so low by natural competition that a few of the biological load-bearing structures will fail mechanically under unaccustomed loads. This is, however, sensible in order to be able to preserve the whole species more cheaply. Our own bones fracture occasionally. They are just as underbuilt for a leap from the 6th floor as a tree in a dense stand is for a wind force 12 which it never experiences. A tree with excessive safety factors would forfeit height and therefore light absorption, just as the overweight mammal would experience competitive disadvantages by increasing immobility. Our technical constructions are an exception in the context of these energy-saving emergency sacrifices. We humans want to avoid any sensibly conceivable damage in the normal operation of a component. The idea of accepting a certain in-service damage rate and hence accident rate with a motor vehicle, in order to reduce the fuel consumption of the totality of motor vehicles by more riskily light-weight construction, is foreign to us. This profoundly human social behaviour is unnatural, when measured only against the merciless criteria of biological design targets. We must wait and see whether this increased safety of the individual based on over-dimensioning will have to be paid for by more rapid destruction of the environment and thus the destruction of the species as a whole.
Claus Mattheck

Critique on Optimum Shape: Sensitization by Specialization

Abstract
Shape-optimization means an adaptation of the component’s shape to a quite special load and bearing situation. The optimum design is advantageous only for these external circumstances. So far, so good. However, in many cases this specialization is associated with a poorer suitability of the design with respect to other cases of load inappropriate to it, against which the component is thus sensitized. We have seen a simple example in the spiral grain of trees. It means an adaptation of the course of the grain to a particular direction of rotation comparable to the strands of a rope, which press on to one another wonderfully with the lay in one direction and strengthen it. By reversing the twist of the rope, its strands loosen from each other and the rope loses its good properties (Fig. 106). In contrast, a co-axially parallel bundle of fibres without any twist would be equally poor in both directions of rotation or equally good, just as you wish. It is not optimized, i.e. it is not specialized to one direction of rotation and thus is not sensitized as regards the other direction of rotation. For the designer, this means that before optimizing the component must be considered all possible cases of load. If combined loadings can occur, the designer must assume the worst possible combination and optimize with respect to this. Then the component is the optimal light-weight structure only for this combination. Admittedly, the component is still strength-optimized for some loads out of the array, but it is no longer lightweight. It is overweight to the extent that the complete array of loads was trimmed down. All this must be remembered if the blessing of CAO is not to turn into the curse of fracture mechanics. This warning should not deter us from progressing along the road to the biologically shaped technical component with the new and promising SKO and CAO methods. But this must be done alertly, for thoughtless optimization is sabotage with loading inappropriate to the design.
Claus Mattheck

Outlook: Ecodesign and Close-to-Nature Computer Empiricism

Abstract
We should have succeeded in making the axiom of uniform stress credible as a biological and technical design prescription of fundamental significance. The SKO and CAO design methods derive directly from this tenet as tools for the practitioner. The combination of SKO and CAO is a complete method for automatic component layout, and we can hope for wide application in the field of industrial design. The acceptance of the CAO method in industry so far confirms this. The enterprises which have purchased CAO come from all fields where fatigue fractures of components must be avoided, e.g. construction of chemical plants, the motor industry and deliverers, electrical machinery manufacture, general machine-building, manufacture of products such as electric razors and washing machines, monitoring organizations, biomechanics, turbine manufacture etc. The diversity of interest alone indicates the rigorous universality of the method, which is naturally expected to cover just as great a diversity of forms in the technical field as does its natural counterpart, adaptive growth, in nature. It is to be expected that these very practical methods will spread increasingly in the future. Thus, in their mechanical design quality, technical components could approach the biological components evolved by brutal natural selection. A machine component grown like the skeleton of an animal or like a tree - an entity of technology and nature: the ecodesign! Success justifies this apparently crazy idea, and increasingly encourages other structural mechanical engineers to try the very promising combination of observation of nature and modern computer methods.
Claus Mattheck

New Examples of Application in Self-Explanatory Illustrations

Abstract
The following examples should illustrate the diversity of kinds of optimized structures, but also make clear their sensitivity to service loading.
Claus Mattheck

Backmatter

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