Abstract:
A modular concrete form system which can also reduce the amount of concrete required, while producing a concrete surface that is equal to or stronger than the conventional construction processes. A matrix is provided having two sidewalls with a plurality of arched segments spaced apart by concave troughs. Multiple matrixes can be linked together to create extended lengths to be terminated at various locations by the means of the termination units. The curing time of the concrete is extended because less concrete is in contact with the surface and slowing the curing time of the concrete has the result of improving the quality and minimizing the cracking.

Description:
FIELD OF THE INVENTION  
       [0001]     This application is a Continuation-in-Part Application from U.S. patent application Ser. No. 10/994,854 filed on Nov. 22, 2004, and currently pending. Molds are used to cast structures out of many types of materials. Typical structures, especially those related to construction, are cast as solid pieces. An example of such a process is the casting of structural concrete. The present invention relates to a new and unique process for the construction of concrete surfaces such as sidewalks, patios, slabs and the like. This process requires less concrete and produces a surface that is equal to or stronger than a concrete surface constructed in a conventional manner.  
       BACKGROUND OF THE INVENTION  
       [0002]     The invention relates to the field of forming and placement of concrete surfaces. In particular, the present invention provides a novel modular concrete form system of construction where less concrete is used to produce a surface that is equal to or stronger than the conventional methods.  
         [0003]     Concrete form and stake assemblies are conventionally employed extensively for the placement of concrete in order to shape and contain the concrete in the process of creating such things as sidewalks, driveways, patios, and slabs. Preparation of a site for the placement of concrete involves, after leveling the area and compaction, erecting a frame to contain the concrete. Erecting wood forms for concrete placement commonly involves the placement of stakes, attaching the form members to the stakes by nailing the form into place and ultimately forming a cavity within the completed assembly of forms into which concrete is placed. To cover a length larger than any one form, forms are abutted in a cooperative engagement, end-to-end, or side to side, or in both directions, to cover the additional length necessary. The concrete is placed into the cavity within this frame over the earthen surface. The surface of the concrete is finished and the frame is then removed once the concrete has set. In some construction projects, such as bridges or road structures, “pre-stressed” concrete is made by casting concrete around cables that are held at a tension. Because typical concrete structures are solid concrete (with the exception of the re-bar pieces), structure strength depends on the thickness of the concrete and the re-bar reinforcement. However, a solid structure is not necessarily the most efficient use of material volume and mass to achieve strength. For example, the base of a tall structure may need to support a great deal of weight, including its own. Thus, what is needed, is a method of casting materials in more efficient shapes, thereby saving material cost and mass, while providing a convenient method of forming structures.  
         [0004]     Forms erected for the placement of concrete conventionally are constructed of lumber. Often, in order to accommodate the various dimensions of forms, the lumber must be cut to shorter lengths to accommodate specific projects, making it unlikely the lumber will be used on a subsequent project of differing dimensions. Further, the necessity of nailing or other means of attaching the wooden forms to the stakes results in damage to the lumber with the result being the lumber is likely consumed in the placement of one slab of concrete. Additionally, the price of lumber has increased greatly over the past few years. Furthermore, because concrete tends to stick to the wood, the wood forms cannot be removed at the end of the day. Instead, the worker must return on a second day to remove the forms after the concrete has sufficiently set up.  
         [0005]     One solution to the drawbacks of wood forming is to provide a metal form that will not be consumed during one project and can therefore be used in subsequent projects. Traditionally, these metal forms were abutted end-to-end, as was the case with the wooden forms, to accommodate lengths longer than a single form board. However, the problem with such an assembly is that without specific lengths of metal forms, it is difficult to modify the form to accommodate the various lengths necessary to build an appropriate size frame. Metal forms are not practical for small projects due to the high initial costs.  
         [0006]     Additional problems occur pouring concrete sidewalks and slabs when the concrete dries too rapidly. Workers should water the area where the concrete is going down prior to the pour, but if the ground is unusually absorbent or if the weather is excessively warm and the concrete loses its moisture content too fast it is more susceptible to cracking.  
       REFERENCES SITED  
       [0007]     More recently, U.S. Pat. No. 6,705,582 of John Osborn presented an assembly of concrete forms for use in the placement of concrete having a pair of longitudinal form members and a ground engaging member that is in contact with at least one of the longitudinal form members. A first longitudinal form member slidably overlaps a second longitudinal form member such that the length of the combination of longitudinal form members is adjustable. Inverted U-shaped channels are provided at the top of each of the longitudinal form members that allows a male/female overlapping relationship and provides a location to receive the ground engaging member. To create an angle, a corner forming bar is provided for the assembly, extending between two of the longitudinal form members. A ground engaging member with a guide slot and locking mechanism is also provided for securing the longitudinal form members in place.  
         [0008]     This patent describes a conventional style of concrete form where the surface is prepared and the forms are staked around the perimeter. Although it may save some time of installation, and is not constructed of wood, it does not offer the capability to reduce the amount of concrete required, and has no effect on the strength of the finished product.  
         [0009]     U.S. Pat. No. 6,761,345 of Willy J. Reyneveld, describes a concrete form having a first wall defining a predetermined thickness and a peripheral edge of a concrete slab, and a second wall transverse to the first wall for supporting a temporary extended border portion of the slab having a thickness less than the predetermined thickness and such that an upper surface of the slab including the temporary extended border portion is substantially flat and continuous. A process for pouring and finishing a concrete slab having at least one peripheral edge and a predetermined thickness includes providing one or more concrete forms in an arrangement defining a periphery of the slab. The form has a recessed top wall providing a support area for a temporary extended border portion of the slab having a thickness less than the predetermined thickness. The concrete is poured within the area defined by the form to a height determined by an upper edge of the form so that the temporary extended border portion of the slab is supported on the recessed top wall. The method includes surface finishing the concrete slab across the top surface thereof, extending outwardly at least to the innermost portion of the temporary extended border portion of the slab. After the concrete has hardened, the form is removed along with the temporary extended border portion.  
         [0010]     This patent describes a unique style of form primarily used in building slab construction and would not be of value in the construction of sidewalks or patio slabs. It offers no ability to reduce the amount of concrete used and has no effect on the strength of the finished product.  
         [0011]     U.S. Pat. No. 6,021,994 of Michael E. Shartzer, Jr. teaches a flexible concrete form which can be arranged to provide both straight and curved configurations, and is adapted to flex both horizontally and vertically. The form includes a face panel and upper and lower flanges having lips on their back edges. An intermediate rib spaced below the upper flange provides a ledge on which a rigid core member can be installed to enhance the rigidity for straight areas. The upper and lower flanges have aligned openings for receiving stakes used to anchor the form to the ground. The form is preferably constructed from polyethylene, polyvinyl chloride, or polybutylene because of the strength and flexibility of these materials as well as their ability to release from concrete without the need for scraping or release agents.  
         [0012]     This patent teaches of another sidewall type of concrete form that is staked around the perimeter of the desired area to retain the concrete when it is installed. None of these previous efforts, however, provides the benefits attendant with the present invention. The present invention achieves its intended purposes, objects and advantages over the prior art through a new and unique modular concrete form system.  
         [0013]     In this respect, before explaining at least one embodiment of the invention in detail it is to be understood that the invention is not limited in its application to the details of construction and to the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting.  
         [0014]     As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based, may readily be utilized as a basis for designing of other methods and systems for carrying out the several purposes of the present invention. It is important, therefore, that the claims be regarded as including such equivalent construction insofar as they do not depart from the spirit and scope of the present invention.  
       OBJECTS OF THE INVENTION  
       [0015]     An object of this invention is the provision of a device and method for paving.  
         [0016]     An additional object of this invention is improving the curing of concrete employed in slabs, sidewalks, patios, and other pavement employing concrete set in forms.  
         [0017]     The object of this invention is to simplify the process of constructing concrete sidewalks and slabs.  
         [0018]     Another object of this invention is to reduce the quantity of concrete required on concrete projects like sidewalks and slabs.  
         [0019]     Another object of this invention is to increase the strength of concrete sidewalks and slabs.  
         [0020]     Another object of this invention is to retard the drying time of the concrete used on sidewalks and slabs.  
         [0021]     Yet, another object of this invention is to decrease the preparation time required to construct concrete sidewalks and slabs.  
         [0022]     A further object of this invention is to eliminate the requirement of coming back to a jobsite to remove the forms from the concrete sidewalks or slabs.  
         [0023]     A final object of this invention is to reduce the costs involved in constructing concrete sidewalks and slabs.  
         [0024]     The foregoing has outlined some of the more pertinent objects of the invention. These objects should be construed to be merely illustrative of some of the features that are more prominent and applications of the intended invention. Many other beneficial results can be attained by applying the disclosed invention in a different manner or by modifying the invention within the scope of the disclosure. Accordingly, other objects and a fuller understanding of the invention may be had by referring to the summary of the invention and the detailed description of the preferred embodiment in addition to the scope of the invention defined by the claims taken in conjunction with the accompanying drawings.  
       SUMMARY OF THE INVENTION  
       [0025]     In some embodiments, one or more interior mold forms are used to displace material inside a structure being cast. The forms are shaped so as to provide structural integrity in the finished structure cast around them.  
         [0026]     In other embodiments, an interior mold form having ridges running in one direction on one side is used to fill the center of a structure during casting. In some embodiments, the structure is cast from concrete and the form is made from polystyrene. In some embodiments, the form is set around a re-bar grid.  
         [0027]     In additional embodiments, the interior mold form has a second set of ridges on its second side. In some embodiments, the second set of ridges runs in a cross-direction to the first. In some embodiments the ridges have semi-cylindrical or trapezoidal cross sections.  
         [0028]     In other embodiments, the form is created by machining out semi-cylindrical ridges with flat walls, separated by troughs, on one side, then on the other side of a sheet of material. In some embodiments, small holes are bored for plastic inserts to hold the form in position. In some embodiments the form is held away from re-bar to allow concrete to flow around the re-bar.  
         [0029]     In some embodiments, the resulting concrete structure, having crossed interior arch-like cells, provides strength equivalent to or greater than that of solid concrete, the displacement of concrete by the form saving weight and cost.  
         [0030]     In some embodiments, a process of concrete casting includes laying down a layer of parallel re-bar, forming a 3-D polystyrene mold, and providing the mold with plastic spacers to hold it in correct alignment to the re-bar. The form is placed over the first layer of re-bar, a second layer of re-bar is added over the mold, and the re-bar intersections are attached together. The mold and re-bar are held between sides of a mold, and concrete is poured, and allowed to harden. The external mold sides are removed, and the internal form remains in the concrete structure.  
         [0031]     In some embodiments, a mold form comprises an array of semi-spherical bumps.  
         [0032]     In some embodiments, a mold is created from an exterior volume and an interior mold form.  
         [0033]     In a particularly preferred embodiment of the disclosed device, there is a modular concrete form system that accomplishes its objectives by the use of a matrix constructed of polypropylene foam, polyethylene foam, expanded polystyrene (EPS), PVC foam, urethane foam, epoxy foam or any other foam suitable for the application. The foam matrix will consist of two sidewalls and a plurality of arched segments separated by concave troughs. The foam matrix will come in a variety of lengths with a modified tongue and groove or keyed means for interconnection to adjacent forms at the distal ends, to create as long a modular concrete form system as desired. The foam matrix can also be employed to create both longer and wider concrete forms by keying side edges also to engage adjacent cooperatively keyed edges. It must be understood at this time the explanation deals with a modified tongue and groove or keyed configuration at the ends of the foam matrix, but a similar configuration can also be employed on one or both side edges of the matrix and will fall within the scope of this patent.  
         [0034]     The foam matrix will be available in varying lengths and widths with the width determined by the number and size of arched segments. Termination units will be available to insert and can be engaged by pins or similiar means for engagement in place into the concave troughs between the two sidewalls at any locations desired to end the form system. A thin section of foam or other suitable material, having the same shape of the termination unit, can also be inserted adjacent to the termination units and left in place to work as an expansion joint when the termination units have been removed and another section is being setup to pour. An alternate mode of the termination unit and expansion joint can be a rectangular metal piece with a sharp edge to be pressed into the foam arch segments, as a means to hold it in a fixed position which would not require the pin or stake.  
         [0035]     On the underside of the foam matrix is a plurality of transverse channels with tapered sides that expand to the outer surface. Where the transverse channels and the upper concave troughs intersect, an orifice allows the fluid concrete to pass through filling the transverse channels and making contact with the ground. By minimizing the contact to the ground by the concrete and having the majority of the surface area of the concrete in contact with the foam surface, the water content of the concrete is maintained much longer than in the conventional processes where the moisture can pass into the ground through the entire lower surface. Slowing the curing time of the concrete has the result of improving quality and minimizing cracking. The unique arch in the concrete created by the arched foam segment is the key to making the concrete equal to or greater in strength than concrete constructed in a conventional manner while using considerably less concrete. The smooth surface of the arched segment and the concave troughs minimize stress risers that would precipitate cracking of the concrete material. Of course, other shapes such as octagons, rectangles, pentagons, or any shape which is calculated to handle the intended load, might be employed for the foam segment and any and all such shapes are anticipated by this application. However, the current preferred mode of the device employs the arched shape due to its superior load-bearing characteristics.  
         [0036]     To understand the theory of the unique arched segments, it is best to review the history and theory of the arch structure. It was inevitable that the arch form should dominate the early history of building as without the availability of a material capable of taking significant tensile stresses, a predominantly compressive system was the only means of forming large spans, hence early structural and architectural forms were primarily based on columns, arches, and domes. Structural efficiency is attributed to the curvature of the arch, which transfers vertical loads laterally along the arch to the abutments at each side. The transfer of vertical forces gives rise to both horizontal and vertical reactions at the abutments. The curvature of the arch and the restraint of the arch by the abutments cause a combination of flexural stress and axial compression. The arch depth, rise and configuration can be manipulated to keep stresses primarily compressive. The compressive loads on the concrete surface in the modular forming system are translated in a uniform manner to the compacted surface of the ground by the means of the transverse channels that contain concrete. A vibratory float or similar apparatus may be used to flatten the surface and aid in settling the concrete into the crevices of the matrix of the modular concrete form system. Additional strength may be added by inserting a number of pieces of steel re-bar into the concave troughs and transverse channels. The concrete in the transverse channels is allowed to extend past the edge of the sidewalk or slab increasing the structural strength of the surface while being covered with the soil adjacent to the edge of the concrete. A wide variety of concrete mixes and sizes of aggregate are available to increase the density of the concrete material resisting the compressive forces.  
         [0037]     With respect to the above description then, it is to be realized that the optimum dimensional relationships for the parts of the invention, to include variations in size, materials, shape, form, function and manner of operation, assembly and use, are deemed readily apparent and obvious to one skilled in the art, and all equivalent relationships to those illustrated in the drawings and described in the specification are intended to be encompassed by the present invention. Therefore, the foregoing is considered as illustrative only of the principles of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation shown and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the invention. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0038]     The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments of the invention and together with the description, serve to explain the principles of this invention.  
         [0039]      FIG. 1A  is a partially exposed view of a typical concrete wall being formed.  
         [0040]      FIG. 1B  is a top view of a typical concrete mold.  
         [0041]      FIG. 2A  is a side view of an embodiment of an interior mold form, according to the present invention.  
         [0042]      FIG. 2B  is a side view of an embodiment of an interior mold form, at 90 degrees to  FIG. 2A , according to the present invention.  
         [0043]      FIG. 2C  is a perspective view of an embodiment of an interior mold form and reinforcing bars, according to the present invention.  
         [0044]      FIGS. 3A through 3F  illustrate an embodiment of a process for casting concrete, according to the present invention.  
         [0045]      FIGS. 4A and 4B  are cross sections (at right angles) of an embodiment of a concrete structure, according to the present invention.  
         [0046]      FIG. 4C  is a perspective view of an embodiment of a cast structure, according to the present invention.  
         [0047]      FIG. 5  is a perspective view of an embodiment of an interior form with trapezoidal structure, according to the present invention.  
         [0048]      FIG. 6  is a perspective view of an embodiment of an interior mold form with bumps within a concrete structure cast in a horizontal inclination, according to the present invention.  
         [0049]      FIG. 7  is a perspective view of an embodiment of an interior mold form having ridges on one side within a concrete structure cast in a horizontal inclination, according to the present invention.  
         [0050]      FIG. 8  depicts an exploded perspective view of the modular concrete form system with foam matrix, the termination unit and expansion joint along with an anchor pin or stake supporting means.  
         [0051]      FIG. 9  depicts an exploded perspective view of the modular concrete form system with the alternate embodiment of a metal termination unit.  
         [0052]      FIG. 10  depicts a perspective view of the under side of the modular concrete form system.  
         [0053]      FIG. 11  depicts a side elevation of the modular concrete form system matrix.  
         [0054]      FIG. 12  depicts an end view of the modular concrete form system matrix.  
         [0055]      FIG. 13  depicts an end view of the termination unit.  
         [0056]      FIG. 14  depicts a section through one of the arched segments illustrating the compressive stresses involved when forces are exerted on the surface of the concrete.  
         [0057]      FIG. 15  depicts a perspective view of a simpler version of the modular concrete form system which provides for interlocking with adjacent matrix units create a form for cementitious material. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0058]     For a fuller understanding of the nature and objects of the invention, reference should be had to the following detailed description taken in conjunction with the accompanying drawings which are incorporated in and form a part of this specification, illustrating embodiments of the invention serve to explain the principles of this invention.  
         [0059]      FIG. 2A  is a side view of an embodiment of an interior mold form, according to the present invention. In some embodiments, form  200  is cut from a thin block (a right rectangular prism) having two large flat faces (sides). Because many structures are walls (or wall-like), it is convenient to describe embodiments of form  200  in terms of constructing walls. However, those skilled in the art will recognize that form  200  can be applied to many different structures of different shapes and sizes.  
         [0060]     In some embodiments, form  200  will resemble a relatively thin sheet, having two major sides (surfaces). For purposes of illustration, an x-axis, which will be “horizontal” in some embodiments, is defined along one side of form  200 , parallel to its surface. A y-axis, which will be “vertical” in some embodiments, is defined along the other long side of form  200 , parallel to that surface, and perpendicular to the x-axis. A z-axis is defined through form  200 , being normal to the surfaces (sides). While the terms “horizontal” and “vertical” are used to illustrate embodiments, because typical vertical walls are commonly cast, such terms are not intended as limiting. In application, embodiments of form  200 , related processes, and structures in which it is used, may take on many shapes, orientations, and contours, which may or may not be symmetric, planar, or aligned with gravity.  
         [0061]     As shown in  FIG. 2A  (looking along the x-axis at the y-z plane), in some embodiments, one face  201  of form  200  has roughly semi-cylindrical ridges  202  running along the x-axis. The term “semi-cylindrical” is to be broadly interpreted, and includes sections of a cylinder of different lengths and angular extent, as shown in  FIG. 2A . Base  203  of each ridge  202  extends the shape of ridge  202  beyond a half cylinder, giving it a cross section, which is roughly a hemisphere with a rectangular base, an arch-shape. In some embodiments, ridges  202  are separated by troughs  204 , which also run along the x-axis. Troughs  204  may be different shapes, for example, roughly rectangular or curved around the re-bar.  
         [0062]      FIG. 2B  is a side view of an embodiment of an interior mold form, at 90 degrees to  FIG. 2A , according to the present invention. As shown in  FIG. 2B , second face  205  of form  200  has ridges  206  running along the y-direction. Similar to first face  201 , ridges  206  have base portions  207 , and troughs  208  separate ridges  206 . Thus, looking in the z-direction the x and y ridges  202 ,  206  and x and y troughs  204 ,  208  cross. In some embodiments, troughs  204  and  208  are deep enough (i.e., bases  203  and  207  are deep enough) such that they intersect inside form  200 .  
         [0063]      FIG. 2C  is a perspective view of an embodiment of an interior mold form and re-bar, according to the present invention. Intersections  220  of x-troughs  204  and y-troughs  208  form holes  220 , substantially extending through form  200 .  
         [0064]     Referring to  FIGS. 1, 2A , and  2 B, when concrete is to be cast around re-bar  106  and  108 , horizontal re-bar  106  lies in troughs  204 , and vertical re-bar  108  lies in troughs  208 , crossing at intersections  220  of  FIG. 2C . Because intersections  220  extend through form  200 , re-bar  108  and  106  can be tied (if desired) through intersections  220 . In some embodiments wire ties are used. As those skilled in the art will recognize, a tying machine with a long nose can be used to facilitate tying. Those skilled in the art will also recognize that not every intersection of re-bar  106  and  108  needs to be tied.  
         [0065]     Referring to  FIGS. 2A and 2B , in some embodiments, holes  210  are formed in form  200 . In some embodiments, holes  210  are formed by cutting into form  200  along lines  212 , because holes  210  may be longer than a conventional drill bit. Holes  210  can be cut along x and y directions or along any other convenient directions through form  200 .  
         [0066]     In some embodiments, plastic rods  214  are inserted in holes  210  of form  200  to aid in positioning form  200  with respect to re-bar  106  and  108 . Plastic rods  214  can stop form  200  from sliding too far onto re-bar  106  or  108 . Plastic rods  214  can also supply means of tying form  200  onto re-bar. In some embodiments, rods  214  are not used, and in some embodiments there are fewer rods than pieces of re-bar  106  and  108 .  
         [0067]     In some embodiments, form  200  is made from 2-lb polystyrene. 2-lb polystyrene has desirable compression (approximately 20 pound per square-inch) and machining properties. Form  200  is stiff enough to resist being crushed by the mass of concrete. Depending on the scale of the casting to be performed other weights of polystyrene may be acceptable, if they provide sufficient compression resistance. In some embodiments, form  200  is made from other lightweight, inexpensive materials, such as fiberglass, composite carbon/graphite, plastic, or other weights of polystyrene. For casting materials other than concrete, form  200  may be formed from materials resistant to adverse conditions during casting (e.g., extreme pressure, chemical damage, high temperatures).  
         [0068]     In some embodiments, form  200  is cut from a 3 by 4 by 8-foot block of 2-lb polystyrene. Billets are typically manufactured in 3 by 4 by 24-foot sizes, and 8-foot lengths are convenient to cut from such a billet (also being roughly the size of typical freeway sound barrier segments). Of course, different applications will require different sizes and shapes of concrete castings, so given dimensions are exemplary. As an example of relative dimensions, in some embodiments form  200  is 3 9/16-inches thick. Ridges  202 ,  206  (and therefore troughs  204 ,  208 ) have a period of 4-inches. Each ridge  202 ,  206  has a semi-cylindrical diameter of 2⅞-inches (radius of 1 7/16-inches) and a  7 / 8 -inch base height, for a total height of 2½-inches. Each trough has a width of 1⅛-inches and a depth of 2½-inches (leaving 1 1/16-inches of material). For a form of these exemplary dimensions, external mold sides  102  are placed so as to create a thickness of 11/16-inch of concrete between each of mold sides  102  and form  200 .  
         [0069]      FIGS. 3A through 3F  illustrate embodiments of a mold and a process for casting concrete, according to the present invention. In  FIG. 3A , form blank  200 ′ is ready to be cut into form  200 .  
         [0070]     In  FIG. 3B , form  200  is shown after ridges  202  and troughs  204  have been machined into it. It has also been provided with plastic rods  214 .  
         [0071]     In  FIG. 3C  vertical pieces of re-bar  108  are set up and form  200  is inserted over them. Horizontal re-bar  106  is added, and (if desired) ties  110  are applied.  
         [0072]      FIG. 3D  shows the completed form and rebar.  
         [0073]      FIG. 3E  shows the completed form  200  and rebar  106 ,  108  inserted between mold barriers  102  to form mold  300 . Those skilled in the art will appreciate that all sides of mold  300  are sealed with additional plywood, plastic sheets, earth, previously cast sections, or another material to prevent mix  120  from leaking out.  
         [0074]      FIG. 3F  illustrates material  120  poured into mold  300 , around form  200 .  
         [0075]     While a vertical mold is exemplary, it is well known to those skilled in the art, that walls for concrete buildings can be cast in a horizontal orientation, on the ground, before being raised into a vertical position. In such a process, all the re-bar (and the x- and y-axis) would be literally horizontal during casting and curing. However, it is convenient to refer to re-bar  106  and  108  as being “vertical” or “horizontal,” and such terms are not intended as limiting.  
         [0076]     By means of using form  200 , a concrete structure can be created, which is lighter than a solid concrete structure of equal size and strength.  
         [0077]     Those skilled in the art will recognize that mold  300  and form  200  need not be rectangular as they can be oval or oddly shaped. Further, those skilled in the art will recognize that mold  300  and form  200  need not be planar, although many applications use planar shapes. Given that modern architecture makes use of many curved and irregular surfaces, embodiments of form  200 , mold  300 , and the molding process will make use of forms and molds of many different shapes, sizes, and contours.  
         [0078]     Further, those skilled in the art will recognize that while re-bar  106  and  108  are commonly used in concrete structures, re-bar is not essential to all embodiments of casting processes or resulting structures. Therefore, in some embodiments of the device herein disclosed, there is no re-bar. In some embodiments, structural integrity is reinforced by means other than inserting re-bar  106  and  108  (e.g., inserting graphite fibers).  
         [0079]      FIGS. 4A and 4B  are cross sections of an embodiment of a concrete structure, according to the present invention.  FIG. 4A  is an x-z view of concrete structure  400 . Half  410  of structure  400  can be seen to have chambers  412  running through it in the y-direction. In some embodiments, form  200  is left in-place after casting concrete  120 , so that form  200  remains in chambers  412 . Similarly, half  420  of structure  400  can be seen to have chambers  422  running through it in the x-direction, also filled with form  200 .  
         [0080]     While chambers  412  and  422  are not filled with concrete, the arched semi-cylindrical shape of chambers  412  and  422  bear stresses within structure  400  more efficiently than solid concrete. Because chambers  412  and  422  are crossed, each of the halves  412  and  422  resists stresses along the different axis. Therefore, the double-arched hollows within structure  400  provide superior strength to solid concrete. Further, by creating structures of lighter weight, each structure in, for example a building, needs to support less weight of itself and other structures, thereby making the entire building more efficiently constructed, than if it were made of solid walls.  
         [0081]      FIG. 4C  is a perspective view of an embodiment of a cast structure, according to the present invention. As in  FIGS. 4A and 4B , it can be seen that structure  400  is formed with interior arches  413  on side  410  running in the y direction and with arches  423  on side  420  running in the x direction.  
         [0082]      FIG. 5  is a perspective view of an embodiment of an interior form with trapezoidal structure, according to the present invention. Referring to  FIGS. 2-4 , some embodiments make use of arch-shaped, semi-circular ridges  202 ,  206  in form  200 , forming arches  412 ,  423  in structure  400 . Interior mold form  500  (shown in  FIG. 5 ) makes use of trapezoidal ridges  502  (having trapezoidal cross-sections). Similar to the semi-circular arch shapes in ridges  202 ,  206  of form  200 , the trapezoidal shape of ridges  502  of form  500  also provides strength in the resulting structure. Those skilled in the art will recognize other ridge configurations that may differ in geometry (e.g., geodesic), but which perform the function of providing structure  400  with material strength y providing a stable internal structure.  
         [0083]      FIG. 6  is a perspective view of an embodiment of an interior mold form with bumps within a concrete structure cast in a horizontal inclination, according to the present invention. Mold form  600  includes hemispherical bumps  602 , which displace material  120  during casting. In some embodiments, mold form  600  is used to cast concrete for roadways. The shape of bumps  602  results in the formation of arches in the resulting structure. In some embodiments, bumps  602  are on one side of form  600 . In some embodiments form  600  is used for horizontal structures (e.g., roads, counter-tops), where the structure is designed to bear the vertical stress of  1  objects pressing down on it.  
         [0084]     In some embodiments, form  600  includes base  610 , having thickness  612 . In some embodiments, thickness  612  is made thick enough to provide convenient strength to mold form  600  for handling and transportation. In some embodiments, thickness  612  is very thin, only thick enough to hold bumps  602  in place during casting. In some embodiments thickness  612  vanishes, and bumps  602  are held in place by wires, rods, or other means, or held in place by friction against the surface under them. In some embodiments, bumps  602  are an array of discrete interior forms.  
         [0085]     In some embodiments, material  120  is cast around form  600  and re-bar  106  and  108 . In some embodiments, lower layer  620  of material  120  has a thickness of approximately 2-inches, form thickness  612  is approximately 2-inches, making form and upper layer  622  of material  120  approximately 12 inches thick. Total thickness  624  is approximately 16-inches.  
         [0086]     In some embodiments, a structure, such as a roadway, is formed by preparing the ground, then pouring a thin layer of concrete. Form  600 , along with rebar  106 , is placed on top of the first layer of concrete, and a thicker main layer is poured.  
         [0087]      FIG. 7  is a perspective view of an embodiment of an interior mold form having ridges on one side within a concrete structure cast in a horizontal inclination, according to the present invention. In some embodiments, material and weight can be saved by using an interior form  700  with ridges  702  on only one side  704 . Provided that the structure cast with form  700  will have sufficient strength for its intended purpose (while having an asymmetric interior structure) mold form  700  is simple to make and will save on material costs. Referring to  FIGS. 2A-2B , in some embodiments ridges  702  are semi-circular, arch shaped. Referring to  FIG. 5 , in some embodiments ridges  702  are trapezoidal. In some embodiments, ridges  702  have other structural cross sections, shapes, or contours.  
         [0088]      FIG. 8-15  depicts an exploded perspective view of another particularly preferred mode of the disclosed invention herein featuring a modular concrete form system  10  with the foam matrix  12 , a termination unit  14  and expansion joint  16  along with an anchor pin  18  or wood stake  20  or similiar elongated member for use as a supporting means. This embodiment is particularly easy to use by both trained and untrained workers and would provide great utility to homeowners who are unfamiliar with the concrete forming process. Employing a number of matrixes, the construction of a form to pour a sidewalk or patio or other paving type construction, is made easier for a professional familiar with the process, and well within reach of the novice or homeowner unfamiliar with constructing form. The foam matrix  12  will be constructed of polypropylene foam, polyethylene foam, Styrofoam, PVC foam, urethane foam, epoxy foam or any other foam suitable for the application. A quantity of anchor pins  18  or wood stakes  20  or other means to secure all the matrix  12  and engaging components in place will be generally required. The anchor pins  18  will also be used to anchor the termination units  14  into position at the end of the structure or the end of a portion of the structure to be poured.  
         [0089]     The foam matrix  12  employs two sidewalls  22  and  24  preferably with beveled edges  26  communicating between the top edge  30  of the sidewall  22  and the planar surface  28  on the exterior of the sidewall  22  and the interior of the sidewall  22 . The thickness of the finished cast structure is determined by the height of the sidewalls  22  and  24 . In an embodiment of the device  10  somewhat less functional but still an improvement, the sidewalls  22  and  24  might be left of the matrix  12  and wooden or other structural members employed instead. While not as functional as providing built-in sidewalls, this embodiment would still provide the aforementioned benefits of the arched matrix  12  engaged with the layered concrete.  
         [0090]     The top side of the matrix  12  has disposed on it, a plurality of arched segments  32  separated by concave troughs  34  and are used to create the central cavity  36  of the foam matrix  12 . The width of the foam matrix  12  will be determined by the number and diameter of the arched segments  30 . The foam matrix  12  will come in a variety of lengths and widths with a modified tongue  38  and groove  40  or other cooperatively engaging connection means  42  at the distal ends  44  and  46  of the matrix  12  to connect it to an adjacent matrix  12  to thereby create as long a modular concrete form system  10  as desired. While a keyed, or tongue and groove means of engagement of adjacent matrix components is shown, those skilled in the art will realize that other configurations that engage adjacent matrix units can be employed and all such means of engagement are anticipated. An angular recess  48  and an angular extension  50  form the current preferred mode of the locking portion of the connection means  42  and they are placed inline with the arched segments  32  and the sidewalls  22  and dimensioned in a fashion to continue both when joined to an adjacent matrix  12  and the smooth planar surfaces  28  as well as the smooth exterior surface of the arched segments  32 .  
         [0091]     On the underside  52  of the foam matrix  12  are a plurality of transverse channels  54  which in the current preferred mode have tapered sides  56  that expand to the underside outer surface  58 . Where the transverse channels  54  and the upper concave troughs  34  intersect, a plurality orifices  60  provide a means for communication of the fluid concrete from the troughs  34  to the travers channels  54  thereby filling the transverse channels  54  with concrete during the pour, and providing contact with the ground to the concrete to support the overhead structures.  
         [0092]     The termination units  14  will be constructed of polypropylene foam, polyethylene foam, Styrofoam, PVC foam, urethane foam, epoxy foam or any other foam suitable for the application. The termination unit  14  will have two distal ends  62  and  64  that fit tightly between the internal planar surfaces  28  of the sidewalls  22  and  24  of the foam matrix  12  when fixed into position. A plurality of concave trough mating segments  66  seal the concave troughs  34  between the arched segments  32 . The top surface  68  of the termination unit  14  will be flush with the top edges  30  of the sidewalls  22  and  24  when properly fixed in position to allow for the purpose of finishing the concrete surface along all of the edges. The expansion joint  16 , if employed, will have a similar configuration to the termination units  14  with distal ends  70  and  72  along with a plurality of concave trough mating segments  74 .  
         [0093]     An alternate embodiment of a termination unit  14  shown in  FIG. 9  is also employed as an expansion joint  16  and consists of a rectangular sheet of galvanized metal  76  with a sharp edge  78  and distal ends  80  and  82  that can be pressed down into the arched segments  32  with the top surface  84  either flush or below the top edges  30  of the matrix  12 . This sheet of galvanized metal  76  may also be used in a similar fashion as a substitute for the termination units  14  to be inserted at each end of the concrete pour and also may be used intermittently along the length of the pour as expansion joints  16 .  
         [0094]      FIG. 10  depicts a perspective view of the matrix underside  52  displaying the plurality of transverse channels  54  and the orifices  60  created by the intersection of the concave troughs  34 . The orifices  60  allow the fluid concrete mixture to flow into the transverse channels  54  extending past the matrix sidewalls  22  and  24  into the subsoil  86 .  
         [0095]      FIG. 11  depicts a side elevation of the foam matrix  12  illustrating the sidewall  22  with the connection means  42  having a tongue  36  and angular recess at the distal end  46  and the mating groove  40  and angular extension  50 . Along the top edge  30  is a beveled edge that extends the full length of the sidewall  22 . A plurality of transverse channels  54  are shown with tapered sides  56  along the matrix underside  52 .  
         [0096]      FIG. 12  depicts an end view of the matrix  12  illustrating the two sidewalls  22  and  24  with the plurality of arched segments  32  separated by the concave troughs  34 .  
         [0097]      FIG. 13  depicts an end view of the termination unit  14  and how it mates with the foam matrix  12  by having the concave trough mating segments  66  fill the gaps of the concave troughs  34 . The distal ends  62  and  64  of the termination unit  14  fit tightly against the matrix sidewall internal surfaces  28  with the top surface  68  flush with the top edges  30  of the matrix sidewalls  22  and  24 . Once the cement has set sufficiently for the form composed of matrix  12  segments to be removed about the perimeter of the formed concrete structure, the sidewalls  22  being formed of foam or other aforementioned material, may be broken off to leave just the concrete surface at ground level. The sidewalls  22  and  24  may also be rendered easily frangible by the addition of a serration or thin perforation or slit  23  at a base edge which does not go completely through the sidewall, to provide an easy and clean separation from the rest of the matrix  12  once the concrete is cured sufficiently. When placed on the outside edge, there is virtually no loss of strength to hold the cementitious material inside.  
         [0098]      FIG. 14  depicts a section through one of the arched segments  32  illustrating the compressive stresses involved when forces  88  are exerted on the surface  90  of the concrete  92  and transfers vertical loads laterally along the arch to the area of the concave trough  34  at each side. The transfer of vertical forces gives rise to both horizontal and vertical reactions in these areas. The curvature of -the arched segments  32  and the restraint of the arch by the concave troughs  34  cause a combination of flexural stress and axial compression  94 , which is then conducted through the concrete in the orifices  60  to the concrete within the transverse channels  54  and then onto the compacted subsoil  86 . A segment  96  of the concrete  92  from the transverse channels  54  extends past the sides  98  of the finished portion to be covered with the surface soil  99 .  
         [0099]     Finally, as noted above, in a simpler embodiment which does not offer the utility of a material core formed into the cured cementitious material,  FIG. 15  depicts a perspective view of the modular concrete form system which provides for means to engage one end of the foam matrix  12  with the other end of an adjacent foam matrix  12 . The means for cooperative engagement shown is a tongue  38  and groove  40  which would overlap and form a planar bottom surface surrounded by sidewalls  22  and  24  and endwalls  62  which would be adapted for engagement on both ends. Also shown is the noted optional perforation or slit  23  which would allow for easy removal of the sidewalls  22  and  24  in the unitary structure form of the matrix  12  once the cementitious material has cured sufficiently. While this embodiment of the device lacks the arched segments  32  disposed on the top side of the sheet of material forming the matrix  12  it could still have the traverse channels  54  communicating through the orifices  60  or in an even simpler version, could eliminate the transverse channels  54  also. While eliminating both of the preferred structures of the channels  54  and the arched segments  32  would eliminate the aforementioned utility and benefits thereof, the interlocking matrix  12  even in such a simple embodiment would yield great utility especially to inexperienced people wishing to form sidewalks and patios since they need only interlock the matrixes and then pour in the cementitious material.  
         [0100]     While concrete casting is exemplary of some embodiments of the present invention, those skilled in the art will recognize that embodiments of the forms and processes herein described are also applicable to other materials on larger or smaller scales. Such materials may include structural plastics, graphite epoxies, metals, and many other materials, where it is desirable to reduce the volume of material required to form a completed structure.  
         [0101]     Additionally, the method and apparatus for casting structures employing the modular concrete form system shown in the drawings and described in detail herein, discloses arrangements of elements of particular construction and configuration for illustrating preferred embodiments of structure and method of operation of the present invention. It is to be understood, however, that elements of different construction and configuration and other arrangements thereof, other than those illustrated and described may be employed for providing a modular concrete form system in accordance with the spirit of this invention, and any and all such changes, alternations and modifications, as would occur to those skilled in the art, are considered to be within the scope of this invention as broadly defined in the appended claims.  
         [0102]     Further, the purpose of the foregoing abstract is to enable the U.S. Patent and Trademark Office and the public generally, and especially the scientists, engineers and practitioners in the art who are not familiar with patent or legal terms or phraseology, to determine quickly from a cursory inspection the nature and essence of the technical disclosure of the application. The abstract is neither intended to define the invention of the application, which is measured by the claims, nor is it intended to be limiting as to the scope of the invention in any way.