: An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.

https://apps.dtic.mil/sti/pdfs/AD0653716.pdf

A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks

Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations. This updated edition provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers, breaking phenomena, and other fields.

Mechanical properties of solid polymers

Hydrogels attract great attention as biomaterials as a result of their soft and wet nature, similar to that of biological tissues. Recent inventions of several tough hydrogels show their potential as structural biomaterials, such as cartilage. Any given application, however, requires a combination of mechanical properties including stiffness, strength, toughness, damping, fatigue resistance and self-healing, along with biocompatibility. This combination is rarely realized. Here, we report that polyampholytes, polymers bearing randomly dispersed cationic and anionic repeat groups, form tough and viscoelastic hydrogels with multiple mechanical properties. The randomness makes ionic bonds of a wide distribution of strength. The strong bonds serve as permanent crosslinks, imparting elasticity, whereas the weak bonds reversibly break and re-form, dissipating energy. These physical hydrogels of supramolecular structure can be tuned to change multiple mechanical properties over wide ranges by using diverse ionic combinations. This polyampholyte approach is synthetically simple and dramatically increases the choice of tough hydrogels for applications.

https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/56662/1/Gong-Manuscript-1.pdf

Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity

Individuals who suffer extensive loss of skin, commonly in fires, are acutely ill, in danger of succumbing either to massive infection of to severe fluid loss. Patients who survive these early threats must often cope with problems of rehabilitation arising from deep, disfiguring scars and crippling contractures. In this report we describe the physiocochemical, biochemical, and mechanical considerations that form the basis for two-stage design of a membrane useful as an experimental wound closure. Stage I of the design, applicable to short-term acute use, calls for a membrane which displaces efficiently air pockets from a carefully prepared woundbed, free of weak boundary layers, and maintains the moisture flux through the wound at an optimal level. Optimization of the surface energy, modulus of elasticity, energy to fracture and moisture permeability of the membrane are among the essential attributes of Stage I design. Stage 2 of the design, applicable to long-term, chronic use, focuses on a nonantigenic membrane which performs as a biodegradable template for synthesis of neodermal tissue. A survey of candidate materials suggests reasons for selection of a porous, crosslinked collagen-glycosaminoglycan coprecipitate as the chemical basis of an evolving design which was initiated 10 years ago. Over the past several years a set of membranes has been iteratively designed on this basis and has been used to cover satisfactorily large experimental full-thickness skin wounds in guinea pigs. Such membranes have effectively protected these wounds from infection and fluid loss for over 25 days without rejection and without requiring change or other invasive manipulation. When appropriately designed for the purpose, the membranes have also strongly retarded wound contraction and have become replaced by newly synthesized, stable connective tissue. Several rules relating the molecular structure and morphology of these membranes to cellular response of adjacent tissue have also been derived. This report is the first in a series which details the methodology of preparation and the record of performance.

Design of an artificial skin. I. Basic design principles.

The resistance to tearing of a rubber vulcanizate is usually determined by loading in a specified manner a test-piece of the vulcanizate of standard shape, in which a notch has been produced, either in the molding process or by cutting the test-piece in a standard fashion. A wide variety of shapes of test-piece and notch and of methods of loading have been recommended by various authors (see, for example, Buist1).

Rupture of rubber. I. Characteristic energy for tearing

A method of investigating the tear behavior of rubber vulcanizates is described. The method, based on the tear criterion of Rivlin and Thomas, involves the determination of the energy required to propagate a tear and its dependence on the rate of propagation. The type of test-piece employed and the methods of measuring the energy and rate of tear propagation are described and discussed. Two principal types of tearing, indicative of different tear processes, are described. Experimental results for natural rubber and GR-S gum vulcanizates, obtained over a wide range of temperature and rate of propagation, are given to illustrate the method. The results indicate that the nature of the tear process and the resistance to tearing, as represented by the energy required to propagate a tear, can change appreciably with the rate of propagation and the temperature. The significance of these changes is discussed.

Rupture of rubber. III. Determination of tear properties

The strain distribution around the tip of an incision in a thin test-piece of highly elastic material is considered. Using the results of a previous paper, relations between this strain distribution and the over-all forces or strains are derived for two particular types of test-piece. Experiments designed to check the theory are described, and agreement is found to be satisfactory. The theory is extended qualitatively to the case where the test-piece is taken to the point of rupture, and experiments are described which confirm the approximate relation derived. The relevance to tearing and to the previously proposed tear criterion is discussed.

Rupture of rubber. II. The strain concentration at an incision

Ein numerisches Verfahren zur Behandlung yon axial-symmetrischen Membranproblemen bei endlichen elastischen FormXnderungen wird auf die Verw61bung einer kreisf6rmigen elastischen Membran angewendet. Die zur L6sung notwendige numerische Integration der Gleichgewichtsbedingungen erfolgt bei den gew~Lhlten Beispielen mit Hilfe einer fiir die Berechnung mit Handrechenmaschine gebrguchlichen Differenzmethode. Gestiitzt auf mehrere experimentelle und theoretisehe Arbeiten werden zur Untersuchung der L6sung des Membranproblems verschiedene Formen der Formgnderungsenergie W bei grossen Deformationen betrachtet (10 < 12 < 1000). Eine Verallgemeinerung der logarithmisehen Form ffir W yon GENT und THOMAS erweist sich als ungeeignet ftir die betrachtete Ordnung der Deformation. Durch Anpassung der Parameter in der Drei-Parameter-Gestalt der Formgnderungsenergie yon CARMICHAEL und HOLDAWAY wird eine gute Ubereinstimmung mit dem Experiment erhalten. Fiir diese L6sungen besitzt OW/O 11 einen konstanten Wert bei der Deformation, was eine friihere Feststellung yon RIVLIN und SAUNDERS fiir Werte yon 12 bis 1000 best~tigt. Das Versagen der logarithmisehen Form von W ist auf die starke Abnahme von OW/OI~ im Bereich grosser Dehnungen zuriickzufiihren.

Forms for the stored (strain) energy function for vulcanized rubber

It has been noted in Part I of this series (referred to hereafter as I), that if a nicked specimen of a natural rubber vulcanizate is slowly stretched, tearing occurs at the tip for quite small applied forces. In the initial stages, this tearing continues only as long as the deformation of the specimen is being increased, and virtually ceases if the deformation is held constant. This tearing is essentially time independent, and is termed “static” cut growth. If, however, the deformation is continued until the cut has grown by a few hundredths of a millimeter the growth becomes time dependent and catastrophic tearing takes place, the cut suddenly increasing in length by perhaps a millimeter or so. If a nicked specimen is alternately stretched and relaxed to the unstrained state, the cut gradually grows even though the applied force is less than that required to produce catastrophic tearing. This phenomenon is termed “dynamic” cut growth. This behavior can be compared to that of gum GR-S vulcanizat...

A. G. Thomas

Papers

Rupture of rubber. I. Characteristic energy for tearing

Rupture of rubber. III. Determination of tear properties

Rupture of rubber. II. The strain concentration at an incision

Forms for the stored (strain) energy function for vulcanized rubber

Rupture of rubber. V. Cut growth in natural rubber vulcanizates