Ceramic blocks for enhanced passive cooling performance

Abstract

A block of at least one material with thermally insulative and passive cooling properties is described. The block of at least one material may be fabricated through extruding, foaming, additively manufacturing, casting, or a combination thereof of the at least one material from a design of the block of the at least one material. The design can use a parametric model, geometrical analysis, thermal analysis, and then further generates iterative models for parameter optimization. Also described herein is a computer-implemented method of designing the block of at least one material.

Description

Docket No. 0050.2403001 (MIT-26094)Ceramic Blocks For Enhanced Passive Cooling PerformanceRELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 694,144, filed on September 12, 2024. The entire teachings of the above application(s) are incorporated herein by reference.BACKGROUND

[0002] With almost two trillion units sold globally annually, concrete and ceramic blocks are a ubiquitous wall construction system in residential buildings, particularly in regions where alternative materials such as timber or steel are less available [1], In their most basic form as hollow concrete blocks or solid clay bricks, these masonry elements typically embody large quantities of carbon due to the use of cement as a binding material or high- temperature firing processes during fabrication. Moreover, concrete and ceramics’ high thermal conductivity compromises the blocks’ ability to minimize heat gains or losses through building envelopes, requiring additional insulative materials to ensure thermal comfort for occupants and reduce operational energy consumption.SUMMARY

[0003] Described herein is a block of at least one material that includes an inner region of the at least one material and defining an inner face, an outer region of the at least one material defining an outer face, and a lattice region of the at least one material between the inner face and outer face defining a two-dimensional lattice structure with a varying density (kg / m3) across a depth of the lattice region of the at least one material, wherein the lattice structure is distributed asymmetrically between the inner region having a higher density than the outer region. In some instances, the lattice structure of the block of at least one material defines at least one cavity having a different thermal conductivity from the at least one material. In some other instances, the block of at least one material may be used as construction material for buildings that provides both thermal insulation and passive cooling performance. In some further instances, the at least one material is used at a reduced amount compared to blocks of comparable thermal insulation.- 1 -4212823. vlDocketNo. 0050.2403001 (MIT-26094)

[0004] Also described are methods of making the block of at least one material. In some instances, the method extrudes, foams, additively manufactures, casts, or a combination thereof of the at least one material from a design of the block of the at least one material, forms an inner region of the at least one material defining the inner face, forms an outer region of the at least one material defining the outer face, forms a lattice region of the at least one material between the inner face and outer face defining a two-dimensional lattice structure with a varying density (kg / m3) across a depth of the lattice region of the at least one material, wherein the lattice structure is distributed asymmetrically between the inner region having a higher density than the outer region, to thereby form the block of at least one material. The design of the block of at least one material may be generated as a function of: i) a parametric model of a plurality of asymmetrical geometrical designs for minimizing weight (kg / m2) of walls of the block of at least one material and maximizing interior areal heat capacity (kJ / m2K) of walls of the block of at least one material, ii) a geometrical analysis with fixed and variable parameters of the parametric model, iii) a thermal analysis of the parametric model, with the thermal analysis generated as a function of: 1) a thermal resistance circuit in-series, a thermal resistance circuit in-parallel, and a plurality of materials, 2) an R-value and a total aspect ratio from the thermal resistance circuit in-series, the thermal resistance circuit in-parallel and the plurality of materials, 3) a plurality of layer matrices and a plurality of heat transfer matrices, and 4) an interior areal heat capacity for a plurality of from the plurality of layer matrices and the plurality of heat transfer matrices, and iv) the design further generated through an iterative parametric model, iterative geometrical analysis, and iterative thermal analysis to achieve an average thermal conductivity from about 0.05 W / mK to about 0.3 W / mK for a design for the block of at least one material.

[0005] Also described herein is a computer-implemented method of designing the block of at least one material that a) defines a parametric model of a plurality of asymmetrical geometrical designs for minimizing weight (kg / m2) of walls of the block of at least one material and maximizing heat capacity (kJ / m2K) of walls of the block of at least one material, b) performs a geometrical analysis with fixed and variable parameters of the parametric model, c) performs a thermal analysis of the parametric model with the thermal analysis i) defines a thermal resistance circuit in-series, a thermal resistance circuit inparallel, and a plurality of materials, ii) determines an R-value and a total aspect ratio from the thermal resistance circuit in-series, the thermal resistance circuit in-parallel and the plurality of materials, iii) defines a plurality of layer matrices and a plurality of heat transfer- 2 -4212823. vlDocket No. 0050.2403001 (MIT-26094) matrices, and iv) determines an interior areal heat capacity for a plurality of from the plurality of layer matrices and the plurality of heat transfer matrices, and d) repeats (a)-(c) to achieve an average thermal conductivity from about 0.05 W / mK to about 0.3 W / mK for the block of at least one material.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.

[0007] FIG. l is a summary of the example activities within the proposed shapeoptimization method and their associated sections.

[0008] FIG. 2A shows a diagram of a baseline geometry for the R-value calculation.

[0009] FIG. 2B shows a diagram of the proposed method that uses a parallel-series configuration to determine its upper and lower bounds. The final R-value results from a weighted average of both values.

[0010] FIG. 3 A is a diagram of a baseline geometry of an air cavity.

[0011] FIGs. 3B-D show air cavities with a higher aspect ratio ARtot present more resistance to a lateral heat transfer, resulting in higher R-values for a given amount of material. AFG, determines the values for wl and w2 following the bounds in equations 12-15.

[0012] FIG. 4A shows a baseline geometry of a block of two different materials that uses the standard ISO 13786 as a baseline.

[0013] FIG. 4B shows the proposed heat capacity calculation method and applies a layer homogenization process for discretizing multi-material components.

[0014] FIG. 4C shows the proposed heat capacity calculation method and applies a heat transfer matrix to the calculation.

[0015] FIG. 5A is a diagram of the numerical calculation for the heat capacity that is conducted using the definitions for thermal admittance included in ISO 13786.

[0016] FIG. 5B is a diagram of the numerical calculation for the heat capacity that is conducted using the definitions for periodic thermal transmittance included in ISO 13786.

[0017] FIG. 6 is a graph showing the results from the Multi-Objective Optimization (MOO) process for the design of extruded ceramic blocks with minimal weight [kg / m2] and maximum heat capacity [kJ / m2K]. The bi-objective plot reveals a large set of block- 3 -4212823. vlDocketNo. 0050.2403001 (MIT-26094) geometries with higher heat capacity (and, in many cases, higher time constant) and lower weight than the reference baseline block.

[0018] FIG. 7 is a graph that shows the results from the MOO process for the design of 3D-printed earthen walls with minimal weight [kg / m2] and maximum heat capacity [kJ / m2K], The bi-objective plot reveals a large set of wall geometries with higher heat capacity (and, in many cases, higher time constant) and lower weight than the reference 10 cm solid wall.

[0019] FIG. 8A is a picture of a prototype fabrication from locally sourced construction waste soils used as feedstock for extrusion based large scale additive manufacturing.

[0020] FIG. 8B is a picture of air temperature, humidity, and surface temperature sensors placing within each of the three cylindrical prototypes.

[0021] FIG. 8C is a picture of data collection during two months within a shaded, unconditioned space in Santa Barbara, CA. Heat flow occurs primarily across the earthen walls - two six inch XPS boards are placed in the top and bottom surfaces to create near- adiabatic surfaces.

[0022] FIG. 9 is a graph showing temperature measurements within each cylindrical prototype relative to the outdoors conditions in Santa Barbara, CA from April 13thto April 19th, 2024. As observed, the ability to dampen temperature fluctuations and time shifting its peak values improves as the time constant increases.

[0023] FIG. 10 is a graph showing the results from the Fast Fourier Transform (FFT) for the measured temperature data. As observed, the daily frequency is the dominant frequency, which is used to experimentally derive the prototype’s time constant.

[0024] FIG. 11 A is an image of design of the baseline prototype that was conducted using the thermal analysis method presented herein and accounting for the tool pathing of the robotic arm.

[0025] FIG. 1 IB is an image of the design of the Thermal Ring 1 prototype that was conducted using the thermal analysis method presented herein and accounting for the tool pathing of the robotic arm.

[0026] FIG. 11C is an image of the design of the Thermal Ring 2 prototype that was conducted using the thermal analysis method presented herein and accounting for the tool pathing of the robotic arm.

[0027] FIG. 12A is an image of seven geometries with constant weight that are explored across one block topology (extruded) with varying geometric properties: void aspect ratio and distribution, and inner wall thickness(es).- 4 -4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0028] FIG. 12B image of three geometries with constant weight that are explored across one block topology (foamed) with varying geometric properties: void aspect ratio and distribution, and inner wall thickness(es).

[0029] FIG. 13 shows the R-value prediction vs numerical simulation plot. The example series-parallel model presented herein stays within a ±15% error relative to the values from the FEA simulation, which range from 0.57 m2K / W to 2.23 m2K / W.

[0030] FIG. 14 shows heat capacity prediction versus numerical simulation plot. The series-parallel model stays within a ±15% error relative to the values from the FEA simulation, which range from 39 kJ / m2K to 91.5 kJ / m2K.

[0031] FIG. 15 is a flowchart depicting a method for designing a block of at least one material.

[0032] FIG. 16 is a schematic view of a computer network or similar digital processing environment in which embodiments of the present invention may be implemented.

[0033] FIG. 17 is a block diagram of an example internal structure of a computer in the environment of FIG.16.DETAILED DESCRIPTION

[0034] A description of example embodiments follows.Abbreviations

[0035] A area (m2)

[0036] AR aspect ratio (-)

[0037] d thickness (m)

[0038] D total depth (m)

[0039] e void-to-solid ratio (-)

[0040] E exponent

[0041] H height (m)

[0042] J objective function

[0043] k thermal conductivity (W / mK)

[0044] P penalty function

[0045] q heat flux (W / m2)

[0046] P design load in compression (kN)

[0047] Q total heat flow rate (W)- 5 -4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0048] R thermal resistance (m2K / W)

[0049] T period of analysis (s)

[0050] U overall heat transfer coefficient (W / m2K)

[0051] V volume (m3)

[0052] V air volume flow (kg / m3)

[0053] w function weight

[0054] W width (m)

[0055] Ymm thermal admittance (W / m2K)

[0056] Ymn periodic thermal transmittance (W / m2K)

[0057] Z heat transfer matrix

[0058] c specific heat (J / kgK)

[0059] 5 penetration depth (m)

[0060] s emissivity (-)

[0061] ratio of layer thickness to penetration depth

[0062] Kin areal heat capacity (J / m2K)

[0063] Gallow material’s allowable stress (N / mm2)

[0064] T time constant (s)

[0065] p density (kg / m3)

[0066] e temperature (K)

[0067] w angular frequency

[0068] Subscripts

[0069] e equivalent

[0070] i design i

[0071] m mean

[0072] t total

[0073] As used herein “about” means within an acceptable error range for the particular value, as determined by one of ordinary skill in the art. Typically, an acceptable error range for a particular value depends, at least in part, on how the value is measured or determined, e.g., the limitations of the measurement system. For example, “about” can mean within an acceptable standard deviation, per the practice in the art. Alternatively, “about” can mean a range of ± 20%, e.g., ± 10%, ± 5% or ± 1% of a given value. It is to be understood that the term “about” can precede any particular value specified herein, except for particular values used in the Exemplification.4212823. vlDocketNo. 0050.2403001 (MIT-26094)Block of at least one material

[0074] Described herein are blocks of at least one material that possess thermal insulating and passive cooling characteristics. In general, blocks of at least one material include an inner region of the at least one material that defines an inner face, an outer region of the at least one material that defines an outer face, and a lattice region of the at least one material between the inner face and outer face defining a two-dimensional lattice structure with a varying density (kg / m3) across a depth of the lattice region of the at least one material, wherein the lattice structure is distributed asymmetrically between the inner region having a higher density than the outer region. Further, these features are applicable to all embodiments described herein.

[0075] The term “inner region,” “inner face,” “outer region,” and “outer face” are all used to distinguish a region or face of the block that is being described throughout the present disclosure. Due to the asymmetric design of the blocks described herein, these terms are used to distinguish / identify portions of the blocks. In some instances, the “inner face” or “inner region” has more of the at least one material density compared to the “outer face” or “outer region.” When used for construction, the alignment of the “inner face” and “outer face” plays a role in the characteristics of the blocks. In some instances, the “inner face” is oriented on the interior side of the construction (i.e. interior of a building) and the “outer face” is oriented on the exterior side of the construction (i.e. exterior of the building), which allows for keeping the interior of the construction to maintain a lower temperature than the exterior when the exterior is warmer than the interior and maintain a higher temperature in the interior compared to the exterior when the exterior is cooler than the interior. The orientation of the block may be reversed as desired when used for construction depending on the needs of the building and does not limit the “inner face” and “outer face” to be oriented to the interior and exterior of a construction, respectively.

[0076] In some instances, the block of at least one material defines a lattice structure with the at least one material and at least one cavity, wherein the at least one cavity has a different thermal conductivity from the at least one material. The term “cavity” is referring to a section, area, region, or a combination thereof where the at least one material of the block changes to either a different material or a void within the block. The term “void” is referring to hollowed space within the block that is filled with either another material, a liquid, a gas, or a combination thereof. In some instances, the at least one cavity is at least one void. In some further instances, the at least one void contains a gas or an insulative material. In some- 7 -4212823. vlDocket No. 0050.2403001 (MIT-26094) instances, the gas is air. In some other instances, the insulative material may be fiber glass, expanded polystyrene (EPS), mineral wool, extruded polystyrene (XPS), perlite, cellulose, or any combination thereof. In some instances, the insulative material may be fiber glass. In some other instances, the at least on void can form an asymmetric void distribution across the lattice structure.

[0077] In some instances, the block of at least one material may have an average thermal conductivity from about 0.05 W / mK to about 0.3 W / mK. In some other instances, the R- value of the block of at least one material may be about 10% to about 130% compared to a baseline block. The term “baseline block” refers to block design that is currently used and is not asymmetrical. The R-value is also dependent upon the material used in the block. In some instances, the block of at least one material has a higher heat capacity than the baseline block for a given amount of material. In some instances, the block of at least one material may have an interior areal heat capacity Kin (as defined in ISO 13786) from about 25 kJ / m2K to about 75 kJ / m2K per 100 kg of the at least one material.

[0078] In some instances, the at least one material may be an earthen material, a cementitious material, fiber glass, expanded polystyrene (EPS), mineral wool, extruded polystyrene (XPS), perlite, cellulose, ceramics, glass, concrete, metals, metal alloys, high- density polymers, or a combination thereof. In some further instances, the at least one material may be an earthen or cementitious material. In some further instances, the at least one material may be ceramic, concrete, or earthen soil. In some further instances, the at least one material may be deposited by additive manufacturing to form the block of at least one material. In some other instances, the at least one material may be deposited by foaming to form the block of at least one material.

[0079] The characteristics of this section “Block of at least one material” is applicable to at least the sections of “Method of Making a Block of at least one material,” “Method of Designing a Block of at least one material,” and “Applications and Uses” of the present disclosure.Method of Making a Block of at least one material

[0080] This disclosure also pertains to methods of making a block of at least one material. The block of at least on material may be produced by extruding, foaming, additively manufacturing, casting, or a combination thereof of the at least one material from a design of the block of at least one material. This may form an inner region of the at least one material- 8 -4212823. vlDocketNo. 0050.2403001 (MIT-26094) defining an inner face, an outer region of the at least one material defining an outer face, and forms a lattice region of the at least one material between the inner face and outer face defining a two-dimensional lattice structure with a varying density (kg / m3) across a depth of the lattice region of at least one material. The lattice structure may be distributed asymmetrically between the inner region having a higher density than the outer region.

[0081] The term “extruding” is referring to pushing or thrusting the at least one material through an opening or mold to take shape of the opening or mold by shaping though applied pressure. The term “foaming” is referring to adding a foaming agent (i.e. a surfactant) to an at least one material (i.e. a concrete mix) to create bubbling within the at least one material creating at least one cavity within the at least one material when solidified. The term “additive manufacturing” may be used interchangeably with 3D-printing, that creates three- dimensional objects through adding layers of at least one material on top of itself to form a structure, in some instances, a block of at least one material. The term “casting” refers to a process that pours a material (typically liquid) into a mold and allows the material to solidify to produce a desired shape, in some instances, a block of at least one material.

[0082] The design of the block of the at least one material may be generated as a function of i) a parametric model of a plurality of asymmetrical geometrical designs for minimizing weight (kg / m2) of walls of the block of at least one material and maximizing interior areal heat capacity (kJ / m2K) of walls of the block of at least one material, ii) a geometrical analysis with fixed and variable parameters of the parametric model, iii) a thermal analysis of the parametric model, and iv) the design further generated through an iterative parametric model, iterative geometrical analysis, and iterative thermal analysis to achieve an average thermal conductivity from about 0.05 W / mK to about 0.3 W / mK for a design for the block of at least one material. The thermal analysis may be generated as a function of 1) a thermal resistance circuit in-series, a thermal resistance circuit in-parallel, and a plurality of materials, 2) an R- value and a total aspect ratio from the thermal resistance circuit in-series, the thermal resistance circuit in-parallel and the plurality of materials, 3) a plurality of layer matrices and a plurality of heat transfer matrices, and 4) an interior areal heat capacity for a plurality of from the plurality of layer matrices and the plurality of heat transfer matrices.

[0083] In some instances, the lattice structure can have at least one material and at least one cavity. In some further instances, the at least one cavity can have a different thermal conductivity from the at least one material. In some further instances, the at least one cavity is at least one void. In some further instances, the at least one void contains a gas or an- 9 -4212823. vlDocket No. 0050.2403001 (MIT-26094) insulative material. In some instances, the gas is air. In some other instances, the insulative material may be fiber glass, expanded polystyrene (EPS), mineral wool, extruded polystyrene (XPS), perlite, cellulose, or any combination thereof. In some instances, the insulative material may be fiber glass. In some other instances, the at least on void can form an asymmetric void distribution across the lattice structure.

[0084] In some other instances, the method may be performed using additive manufacturing (z.e. 3D-printing). In some other instances, the method may be performed using foaming. In some instances, the at least one material may be an earthen material, a cementitious material, fiber glass, expanded polystyrene (EPS), mineral wool, extruded polystyrene (XPS), perlite, cellulose, ceramics, glass, concrete, metals, metal alloys, high- density polymers, or a combination thereof. In some further instances, the at least one material may be an earthen or cementitious material. In some further instances, the at least one material may be ceramic, concrete or earthen soil.Method of Designing a Block of at least one material

[0085] This disclosure also pertains to a computer-implemented method of designing a block of at least one material. FIG. 15 illustrates an example method 1510 for designing a block of at least one material. The method 1510 is computer-implemented and may be performed via any combination of hardware and software as is known in the art. For example, the method 1510 may be implemented via one or more processors with associate memory storing computer code that causes the processor to implement 1511, 1512, 1513, and 1514 of the method 1510. Further, the method 1510 may be implemented in existing simulation and / or design software. Further, it is noted that herein embodiments are described as being capable of being implemented in existing software products or systems supported by Applicant, however, embodiments are not limited to being implemented into existing software and, instead, embodiments may be performed using any combination of hardware and software as is known in the art. Embodiments may be part of the software system or suite that supports, monitors, controls, provides maintenance of, etc. industrial processing plants, refineries, chemical or pharmaceutical processing plants, and the like.

[0086] The method 1510 of designing may a) define a parametric model of a plurality of asymmetrical geometrical designs for minimizing weight (kg / m2) of walls of the block of at least one material and maximizing interior areal heat capacity (kJ / m2K) of walls of the block of at least one material 1511, b) perform a geometrical analysis with fixed and variable- 10 -4212823. vlDocket No. 0050.2403001 (MIT-26094) parameters of the parametric model 1512, c) perform a thermal analysis of the parametric model 1513, and d) repeat (a)-(c) to achieve average thermal conductivity from about 0.05 W / mK to about 0.3W / mK for the block of at least one material 1514. The thermal analysis may i) define a thermal resistance circuit in-series, a thermal resistance circuit in-parallel, and a plurality of materials, ii) determine an R-value and a total aspect ratio from the thermal resistance circuit in-series, the thermal resistance circuit in-parallel and the plurality of materials, iii) define a plurality of layer matrices and a plurality of heat transfer matrices, and iv) determine an interior areal heat capacity for a plurality of from the plurality of layer matrices and the plurality of heat transfer matrices.

[0087] In some instances, the computer-implemented method designs blocks of at least one material that are described in the section “Block of at least one material.” In some other instances, the computer-implemented method can design other objects subjectable to thermal insulation and passive cooling. In some instances, the objects include, but are not limited to, food preservation items (i.e. a cooler, a wine cooler, a water bottle, a food storage container), metamaterials, mechanical systems for energy conservation (i.e. incubators, kilns, heat exchangers, engines used in extreme climates) and building systems for space applications.

[0088] FIG. 16 illustrates a computer network or similar digital processing environment in which an embodiment may be implemented.

[0089] Client computer(s) / devices 50 and server computer(s) 60 provide processing, storage, and input / output devices executing application programs and the like. Client computer(s) / devices 50 may also be linked through communications network 70 to other computing devices, including other client devices / processes 50 and server computer(s) 60. Communications network 70 may be part of a remote access network, a global network (e.g., the Internet), cloud computing servers or service, a worldwide collection of computers, Local area or Wide area networks, and gateways that currently use respective protocols (TCP / IP, Bluetooth, etc.) to communicate with one another. Other electronic device / computer network architectures are suitable.

[0090] FIG. 17 is a diagram of the internal structure of a computer (e.g., client processor / device 50 or server computers 60) in the computer system of FIG. 16. Each computer 50, 60 contains system bus 79, where a bus is a set of hardware lines used for data transfer among the components of a computer or processing system. Bus 79 is essentially a shared conduit that connects different elements of a computer system (e.g., processor, disk storage, memory, input / output ports, network ports, etc.) that enables the transfer of- 11 -4212823. vlDocket No. 0050.2403001 (MIT-26094) information between the elements. Attached to system bus 79 is I / O device interface 82 for connecting various input and output devices (e.g., keyboard, mouse, displays, printers, speakers, etc.) to the computer 50, 60. Network interface 86 allows the computer to connect to various other devices attached to a network (e.g., network 70 of FIG. 22). Memory 90 provides volatile storage for computer software instructions 92 and data 94 (such as method 330, workflow 2100, MB EORXR, etc. detailed above) used to implement an embodiment of the present invention. Disk storage 95 provides non-volatile storage for computer software instructions 92 and data 94 used to implement an embodiment of the present invention. Central processor unit 84 is also attached to system bus 79 and provides for the execution of computer instructions.

[0091] In one embodiment, the processor routines 92 and data 94 are a computer program product (generally referenced 92), including a computer readable medium (e.g., a removable storage medium such as one or more DVD-ROM’s, CD-ROM’s, diskettes, tapes, etc.) that provides at least a portion of the software instructions for the invention system. Computer program product 92 may be installed by any suitable software installation procedure, as is well known in the art. In another embodiment, at least a portion of the software instructions may also be downloaded over a cable, communication and / or wireless connection. In other embodiments, the invention programs are a computer program propagated signal product 107 embodied on a propagated signal on a propagation medium (e.g., a radio wave, an infrared wave, a laser wave, a sound wave, or an electrical wave propagated over a global network such as the Internet, or other network(s)). Such carrier medium or signals provide at least a portion of the software instructions for example embodiments of the present invention routine s / program 92.

[0092] In alternate embodiments, the propagated signal is an analog carrier wave or digital signal carried on the propagated medium. For example, the propagated signal may be a digitized signal propagated over a global network (e.g., the Internet), a telecommunications network, or other network. In one embodiment, the propagated signal is a signal that is transmitted over the propagation medium over a period of time, such as the instructions for a software application sent in packets over a network over a period of milliseconds, seconds, minutes, or longer. In another embodiment, the computer readable medium of computer program product 92 is a propagation medium that the computer system 50 may receive and read, such as by receiving the propagation medium and identifying a propagated signal- 12 -4212823. vlDocket No. 0050.2403001 (MIT-26094) embodied in the propagation medium, as described above for computer program propagated signal product.

[0093] Generally speaking, the term “carrier medium” or transient carrier encompasses the foregoing transient signals, propagated signals, propagated medium, storage medium and the like.

[0094] In other embodiments, the program product 92 may be implemented as a so-called Software as a Service (SaaS), or other installation or communication supporting end-users.

[0095] Embodiments or aspects thereof may be implemented in the form of hardware, firmware, or software. If implemented in software, the software may be stored on any nontransient computer readable medium that is configured to enable a processor to load the software or subsets of instructions thereof. The processor then executes the instructions and is configured to operate or cause an apparatus to operate in a manner as described herein.

[0096] Further, firmware, software, routines, or instructions may be described herein as performing certain actions and / or functions of the data processors. However, it should be appreciated that such descriptions contained herein are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc.

[0097] It should be understood that the flow diagrams, block diagrams, and network diagrams may include more or fewer elements, be arranged differently, or be represented differently. But it further should be understood that certain implementations may dictate the block and network diagrams and the number of block and network diagrams illustrating the execution of the embodiments be implemented in a particular way.

[0098] Accordingly, further embodiments may also be implemented in a variety of computer architectures, physical, virtual, cloud computers, and / or some combination thereof, and thus, the data processors described herein are intended for purposes of illustration only and not as a limitation of the embodiments.Applications and Uses

[0099] In some instances, the block of at least one material described herein may be used as a construction block or construction piece to build architecture that can inhabit living organisms, including, but not limited to, buildings, houses, office spaces, and shelters. In some instances, the living organisms include humans, pets, plants, or a combination thereof.- 13 -4212823. vlDocket No. 0050.2403001 (MIT-26094)In the instances where the block of at least one material is used, multiple blocks may be used to build the building to achieve thermal insulation and passive cooling.

[0100] Building components with integrated air cavities, such as thermal-insulating clay blocks or 3D-printed earthen walls, leverage the low thermal conductivity of still air to increase their thermal resistance (R-value) while removing an often high-carbon material. Yet, the design of these components (referred to in this disclosure as multi-hollowed wall components) usually neglects their ability to store heat, hindering the development of blocks and walls with enhanced thermal mass performance. Moreover, blocks and walls are seldom designed for an optimal balance between their embodied and operational performance, an aspect when considering the whole-cycle impact of buildings. This disclosure fills these gaps through a shape-optimization method that combines state-of-the-art computational design tools with fundamental heat transfer theory to facilitate the discovery of wall designs with optimal passive cooling performance (measured as the heat capacity [kJ / m2K]) and minimum weight [kg / m2]. The benefits of applying this method are illustrated herein through the multiobjective optimization of two distinct wall systems: (1) extruded ceramic blocks with multiple air cavities and (2) 3D-printed earthen wall systems. The results provide quantifiable evidence in favor of designing building components specifically for heat resilience, achieving shape-optimized blocks that can double their heat capacity without additional material or increase their heat capacity by about 23% while reducing their weight by about 33%.

[0101] The present disclosure describes a block design that achieves enhanced passive cooling performance at no additional material cost. Multi-hollowed ceramic blocks are currently used in many parts of the world as a durable and high-performing wall system solution - thanks to the addition of air pockets, existing commercial products achieve code- compliant insulation values through a single monolithic component. However, the design of these blocks does not account for their ability to store heat and act as thermal batteries that moderate temperature fluctuations within buildings, a feature to cool down buildings passively and reduce the dependence on air-conditioning (AC) systems. The disclosure solves this challenge through a block design that optimally distributes material to improve its dynamic thermal performance and provide "free cooling" with the minimal amount of material possible. A distinct feature of these designs is the asymmetric distribution of material: more mass is accumulated on the inside, increasing its heat storage capacity, whereas the quantity and size of air pockets increase on the outer side of the block. This shape-optimized block design is conceived for conventional extruded clay fabrication- 14 -4212823. vlDocket No. 0050.2403001 (MIT-26094) techniques, although it could also be suited for novel fabrication methods such as additive manufacturing.

[0102] In some other instances, the block of at least one material may be used for construction of facades in residential and commercial buildings around the world, primarily in cooling-dominated climates, landscaping (i.e. retaining walls, benches, green walls), furniture, product design, agricultural construction, industrial applications (i.e. storage, packaging). In some instances, design of the block of at least one material may be fine-tuned to the requirement of each climate to find an optimal balance between weight, heat capacity, and R-value. In some instances, the block of at least one material may be fabricated as small, discrete units and combined to form a building facade, or may be fabricated as a larger prefabricated facade panel, or as an on-site 3D-printed wall.EXEMPLIFICATION

[0103] The present disclosure investigates block designs through a multi-domain approach that simultaneously accounts for their environmental impact and ability to improve buildings’ resilience to heat. Before delving into the developed methods and proposed solutions, the following presents an overview of the role of thermal mass, a well-studied passive cooling strategy, in the current climate crisis and its application within shape- optimized building components as an emerging field of research.

[0104] Thermal-insulating clay blocks are an available alternative that offers a significant performance advantage thanks to the addition of small voids that trap still air, reducing the element’s overall density and improving its steady-state thermal resistance [2], The design of these blocks seldom accounts for their ability to store heat (a feature to cool buildings passively) nor for the climate-specific tradeoffs between their embodied and operational impact. This disclosure, therefore, aims to investigate the potential benefits of designing wall components with integrated air cavities (referred to in this disclosure as multi -hollowed blocks or walls) for enhanced passive cooling performance while accounting for their embodied impact. Before delving into the proposed analysis methods and design solutions, the present disclosure presents an overview of the role of thermal mass, a well-studied passive cooling strategy, in the current climate crisis and its application within shape- optimized building components as an emerging field of research.- 15 -4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0105] The current state of the art blocks is still far from ideal as they do not account for the ability to store heat (a feature to cool buildings passively) nor for the climate-specific tradeoffs between their embodied and operational impact.

[0106] From mudbricks to compressed earth blocks and rammed earth walls, thermal mass is a passive cooling strategy commonly found in vernacular construction in temperate and hot-dry regions. The high specific heat and density of these envelopes allow buildings to act as thermal batteries that store energy during the day and release it throughout the night (typically at a higher air exchange rate to leverage the cooler outside air), dampening indoor air temperature fluctuations and avoiding indoor temperatures that are excessively warm. In the current climate crisis, thermal mass is often revisited as an effective adaptation strategy thanks to its peak-reduction effect and ability to delay and dampen the consequence of disruptive events such as heat waves or power outages [3], Unlike lightweight construction systems, which typically rely on insulation and thus react to changing conditions faster, buildings with sufficient heat capacity will respond more slowly to a sudden rise in temperatures and give occupants time to respond accordingly through additional passive cooling strategies or, if necessary, seek emergency options such as a cooling center.Moreover, buildings with a high thermal time constant (sufficient interior thermal mass and adequate exterior insulation) allow for implementing pre-cooling and pre-heating control strategies more effectively, preventing the electric grid from being excessively loaded during high-demand periods, an increasing concern as cities rapidly electrify [4] [5],

[0107] These multi-domain benefits highlight the importance of implementing thermal mass (mainly in building envelopes) as an effective and often affordable climate adaptation strategy. Yet, quantifying the thermal mass performance of a wall component is a procedure that, unlike thermal resistance, is relatively uncommon in architectural practice and only included in a few building codes worldwide [6], The lack of evaluation tools can become critical, as designing enclosures that provide the right amount of heat storage capacity for specific climatic and programmatic needs is a non-trivial task. This disclosure responds to this challenge by developing novel computational design methods that simultaneously account for the envelope’s passive cooling performance and embodied impact.

[0108] Shape-optimization is an increasingly relevant research topic in the fields of architecture and construction, leveraging advances in computational methods to unlock high- performance and low-carbon building designs. In the realm of wall components specifically, this technique offers a unique opportunity to optimize the geometry and distribution of- 16 -4212823. vlDocket No. 0050.2403001 (MIT-26094) material layers (and air cavities) within building envelopes for given performance and carbon goals. The following lines include a selection of relevant studies that focus on optimizing the geometry of wall components across fabrication methods.

[0109] A large body of research on extruded ceramic blocks has focused on optimizing their inner structure for enhanced thermal resistance, accounting in some cases for the convective and radiative heat transfer within the air cavities [7], Other studies have introduced a multi-objective design approach through topology optimization and accounting for their structural performance [8], However, few studies have studied the dynamic thermal properties of these components, and these studies focus exclusively on experimental analysis [9], Other lines of work have investigated the potential of Foamed Concrete (FC) and Autoclaved Aerated Concrete (AAC) for structural and heat storage purposes, finding a promising balance between thermal mass and insulation properties

[0010]

[0011] , These cellular components may be fabricated with variable densities, making the mix denser towards the interior (increasing the heat storage capacity) and more porous (less conductive) on the outermost part

[0012] , While a promising concept, no studies offer an in-depth analysis of these types of blocks.

[0110] Additive manufacturing (AM) is an ideal option for manufacturing shape- optimized wall components at scale thanks to the geometric freedom offered by this digital fabrication technology

[0013] , Work by Briels et al highlights the opportunities of using computational methods to improve the thermal insulation properties of additively manufactured walls, linking parametric models with 2D heat flux simulations to find optimal air cavity distributions for different AM methods

[0014]

[0027] , Other prototypes, such as TOVA, built by IAAC, use local 3D-printed soils for thermal mass purposes, combining air cavities with the high density and specific heat of the printed material

[0026] , These examples open a promising path towards low-carbon and heat-resilient assemblies yet highlight an existing gap in the literature: the need to integrate the dynamic thermal analysis directly into the design process to generate wall component designs tailored to cooling-dominated climates.

[0111] Building components with integrated air cavities, such as thermal -insulating clay blocks or 3D-printed earthen walls, leverage the low thermal conductivity of still air to increase their thermal resistance (R-value) while removing an often high-carbon material. Yet, the design of these components usually neglects their ability to store heat, hindering the development of blocks and walls with enhanced thermal mass performance. Moreover, block and wall geometries are seldom designed for an optimal balance between their embodied and- 17 -4212823. vlDocket No. 0050.2403001 (MIT-26094) operational performance, an aspect when considering the whole life-cycle impact of buildings. The present disclosure fills these gaps through a shape-optimization method that combines state-of-the-art computational design tools with fundamental heat transfer theory to facilitate the discovery of wall designs that optimally store heat with the precise amount of material.

[0112] The present disclosure develops a computational design method that facilitates finding wall components with enhanced passive cooling performance at a minimal material cost.Method: Shape-Optimization of Wall Components for Enhanced Thermal Mass Performance and Reduced Material Consumption

[0113] An example embodiment of this method uses a computational design framework to optimize the internal geometry of wall components for enhanced dynamic thermal performance and minimal material consumption, while also accounting for fabrication constraints. FIG. 1 summarizes the main example activities in the methodology. First, the multi-objective optimization problem is formulated by parametrizing the component geometry and defining the required fabrication constraints and performance objectives (Shape-Optimization Problem Formulation section) through a parametric model 110. Second, a parallel-series thermal circuit model is used to guide the optimization algorithm towards designs that perform best from a steady-state and dynamic thermal performance perspective - this example activity is a contribution of this disclosure and explained in detail in the Steady- State and Dynamic Thermal Analysis Through a Parallel Series Thermal Resistance Circuit Approach section through a tandem thermal analysis 111. Finally, the best-performing designs are selected from the optimization's outcome and validated through numerical methods for final characterization of their passive cooling behavior (Design Validation Through Numerical Simulations section) in the design selection 112. A simulation driven validation 113 can also be performed to validate the method.

[0114] The goal of this shape-optimization process is to find designs that fall within the Pareto front, i.e., those designs that perform optimally across two performance metrics of interest: the walls’ weight [kg / m2] and heat capacity [kJ / m2K] a measure of their passive cooling performance. While these two objectives may seem opposing at first glance (more material generally leads to a higher heat capacity), the goal here is to find the geometries that optimally balance them through a more intelligent material allocation - finding a lightweight thermal mass.- 18 -4212823. vlDocket No. 0050.2403001 (MIT-26094)Shape-Optimization Problem Formulation

[0115] An example activity in the presented methodology includes developing a parametric model that allows iterating across large quantities of design options (the design space) and finding those that perform best across the above-mentioned performance objectives. This approach often involves linking computer-aided design (CAD) tools with the required performance analysis processes and an optimization engine that guides the formfinding process. In the present disclosure, the visual computing tool Grasshopper3D (integrated within the Rhinoceros CAD environment) is used for geometry processing and thermal analysis through custom Python-coded components. The Design Space Exploration toolbox, developed by the Digital Structures group at MIT

[0020] , enables the optimization routine through the genetic algorithm NSGA-II.Geometric Variables

[0116] FIG. 1 defines the main geometric parameters (fixed and variable) for the proposed parametric model of a wall component with variable-size air pockets. The design goal is to enable an asymmetric solid material distribution while incorporating the relevant fabrication constraints. First, interior and exterior solid walls are defined with thickness tt and text, respectively, for a fixed wall depth Y and width X. The remaining surface is then subdivided into Nxparts along the block’s width, spaced evenly, and Nyparts along the Y axis. In this case, the spacing results from evaluating Nypoints between 0 and 1 along the exponential function xE, where E is the exponent defined here as a variable, and mapping those to the block’s depth Y. The resulting “grid” is filled with multiple alternating diagonals (giving the block a diamond-shaped pattern) that are offset by a distance twaii. As a result of this process, the design vector is defined as:

[0117] For each iteration within the optimization process, the parametric definition outputs the geometry for both the solid material and the air cavities. The resulting 2D surfaces are then used to compute the component’s constraints and performance objectives, as defined in the following lines, to guide the heuristic algorithm towards the best combination of variables.Constraints and Performance Objectives- 19 -4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0118] Constraint functions are commonly used within optimization routines to define a feasibility region within the design space, ensuring that all outcomes from the optimization process meet specific pre-defined requirements. In the present disclosure, three constraint functions are defined related to their structural-thermal performance and constructability: (1) a minimum characteristic compressive strength,^, (2) a maximum void-to-solid ratio, emax, and (3) a minimum R-value Rmin.tot . ) min 0 (4)

[0119] In order to guide the optimization algorithm towards the feasible design space, a penalty function P(x) is defined according to a series of constraints gi(x). Each constraint function, gi(x), is normalized so that only those values greater than zero are feasible.Therefore, the penalty value for pi(gi(x)) increases for more negative - less feasible - values.

[0120] Finally, the objective functions guide the optimization algorithm towards those designs that are as lightweight and as thermally massive as possible. To that end, Ji(x) computes the component’s normalized weight (to be minimized) and J2(x) the heat capacity (to be maximized) as a measure of its passive cooling performance.

[0121] Finding a way to compute the heat capacity in a fast and reliable manner (compatible with computational design workflows such as the one described above) is one of the main contributions of this disclosure and is described in more detail next.- 20 -4212823. vlDocket No. 0050.2403001 (MIT-26094)Steady-State and Dynamic Thermal Analysis through a Parallel Series Thermal Resistance Circuit Approach

[0122] As anticipated, this section presents a design-oriented approach to quantifying the steady-state and dynamic thermal properties (the thermal resistance R (m2K / W) and areal heat capacity Kin (J / m2K) metrics, respectively) of wall components with internal air cavities. The method is specifically designed for early design stages, prioritizing speed of response and geometric flexibility while maintaining an acceptable level of accuracy to guide the decisionmaking process (made by the designer or an optimization algorithm) in a physics-informed way.Parallel-Series Thermal Circuit Model

[0123] At its core, the presented methodology is based on a parallel-series thermal resistance circuit method. This analytical technique is often included in heat transfer textbooks to estimate the thermal resistance of composite walls with small differences in the thermal conductivity of the constituent materials

[0015] , Such is the case for the materials considered in the present disclosure: earth (with a conductivity ki ranging from 0.5 to 1 W / mK) and pockets of still air (with a conductivity k ranging from 0.07 to 0.31 W / mK for the considered thicknesses) result in a ratio (ki / ki) no larger than 15.

[0124] By representing a given wall component geometry as two independent thermal resistance circuits (one in series and one parallel), it is possible to define the upper and lower bounds of the quantity of interest R . The parallel circuit 221 yields an optimistic R-value (Rparaiiei , as it assumes adiabatic planes between each resistance, neglecting any lateral heat transfer. On the other hand, the in-series circuit 222 assumes infinite lateral heat transfer and thus results in a more conservative estimate of the resistance value (Rsenes). FIGs. 2A-B exemplifies the application of this method to a hypothetical block geometry 220A with diamond-shaped cavities 220B, discretizing the geometry in both directions into multiple thermal resistances.

[0125] As a result, the final resistance value RM can be expressed as a weighted average of Rparaiiei and Rseries (Equation 9). The weights associated with each thermal circuit (wi and M’2) are assigned based on the geometry of the air cavities (more specifically, their aspect ratio).Air Cavities- 21 -4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0126] Given their lower thermal conductivity relative to the solid material surrounding them, the geometry and distribution of air cavities play a role in defining the component’s overall thermal resistance. More specifically, the ratio of the air cavity width Wi to its height Hi (its aspect ratio AR,) is a geometric property used in the present disclosure to evaluate the relative impact of each thermal resistance circuit. Whenever the air cavities have a lower aspect ratio, heat will tend to find more resistance to flow laterally, and consequently, the weight associated with Rparaiie will be higher. On the contrary, if the cavities have a larger aspect ratio, lateral heat flow will happen more easily, increasing the impact of Rseries.

[0127] The total aspect ratio AR results from computing the area- weighted average of the different air cavities based on their associated aspect ratio ARt and areas At (Equations 10 and 11). After calculating AR , the value for wi (where 0< wi<\ and W2 = l-w) is obtained by normalizing it relative to a preset range of considered aspect ratios ARmin < ARM < ARmax. Equations 12 to 15 describe the applied normalization process- for the geometries explored in this disclosure, ARmin is set to 0.2 and ARmaxto 5 based on the simulation of ten different block geometries (appendix A). These bounds must be redefined when exploring larger thermal conductivity differences between both materials or a significantly different. if ARtot< 0.2 w1 =0.1 (12) if ARmin< ARtot< 1W1= 0.1 where ARmin= 0.2 (13)if J 1 < ARtLoUtL < ARmIILLaLAxWi = 0.2 + GRt°t~1)(o.9-o.2) where ARmax= 5 (14) iKmax1if ARtot> 5 w1= 0.9 (15)

[0128] Another aspect is determining the cavity’s thermal conductivity, which varies as a function of thickness (convective heat exchange will increase with depth) and surface emissivity. This disclosure uses the values included in chapter 26 of the ASHRAE Handbook of Fundamentals

[0016] , which are based on experimental data from Yarbrough et al.

[0017] , The simulation tool used in this disclosure (Simscale

[0018] ) was validated against this data using two different turbulence models (k-omega and laminar), obtaining the best overall results for the k-omega model across cavity dimensions. Surface emissivity is kept at 0.9 in this- 22 -4212823. vlDocket No. 0050.2403001 (MIT-26094) disclosure, while the cavity thickness is determined by the depth of the rectangle with area and width equivalent to the original cavity shape.

[0129] FIGs. 3 A-D provide a representation of the simulation described based on the air cavity aspect ratio. A baseline block 330 is initially shown and then three different blocks are shown with varying heights and widths (FIG. 3 A). The block of FIG. 3B 331 shows an air cavity with a width greater than the height. The block of FIG. 3C 332 shows an air cavity with a height greater than the width. The block of FIG. 3D 333 shows an air cavity with a height and width that are equivalent. Each block has a different calculated R-value as a result of the differences in the height and width ratios.Dynamic Thermal Performance Assessment

[0130] The ability of enclosures to store heat throughout daily cycles depends on multiple factors, such as the dimension, thermophysical properties, and distribution of their constituent materials. The standard ISO 13786

[0019] is one of the few documents that establishes a framework to characterize the dynamic thermal properties of building components and is therefore used as the baseline of the methodology presented here. Among all the metrics included, this disclosure focuses on the areal heat capacity / <>«, which expresses the total heat stored by a given component within a 24-hour cycle for a 1 -degree temperature fluctuation. The units are in kJ / m2K: a higher value is more desirable whenever thermal mass is climate appropriate.

[0131] The ISO document offers, among other things, an analytical expression that solves the heat transfer equation for a multi-layered wall under periodic boundary conditions (such as those from the daily fluctuations of temperatures) through a series of matrix-based operations. The key quantity for each layer n is the dimensionless ratio expressed as the thickness d over the penetration depth b, a quantity intrinsic to the material’s thermophysical properties, and the period of analysis T (in this case, the 86400 seconds in a 24-hour day): f = J (16)

[0132] The ratio c, is used to compute the heat transfer matrices Z« of each layer A, defined in the standard as the matrix relating the complex amplitudes of temperature and heat flow rate on one side of the component to those on the other side:Z11JV= Z22JV= cosh(<0 cos(^) + j slnh(^) sin(^) (18)4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0133] The total assembly matrix Zeeis then obtained by multiplying the different layer matrices ZN (where Zi is the innermost layer) and the heat transfer matrices of the boundary layers Zsi and ZS2. The values within Zee are finally used to calculate the heat capacity Km value:

[0134] This closed-form expression results in a fast and physics-based method applicable to any multi-layered assembly with varying dimensions and layer configurations. Yet, its application to components with intricate geometries (that is, with significant two-dimensional heat transfer effects) is not included in the standard, leaving numerical methods as the commonly accepted but cumbersome alternative. This disclosure proposes an additional option that relies on a layer homogenization process that abstracts wall geometries into discrete layers.

[0135] The initial example activity of the proposed method, summarized in FIGs. 4A-C, incorporates subdividing a given component geometry 440 with non-planar cavities into multiple multi-material layers 441 with thickness L. An equivalent value of the main thermophysical properties (density / ), specific heat c, and thermal conductivity k) is found for each layer using the expressions defined in equations 15 and 16. The objective is thus to create a set of virtual homogeneous layers 442 that have an equivalent thermal behavior to the heterogeneous block geometries and, in this way, facilitate the application of the analytical method from ISO 13786.

[0136] The product of specific heat and density pceis computed for each layer as a volume-weighted average of their individual properties, while the equivalent thermal conductivity keresults from dividing the components’ total depth D over Rtot (as computed in Shape-Optimization Problem Formulation section). The values Ai and A2 are the ratios of each material’s area to the layer’s total area.(pc)e= (pcty / ty + (pc)2l2- 24 -4212823. vlDocket No. 0050.2403001 (MIT-26094)Design Validation through Numerical Simulations

[0137] The last example activity in the proposed methodology focuses on characterizing and validating the thermal performance of the selected component geometries using numerical methods. These simulations serve as a higher-precision alternative to the thermal resistance circuit method used in the multi-objective optimization process. The present disclosure specifically uses Rhinoceros for geometry generation, and the cloud-based simulation tool Simscale for meshing and finite-element thermal simulations.R-Value Validation

[0138] R-value simulations are conducted through Simscale’ s Conjugate Heat Transfer (CHT) module, which allows simulating solid and fluid domains simultaneously. This aspect is relevant for this research to accurately model the convective and radiative heat exchange within the air cavities. More specifically, the turbulence model k-omega SST is used and validated against available experimental data for air cavities of varying depths

[0017] , The meshing uses a hex core mesh, a hybrid technique that combines hexahedral cells in the domain interior with tetrahedral and pyramid cells on the boundaries.

[0139] Simulations are run in steady-state mode until the total heat flow rate Qtot going through each surface is equal on both sides. Once the simulation converges, the R-value (m2K / W) of a given brick is defined as:

[0140] where Abiock is the area of the block in elevation (m2) and AZ the inside-outside temperature difference, which is fixed to 5K for the results shown in the Performance Characterization sections of both Extruded Ceramic Blocks and 3D-Printed Earthen Walls sections.Heat Capacity Validation

[0141] The thermal mass performance of the blocks is assessed following the general definitions included in ISO 13786 for the dynamic thermal performance of building components. In this case, and unlike the R-value simulations, transient Finite Element Analysis (FEA) methods are used - while this technique simplifies the air cavities modeling (which are now modeled as solid domains with a fixed conductivity value), it allows for significantly longer simulation times of up to 72h. This is an aspect in order to capture the metrics of interest specified in the ISO standard.- 25 -4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0142] More specifically, the thermal admittance Ymm and the periodic thermal transmittance Ym are the two quantities used to derive the areal heat capacity Kin. The former is defined as the complex amplitude of the heat flux through the component’s side m divided by the complex amplitude of the temperature on the same surface when the temperature on the side n is held constant (equation 18). The periodic thermal transmittance, instead, assumes that temperature is held constant on side m (equation 27).

[0143] Both quantities are modeled through transient FEA simulations by imposing a sinusoidal temperature boundary condition on each surface and measuring the heat flux (W / m2) on side m. A sinusoidal curve is then fitted to the time-dependent heat flux values to obtain the complex quantity qmincluded in equations 26 and 27. Once the thermal admittance and the periodic thermal transmittance are defined, the areal heat capacity (presented here in its general form, unlike in equation 22) results from the modulus of the net difference between both quantities divided by the angular frequency.

[0144] Table 1 summarizes the opportunities and challenges associated with four possible fabrication methods for the manufacturing of shape-optimized blocks made from earthen and cementitious materials. The first two - extruded ceramic blocks and foamed concrete blocks - are two well-established and industrialized methods that present the largest scalability potential (at least currently) yet face implementation challenges that need to be addressed. The remaining methods fall within the realm of digital fabrication (more specifically, additive manufacturing) at a block and wall scale, using either wet clay (which is then fired, similarly to an extruded block) or minimally processed earth. These two alternatives offer a much larger geometrical flexibility but are in much earlier stages of technological development and deployment.4212823. vlDocket No. 0050.2403001 (MIT-26094)Table 1 : Summary of the opportunities and challenges associated with four different fabrication methods for assymetric block geometries.

[0145] Among the analyzed options, this last section focuses on 3D-printing earthen walls, given its technological potential as a fast and customizable fabrication method that relies on a local and low-carbon material. The main goal here is to demonstrate the applicability of the presented thermal analysis methods in a full-scale prototype and obtain experimental data that quantitatively supports the research objectives of this disclosure.Results

[0146] This section presents the results of applying the proposed shape-optimization method to two wall components with distinct fabrication systems. Extruded Ceramic Blocks- 27 -4212823. vlDocket No. 0050.2403001 (MIT-26094) section focuses on a more conventional solution in extruded ceramic blocks, while 3D- Printed Earthen Walls Section focuses on 3D-printed earthen walls as a more experimental and increasingly relevant low-carbon construction technique. The parametric model presented in the previous section is adapted here to the fabrication constraints and design goals of each case, uncovering high-performing wall components that are unique to each application.Extruded Ceramic Blocks

[0147] A baseline multi-hollowed is initially defined using standard dimensions in commercially available extruded ceramic blocks. Table 2 summarizes the fixed values and fabrication constraints used in this initial parametric model, which are mainly constrained by the extrusion process of wet clay through a dye. The rest of geometric properties are the variables already defined in the Geometric Variables section. FIGs. 5A-B also show the thermal admittance and periodic thermal transmittance in a block 550 evaluating the interior side 551 A and the exterior side 55 IB of the block for assessing these parameters.

[0148] Table 2. Summary of the fixed design parameters and constraint values for the ceramic block parametric model.Design Exploration

[0149] The MOO process is run for a population size of 400 designs and 20 generations and the performance objectives defined in equations 7 and 8: (1) minimizing the overall piece weight, and (2) maximizing its heat capacity K,„.. FIG. 6 shows the resulting Pareto front: as expected, the tradeoff between the thermal performance and weight is defined clearly with values ranging from 127.5 kg / m2to 387.9 kg / m2for the weight and from 35.4 to 113.4 kJ / m2K for the heat capacity. A closer look at the results reveals how designs are organized in two distinctive fronts when filtering the results according to their R-values. Designs with lower insulation properties (l<R-value<1.4,) perform better across both objectives compared to those with a higher R-value (>1.4). This trend responds to the fact that the best-performing blocks include, in most cases, large air pockets on the exterior side, which is an effective way- 28 -4212823. vlDocket No. 0050.2403001 (MIT-26094) of reducing the weight without impacting the heat capacity yet at the detriment of a less- optimal air pocket size for insulation purposes.

[0150] Almost all results outperform the high-performing baseline design indicated in biobjective plot in FIG. 6. Block Bl 1, for example, performs better than the baseline in both objectives (heat capacity and weight) without compromising its R-value, while B12 doubles the heat capacity for the same weight, and B13 significantly reduces the weight by 32.6% while slightly increasing the heat capacity. While it is true that the increase in heat capacity for B12 and B13 comes at the cost of a recued R-value, it is worth noting that the blocks’ time constant (defined as the product of the R-value times the heat capacity K,„) is only kept constant or improved.T — R Kin(29)Performance Characterization

[0151] Following the process described in the Design Validation Through Numerical Simulations section, the CHT module in Simscale is used to numerically obtain the metrics of interest for the four selected blocks as a final validation. The results confirm the trends captured in the MOO process. Indeed, all three blocks outperform the baseline in one or both performance metrics (weight and heat capacity) without compromising their time constant performance. B13 is the only exception to this, where the time constant is slightly reduced by 9% after updating the results. More importantly, Table 3 highlights how the results from the parallel-series method stay within a ±15% deviation relative to the simulation results in consistency with the data included in Appendix A.

[0152] Table 3: Summary of numerical simulations results for the selected block geometries. Percentages are relative to the baseline.- 29 -4212823. vlDocketNo. 0050.2403001 (MIT-26094)3D-Printed Earthen Walls

[0153] This last results section focuses on the design and evaluation of 3D-printed earthen walls for passive cooling purposes. Additive manufacturing (AM) is a digital fabrication technology highly relevant to the scope of this disclosure, given its potential to fabricate climate-specific wall components (finding an optimal balance between heat capacity and weight) at scale through local materials such as excavation soils

[0023] , The following lines further explore this idea through the fabrication and experimental analysis of three full-scale prototypes, whose designs result from the multi-objective optimization method proposed in this research.

[0154] First, the initial parameters of the parametric model are updated to account for the new fabrication constraints. In this case, the wall components are built using a 6-axis robotic system in a room-sized space within a shaded, unconditioned industrial building in Santa Barbara, California. The total wall depth is fixed to 0.2m, and the value for twaii is set to 29 mm as defined by the nozzle size.

[0155] Table 4: Summary of the fixed design parameters and constraint values for the 3D -printed walls parametric model.Design Exploration

[0156] The multi-objective optimization process is conducted for the same population size and number of generations used in the previous section. As observed in FIG. 7, and similarly to the results in the Design Exploration of Extruded Ceramic Blocks section., a series of Pareto fronts are formed for the different R-value ranges considered. Geometries such as W1 achieve a 38% increase in heat capacity and 68% in the R-value for almost the- 30 -4212823. vlDocket No. 0050.2403001 (MIT-26094) same weight (5% more) than a 10-cm solid wall baseline. Within the same Pareto front, W2 pushes the passive cooling benefits to a 51% increase in heat capacity and 122% in R-value for a modest 30% increase in weight. W3 has the highest increase in R-value (+134%) thanks to the added third layer of air cavities while significantly increasing the heat capacity to 34% relative to the solid baseline.Performance Characterization

[0157] In this section, the performance characterization process is divided into two example activities. First, the thermal performance of the selected wall geometries is once again simulated through CHT simulations, modeling both the solid material and the air cavities. As summarized in Table 5, the obtained R-values show very similar results to the ones in the MOO process with accuracy values ranging from +3% to - 9%. As additional validation, this section also includes the experimental testing of three full-scale prototypes based on the designs for the 10-cm solid baseline and wall geometries W1 and W3. The site for the prototypes is Santa Barbara, a coastal city in California with a warm-summer Mediterranean climate, which presents an ideal opportunity to obtain relevant data that experimentally quantifies the passive cooling benefits of the presented method.

[0158] Table 5: Summary of numerical simulations results for the selected wall geometries. Percentages are relative to the baseline.

[0159] Three different cylinders are designed with fixed overall dimensions (inner diameter of 70 cm) yet varying dynamic thermal properties: (1) baseline, a 10 cm thick solid wall; (2) thermal ring 1, a cylinder based on W1 with very similar volume as the baseline but a maximized heat capacity; and (3) thermal ring 2, a cylinder based on W3 with the same overall thickness as thermal ring 1, and a maximized heat capacity. FIGs. 11 A-C summarize the metrics of interest for each prototype.- 31 -4212823. vlDocketNo. 0050.2403001 (MIT-26094)

[0160] The fabrication process, explained more in detail in previous publications from Curth et al.

[0024] , consists of multiple example activities, mainly sourcing the soil, preparing and characterizing the mix, and feeding it into a pumping system directly connected to a robotic arm 880 (FIG. 8A). In this disclosure, the base material is a sandy clay loam sourced from local construction sites with characteristics of a typical adobe mix that contains no more than 30% clay. This earthen material is sifted and mixed with straw and water to achieve the appropriate consistency for its printing - the size of the nozzle limits the printing thickness to a minimum of 30 mm. Once the prototypes have been fabricated and allowed to adequately dry, air and humidity sensors are placed in the center of each cylinder together with three surface temperature sensors (FIG. 8B). The surface temperature sensors were connected to the interior surface 88 IB, while the exterior surface 881 A was monitored based on the temperature of the climate. The air cavities 881C were not monitored. Insulation boards are placed above and below each prototype, minimizing heat exchange through these surfaces and ensuring air tightness within the cavities 882 (FIG. 8C).

[0161] The data measurement campaign was run for two months, from March 1st2024 to April 30th2024. FIG. 9 shows six days in mid-April with mean daily temperatures between 18 and 21 °C and amplitudes from two to four degrees. These outdoor reference conditions correspond to the temperatures within a fully shaded space with a constant airflow that ensures equal conditions across prototypes. As observed in FIG. 9, the temperatures inside the different cylinders decrease in amplitude and experience a more pronounced time shift as their time constant increases. More importantly, the temperature within Thermal Ring 1 is 0.6°C lower than the baseline cylinder during the warmest day (April 16th) despite having equal material quantities. These results mean that, in relative terms, the decrement factor (defined here as (Tin, max_Tout,ave) / (Tout,max_Tout,ave )) decreases from 0.55 to 0.32. thanks to the two additional layers of air pockets and the thicker inner layer of soil. Thermal Ring 2 pushes the decrement factor further down to 0.11, with a peak temperature 1.1°C lower than the baseline.

[0162] In addition to this daily analysis, the Fast Fourier Transform (FFT) algorithm is applied on the two-month measured data for a more comprehensive analysis of the prototypes’ performance. This technique translates the different temperature signals from the time domain into the frequency domain, enabling the detection of weather patterns beyond daily fluctuations

[0028] , The FFT results shown in FIG. 10 reveal that the daily frequency (1.16*10A-5 Hz) is the dominant frequency, as expected, followed by the frequencies- 32 -4212823. vlDocket No. 0050.2403001 (MIT-26094) corresponding to 29 days (4*10A-7 Hz) and 12h (2.31*10A-5 Hz). More importantly, isolating the daily frequency allows to experimentally derive the time constant of the prototypes and compare those results against the output of the parallel-series method. This process is conducted by measuring the amplitude differences across prototypes in the daily frequency (the decrement factor) and deriving the time constant that would yield this experimentally measured decrement factor value.

[0163] As observed in FIGs. 11B-C, thermal rings 1 and 2 obtain time constants 84% and 212% larger than the baseline with comparatively minor increments in their weight (5% and 45%, respectively), thanks to their optimized geometries. While the analytical method tends to overestimate the time constant of the walls by as much as 17% for thermal ring 1, compared to the experimental results, this error range is considered acceptable for the designguidance purpose of the tool. It is also necessary to account for potential experimental imprecision during the construction of the prototypes, which, although minimized, could have compromised the cavity air tightness to some extent. While only a first full-scale test, these results consolidate the findings in previous sections and add an experimental demonstration of the potential of using geometry to improve the dynamic thermal performance at minimal material cost. Further, FIGs. 11B-C shows the inner face 111 IB and 1112B, outer face 1111 A and 1112A, the air cavities 1111C and 1112C, and the lattice structure 111 ID and 1112D of the prototype thermal rings 1 and 2, respectively, in comparison to the baseline 1110.Conclusions

[0164] Optimizing the internal geometry of earth-based wall components is presented here as a promising approach to enhance the passive cooling performance of buildings without compromising material impact. This disclosure has (1) presented a new computational design method to generate wall component geometries with optimal passive cooling performance and (2) demonstrated the possibility of achieving high-performing designs by applying this method within two different fabrication methods in extruded ceramic blocks and 3D-printed earthen walls. Indeed, the results obtained demonstrate how it is possible to increase the heat capacity of existing high-performing insulative blocks by more than 60% without additional material or reduce their weight by 10% while increasing the heat capacity by 15% and the R-value by 10%. Similar results were obtained for a full-scale experimental test developed in a temperate climate in California, US. By using the proposed- 33 -4212823. vlDocketNo. 0050.2403001 (MIT-26094) method in the design of two full-scale prototypes, it was possible to obtain time constants 84% and 212% larger than a 10-cm solid baseline with comparatively minor increments in their weight (5% and 45%, respectively). These results highlight the benefits of asymmetrical material distribution in improving thermal mass performance (accumulating mass towards the interior for heat storage) and the opportunities of integrating this design strategy across fabrication methods.

[0165] The present disclosure designs ceramic blocks and earthen walls as components that integrate multiple functions in a simple and efficient manner. The main contributions of this disclosure focus on the thermal performance of these systems and their relation to the heat resilience of buildings, yet other areas remain to be explored for future work. More importantly, including a more comprehensive structural analysis of these wall components could help validate the integrity of the found geometries in more complex loading cases, such as those related to seismic areas. Building standards such as BS EN 1052 or Eurocode 6

[0025] include procedures for quantifying the characteristic shear and flexural strength of masonry at a component and wall scale, which could be integrated into the computational method. Other areas of analysis include acoustic and hygrothermal performance, which are active areas of research and essential aspects in providing a comfortable indoor environment.

[0166] The presented methodology is limited to materials with conductivity values close to those used in this research: earth (0.5 --- 1 W / mK) and still air (0.07 to 0.31 W / mK). Larger differences \ki -would require recalibrating the weights and repeating the validation process included in Appendix A.AppendixAppendix A: Validation Details

[0167] The validation process focuses on two main block typologies - extruded and foamed - with varying geometric properties. The conductivity value for the ceramic material is fixed at 0.8 W / mK, while the resistance for the air cavities is selected as a function of the cavity depth, as defined in the Shape-Optimization Problem Formulation section. FIGs. 12A- B summarizes the ten blocks explored, all of which have the same weight within a ±10% variation relative to G1 1210. The goal of this study is two-fold: (1) to evaluate the accuracy of the proposed series-parallel model in early design stages, and (2) to identify patterns between the geometric properties of interest - mainly the void aspect ratio, the inner walls thickness, and the void distribution - and their thermal performance. For the R-value- 34 -4212823. vlDocket No. 0050.2403001 (MIT-26094) calculations, a temperature differential is imposed by applying fixed temperature boundary conditions to the blocks’ outside and inside surfaces.

[0168] As shown in FIGs. 12A-B, the values predicted using the analytical model stay within a ±15% error relative to the results from the FEA simulation and across a wide range of R-values (from 0.57 to 2.23 m2K / W). The predictions tend to underpredict the R-value (except for G5 1214 and G8 1217), which is a desired behavior as it is a more conservative approach. More importantly, the series-parallel model correctly captures the impact of geometry on performance: G1 1210, for example, has a significantly higher R-value than G2 1211 and G3 1212 thanks to the higher aspect ratio of its cavities. Similarly, reducing the inner wall thickness (from G4 1213 to G1 1210 to G5 1214) has a clear benefit in the overall thermal resistance of the blocks, as it allows for a larger quantity of air pockets within the same block depth.

[0169] Similarly to the R-value, the analytical model also does a good job in predicting the heat capacity of the walls, staying within the same ±15% error margin. The trend here reverses, as the block geometries with higher R-values (G5 1214, for example) have the lowest heat capacity precisely due to the decreased ability to defuse heat within the block structure. However, this is not true for all designs. Both the analytical model and the numerical simulations highlight the benefits of having gradients in the distribution and air cavity sizes: G6 1215 and G7 1216, for example, have larger heat capacity values with respect to G1 1210 without compromising their insulation properties.

[0170] As a final validation activity, blocks G1 1210, G6 1215, and G7 1216 are simulated through Conjugate Heat Transfer (CHT) simulations (a process that involves modeling the air pockets as fluid domains), yielding similar error margins to the FEA simulations (±9%). In summary, the accuracy of the proposed series-parallel model is considered acceptable for the scope of this disclosure, i.e. guiding design decisions in the correct decision in a computationally fast way. This is particularly relevant when coupling thermal analysis with computational design workflows that require iterating across tens of thousands of designs.References

[0171] [1] Global Industry Analysts, Inc, Global Concrete Block and BrickManufacturing Report 2021, 2021.- 35 -4212823. vlDocket No. 0050.2403001 (MIT-26094)

[0172] [2] J. Koci, J. Madera, M. Jerman, R. Cerny, Computational assessment of thermal performance of contemporary ceramic blocks with complex internal geometry in building envelopes, Energy and Buildings 99 (2015) 61-66. https: / / doi.Org / 10.1016 / j.enbuild.2015.04.017.

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[0199] The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.

[0200] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.- 38 -4212823. vl

Claims

1. DocketNo. 0050.2403001 (MIT-26094)CLAIMSWhat is claimed is:

1. A block of at least one material comprising: an inner region of the at least one material and defining an inner face; an outer region of the at least one material defining an outer face; and a lattice region of the at least one material between the inner face and outer face defining a two-dimensional lattice structure with a varying density (kg / m3) across a depth of the lattice region of the at least one material, wherein the lattice structure is distributed asymmetrically between the inner region having a higher density than the outer region.

2. The block of at least one material of claim 1, wherein the lattice structure comprising the at least one material and at least one cavity, wherein the at least one cavity has a different thermal conductivity from the at least one material.

3. The block of at least one material of claim 2, wherein the at least one cavity is at least one void.

4. The block of at least one material of claim 3, wherein the at least one void form an asymmetric void distribution across the lattice structure.

5. The block of at least one material of claim 3, wherein the at least one void comprises a gas, or an insulative material.

6. The block of at least one material of claim 1, wherein the block of at least one material has an average thermal conductivity from about 0.05 W / mK to about 0.3 W / mK.

7. The block of at least one material of claim 1, wherein the block of at least one material has an interior areal heat capacity Kin (as defined in ISO 13786) from about 25 kJ / m2K to about 75 kJ / m2K per 100 kg of the at least one material.

8. The block of at least one material of claim 1, wherein the at least one material is an earthen or cementitious material.- 39 -4212823. vlDocket No. 0050.2403001 (MIT-26094)9. The block of at least one material of claim 8, wherein the at least one material is deposited by additive manufacturing to form the block of at least one material.

10. The block of at least one material of claim 8, wherein the at least one material is ceramic, concrete, or earthen soil.

11. A method of making a block of at least one material, the method comprising: extruding, foaming, additively manufacturing, casting, or a combination thereof of the at least one material from a design of the block of at least one material, the design generated as a function of: i) a parametric model of a plurality of asymmetrical geometrical designs for minimizing weight (kg / m2) of walls of the block of at least one material and maximizing interior areal heat capacity (kJ / m2K) of walls of the block of at least one material; ii) a geometrical analysis with fixed and variable parameters of the parametric model; iii) a thermal analysis of the parametric model, the thermal analysis generated as a function of:1) a thermal resistance circuit in-series, a thermal resistance circuit in-parallel, and a plurality of materials;2) an R-value and a total aspect ratio from the thermal resistance circuit in-series, the thermal resistance circuit in-parallel and the plurality of materials;3) a plurality of layer matrices and a plurality of heat transfer matrices; and4) an interior areal heat capacity for a plurality of from the plurality of layer matrices and the plurality of heat transfer matrices; and iv) the design further generated through an iterative parametric model, iterative geometrical analysis, and iterative thermal analysis to achieve an average thermal conductivity from about 0.05 W / mK to about 0.3 W / mK for a design for the block of at least one material; forming an inner region of the at least one material defining an inner face; forming an outer region of the at least one material defining an outer face; and- 40 -4212823. vlDocket No. 0050.2403001 (MIT-26094) forming a lattice region of the at least one material between the inner face and outer face defining a two-dimensional lattice structure with a varying density (kg / m3) across a depth of the lattice region of at least one material, wherein the lattice structure is distributed asymmetrically between the inner region having a higher density than the outer region; thereby forming the block of at least one material.

12. The method claim 11, wherein the lattice structure comprising the at least one material and at least one cavity, wherein the at least one cavity has a different thermal conductivity from the at least one material.

13. The method of claim 12, wherein the at least one cavity is at least one void.

14. The method of claim 13, wherein the at least one void form an asymmetric void distribution across the lattice structure.

15. The method of claim 13, wherein the at least one void comprises a gas, or an insulative material.

16. The method of claim 11, wherein the block of at least one material has an interior areal heat capacity Kin from about 25 kJ / m2K to about 75 kJ / m2K per 100 kg of material.

17. The method of claim 11, wherein the at least one material is an earthen or cementitious material.

18. The method of claim 17, wherein the at least one material is ceramic, concrete, or earthen soil.

19. The method of claim 11, wherein performing the method is via additive manufacturing.

20. The method of claim 11, wherein performing the method is via foaming.

21. A computer-implemented method of designing a block of at least one material, the method comprising: a) defining a parametric model of a plurality of asymmetrical geometrical designs for minimizing weight (kg / m2) of walls of the block of at least one- 41 -4212823. vlDocket No. 0050.2403001 (MIT-26094) material and maximizing interior areal heat capacity (kJ / m2K) of walls of the block of at least one material; b) performing a geometrical analysis with fixed and variable parameters of the parametric model; c) performing a thermal analysis of the parametric model, the thermal analysis comprising: i) defining a thermal resistance circuit in-series, a thermal resistance circuit in-parallel, and a plurality of materials; ii) determining an R-value and a total aspect ratio from the thermal resistance circuit in-series, the thermal resistance circuit in-parallel and the plurality of materials; iii) defining a plurality of layer matrices and a plurality of heat transfer matrices; and iv) determining an interior areal heat capacity for a plurality of from the plurality of layer matrices and the plurality of heat transfer matrices; and d) repeating (a)-(c) to achieve an average thermal conductivity from about 0.05 W / mK to about 0.3W / mK for the block of at least one material.- 42 -4212823. vl

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